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Solving Ratio Problems

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  • We add the parts of the ratio to find the total number of parts.
  • There are 2 + 3 = 5 parts in the ratio in total.
  • To find the value of one part we divide the total amount by the total number of parts.
  • 50 ÷ 5 = 10.
  • We multiply the ratio by the value of each part.
  • 2:3 multiplied by 10 gives us 20:30.
  • The 50 counters are shared into 20 counters to 30 counters.

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  • 2 + 3 = 5 and so there are 5 parts in the ratio in total.
  • We divide by this total number of parts to find the value of each part.
  • We multiply the original ratio by the value of each part.
  • We have 20:30.

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  • Sharing in a Ratio: Part 1

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Ratio Problems: Worksheets and Answers

ratio problems worksheet pdf

How to Solve Ratio Problems

Share £50 in the ratio 2:3

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How to Calculate Ratios

Last Updated: January 29, 2024 References

This article was co-authored by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been viewed 3,081,653 times.

Ratios are mathematical expressions that compare two or more numbers. They can compare absolute quantities and amounts or can be used to compare portions of a larger whole. Ratios can be calculated and written in several different ways, but the principles guiding the use of ratios are universal to all.

Practice Problems

how to solve problem with ratio

Understanding Ratios

Step 1 Be aware of how ratios are used.

  • Ratios can be used to show the relation between any quantities, even if one is not directly tied to the other (as they would be in a recipe). For example, if there are five girls and ten boys in a class, the ratio of girls to boys is 5 to 10. Neither quantity is dependent on or tied to the other, and would change if anyone left or new students came in. The ratio merely compares the quantities.

Step 3 Notice the different ways in which ratios are expressed.

  • You will commonly see ratios represented using words (as above). Because they are used so commonly and in such a variety of ways, if you find yourself working outside of mathematic or scientific fields, this may the most common form of ratio you will see.
  • Ratios are frequently expressed using a colon. When comparing two numbers in a ratio, you'll use one colon (as in 7 : 13). When you're comparing more than two numbers, you'll put a colon between each set of numbers in succession (as in 10 : 2 : 23). In our classroom example, we might compare the number of boys to the number of girls with the ratio 5 girls : 10 boys. We can simply express the ratio as 5 : 10.
  • Ratios are also sometimes expressed using fractional notation. In the case of the classroom, the 5 girls and 10 boys would be shown simply as 5/10. That said, it shouldn't be read out loud the same as a fraction, and you need to keep in mind that the numbers do not represent a portion of a whole.

Using Ratios

Step 1 Reduce a ratio...

  • In the classroom example above, 5 girls to 10 boys (5 : 10), both sides of the ratio have a factor of 5. Divide both sides by 5 (the greatest common factor) to get 1 girl to 2 boys (or 1 : 2). However, we should keep the original quantities in mind, even when using this reduced ratio. There are not 3 total students in the class, but 15. The reduced ratio just compares the relationship between the number of boys and girls. There are 2 boys for every girl, not exactly 2 boys and 1 girl.
  • Some ratios cannot be reduced. For example, 3 : 56 cannot be reduced because the two numbers share no common factors - 3 is a prime number, and 56 is not divisible by 3.

Step 2 Use multiplication or...

  • For example, a baker needs to triple the size of a cake recipe. If the normal ratio of flour to sugar is 2 to 1 (2 : 1), then both numbers must be increased by a factor of three. The appropriate quantities for the recipe are now 6 cups of flour to 3 cups of sugar (6 : 3).
  • The same process can be reversed. If the baker needed only one-half of the normal recipe, both quantities could be multiplied by 1/2 (or divided by two). The result would be 1 cup of flour to 1/2 (0.5) cup of sugar.

Step 3 Find unknown variables when given two equivalent ratios.

  • For example, let's say we have a small group of students containing 2 boys and 5 girls. If we were to maintain this proportion of boys to girls, how many boys would be in a class that contained 20 girls? To solve, first, let's make two ratios, one with our unknown variables: 2 boys : 5 girls = x boys : 20 girls. If we convert these ratios to their fraction forms, we get 2/5 and x/20. If you cross multiply, you are left with 5x=40, and you can solve by dividing both figures by 5. The final solution is x=8.

Grace Imson, MA

Grace Imson, MA

Look at the order of terms to figure out the numerator and denominator in a word problem. The first term is usually the numerator, and the second is usually the denominator. For example, if a problem asks for the ratio of the length of an item to its width, the length will be the numerator, and width will be the denominator.

Catching Mistakes

Step 1 Avoid addition or subtraction in ratio word problems.

  • Wrong method: "8 - 4 = 4, so I added 4 potatoes to the recipe. That means I should take the 5 carrots and add 4 to that too... wait! That's not how ratios work. I'll try again."
  • Right method: "8 ÷ 4 = 2, so I multiplied the number of potatoes by 2. That means I should multiply the 5 carrots by 2 as well. 5 x 2 = 10, so I want 10 carrots total in the new recipe."

Step 2 Convert...

  • A dragon has 500 grams of gold and 10 kilograms of silver. What is the ratio of gold to silver in the dragon's hoard?

{\frac  {1,000grams}{1kilogram}}

  • The dragon has 500 grams of gold and 10,000 grams of silver.

{\frac  {500gramsGold}{10,000gramsSilver}}={\frac  {5}{100}}={\frac  {1}{20}}

  • Example problem: If you have six boxes, and in every three boxes there are nine marbles, how many marbles do you have?

6boxes*{\frac  {3boxes}{9marbles}}=...

One common problem is knowing which number to use as a numerator. In a word problem, the first term stated is usually the numerator and the second term stated is usually the denominator. If you want the ratio of the length of an item to the width, length becomes your numerator and width becomes your denominator.

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You Might Also Like

Calculate Compression Ratio

  • ↑ http://www.virtualnerd.com/common-core/grade-6/6_RP-ratios-proportional-relationships/A
  • ↑ http://www.purplemath.com/modules/ratio.htm
  • ↑ http://www.helpwithfractions.com/math-homework-helper/least-common-denominator/
  • ↑ http://www.mathplanet.com/education/algebra-1/how-to-solve-linear-equations/ratios-and-proportions-and-how-to-solve-them
  • ↑ http://www.math.com/school/subject1/lessons/S1U2L2DP.html

About This Article

Grace Imson, MA

To calculate a ratio, start by determining which 2 quantities are being compared to each other. For example, if you wanted to know the ratio of girls to boys in a class where there are 5 girls and 10 boys, 5 and 10 would be the quantities you're comparing. Then, put a colon or the word "to" between the numbers to express them as a ratio. In this example, you'd write "5 to 10" or "5:10." Finally, simplify the ratio if possible by dividing both numbers by the greatest common factor. To learn how to solve equations and word problems with ratios, scroll down! Did this summary help you? Yes No

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Ratio Math Problems - Three Term Ratios

In these lessons, we will learn how to solve ratio word problems that involve three terms.

Related Pages Two-Term Ratio Word Problems More Ratio Word Problems Math Word Problems More Algebra Lessons

Ratio problems are word problems that use ratios to relate the different items in the question.

Ratio problems: Three-term Ratios

Example 1: A special cereal mixture contains rice, wheat and corn in the ratio of 2:3:5. If a bag of the mixture contains 3 pounds of rice, how much corn does it contain?

Step 2: Solve the equation: Cross Multiply

2 × x = 3 × 5 2x = 15

Answer: The mixture contains 7.5 pounds of corn.

Example 2: Clothing store A sells T-shirts in only three colors: red, blue and green. The colors are in the ratio of 3 to 4 to 5. If the store has 20 blue T-shirts, how many T-shirts does it have altogether?

Solution: Step 1: Assign variables: Let x = red shirts y = green shirts

Step 2: Solve the equation: Cross Multiply both equations 3 × 20 = x × 4 60 = 4x x = 15

5 × 20 = y × 4 100 = 4y y = 25

The total number of shirts would be 15 + 25 + 20 = 60

Answer: There are 60 shirts.

How to solve Ratio Word Problems with three terms?

Example: A piece of string that is 63 inches long is cut into 3 parts such that the lengths of the parts of the string are in the ratio of 5 to 6 to 10. Find the lengths of the 3 parts.

How to solve Two Term and Three Term Ratio Problems?

A Ratio compares two things that have the same units A Part to Part Ratio compares one thing to another thing A Part to Total (whole) Ratio compares one thing to the total number

Example: In a class of 30 students, there are 18 girls and 12 boys. What is the ratio of boys to girls? What is the ratio of girls to boys? What is the ratio of girls to total?

We can have a three term ratio of red to blue to green marbles.

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Unit 3: Ratios and rates

About this unit, intro to ratios.

  • Intro to ratios (Opens a modal)
  • Basic ratios (Opens a modal)
  • Part:whole ratios (Opens a modal)
  • Ratio review (Opens a modal)
  • Basic ratios Get 5 of 7 questions to level up!

Visualize ratios

  • Ratios with tape diagrams (Opens a modal)
  • Equivalent ratio word problems (Opens a modal)
  • Ratios and double number lines (Opens a modal)
  • Ratios with tape diagrams Get 3 of 4 questions to level up!
  • Equivalent ratios with equal groups Get 3 of 4 questions to level up!
  • Create double number lines Get 3 of 4 questions to level up!
  • Ratios with double number lines Get 3 of 4 questions to level up!
  • Relate double number lines and ratio tables Get 3 of 4 questions to level up!

Equivalent ratios

  • Ratio tables (Opens a modal)
  • Solving ratio problems with tables (Opens a modal)
  • Equivalent ratios (Opens a modal)
  • Equivalent ratios: recipe (Opens a modal)
  • Understanding equivalent ratios (Opens a modal)
  • Ratio tables Get 3 of 4 questions to level up!
  • Equivalent ratios Get 3 of 4 questions to level up!
  • Equivalent ratio word problems Get 3 of 4 questions to level up!
  • Equivalent ratios in the real world Get 3 of 4 questions to level up!
  • Understand equivalent ratios in the real world Get 3 of 4 questions to level up!

Ratio application

  • Ratios on coordinate plane (Opens a modal)
  • Ratios and measurement (Opens a modal)
  • Part to whole ratio word problem using tables (Opens a modal)
  • Ratios on coordinate plane Get 3 of 4 questions to level up!
  • Ratios and units of measurement Get 3 of 4 questions to level up!
  • Part-part-whole ratios Get 3 of 4 questions to level up!

Intro to rates

  • Intro to rates (Opens a modal)
  • Solving unit rate problem (Opens a modal)
  • Solving unit price problem (Opens a modal)
  • Rate problems (Opens a modal)
  • Comparing rates example (Opens a modal)
  • Rate review (Opens a modal)
  • Unit rates Get 5 of 7 questions to level up!
  • Rate problems Get 3 of 4 questions to level up!
  • Comparing rates Get 3 of 4 questions to level up!

A ratio compares values .

A ratio says how much of one thing there is compared to another thing.

Ratios can be shown in different ways:

A ratio can be scaled up:

Try it Yourself

Using ratios.

The trick with ratios is to always multiply or divide the numbers by the same value .

Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk.

So the ratio of flour to milk is 3 : 2

To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4:

3 ×4 : 2 ×4 = 12 : 8

In other words, 12 cups of flour and 8 cups of milk .

The ratio is still the same, so the pancakes should be just as yummy.

"Part-to-Part" and "Part-to-Whole" Ratios

The examples so far have been "part-to-part" (comparing one part to another part).

But a ratio can also show a part compared to the whole lot .

Example: There are 5 pups, 2 are boys, and 3 are girls

Part-to-Part:

The ratio of boys to girls is 2:3 or 2 / 3

The ratio of girls to boys is 3:2 or 3 / 2

Part-to-Whole:

The ratio of boys to all pups is 2:5 or 2 / 5

The ratio of girls to all pups is 3:5 or 3 / 5

Try It Yourself

We can use ratios to scale drawings up or down (by multiplying or dividing).

Example: To draw a horse at 1/10th normal size, multiply all sizes by 1/10th

This horse in real life is 1500 mm high and 2000 mm long, so the ratio of its height to length is

1500 : 2000

What is that ratio when we draw it at 1/10th normal size?

We can make any reduction/enlargement we want that way.

"I must have big feet, my foot is nearly as long as my Mom's!"

But then she thought to measure heights, and found she is 133cm tall, and her Mom is 152cm tall.

In a table this is:

The "foot-to-height" ratio in fraction style is:

We can simplify those fractions like this:

And we get this (please check that the calcs are correct):

"Oh!" she said, "the Ratios are the same".

"So my foot is only as big as it should be for my height, and is not really too big."

You can practice your ratio skills by Making Some Chocolate Crispies

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Step by Step tutorial on How to Solve Ratios In Mathematics

When we have to compare two or more than two numbers in mathematics then we can use ratios for the same as ratios can compare two or more quantitative numbers or amount or you can compare the portions of numbers of the larger numbers. Ratio is one of the tools of data analysts. This is why many people face difficulty in solving ratios so they are always in search of methods on how to solve ratios. If you are also stuck with solving ratios then this article will help you to understand the concept of ratios and methods on how to solve ratios.

Assignment help

Concept of ratio

Before learning the steps on how to solve ratios one must be well versed with ratios. As you can’t mug up mathematics you have to understand the concepts then only you can solve ratios. 

First thing to learn is that ratios are used only in academics but also by data analysts for analysing the data in the form of comparison. Generally we think ratio compares only two numbers rather you can compare more than two numbers such as 3 or 4 through ratios. 

Second thing to learn on how to solve ratios is that ratio basically states the relation of two or more numbers with each other. 

Thirdly the sign of ratio is “:”. So if you want to tell someone that you got 75 marks in maths and your friend got 50 marks in maths then you can write it in the form of ratio as 75:50 that is 3:2.

Likewise you can write sex ratio of your class like 15 males and 10 females then you can write it as 15:10 that is 3:2.  And we read the ratio as “isto”. So you will read it as 3 isto 2. 

You can also write it in division form like 3/2. 

Thus there are 3 ways to write ratios. 

Steps – How to solve Ratios 

The first step on how to solve the ratio is to write the values you want to compare and you can write such values in any given form like using colon or through division sign or by writing isto. Let’s understand the steps through an example. Suppose you want to take out the ratio of your maths and physics marks. You have got 90 marks in maths and 70 marks in physics. So firstly I will write it in the form of a ratio. 

90 isto 70 or 90:70 or 90/70.

Second step on how to solve the problem is to reduce the values into their simplest way. So for that you can take out the common factors from the numbers. And then we can divide both of the numbers from such a common factor so that we can get the numbers in their simplest form. For example we have a number 90 : 70 then after writing it in the format of ratios now you have to bring out the common factors between the terms of ratios. So in this example we have 10 as a common factor. Thus you will divide both the numbers 90 and 70 by 10 so that you get the numbers in their simplest form so you will get 90/10:70/10 = 9:7.

Thus the ratio is 9:7.

Let’s take another example of three digits and three digits are 75 marks in biology, 25 marks in physics and 100 marks in maths. So let’s first write it in the form of ratio that is 

75 : 25 : 100

Now we need to follow the next step of how to solve ratios. That is to find out the common factor from all the numbers thus we can clearly see that 25 is the common factor so you will have to divide each number with 25. 

75/25 : 25/25 : 100/25 

= 3 : 1 : 4

Thus the answer is 3:1:4.

The important point to learn in ratio is that it does not change with the multiplication or division of same numbers. It will remain the same. For example if you multiply the above number with 2 then they will become 75 x 2 : 25 x 2 : 100 x 2 = 150 : 50 : 200. Now also the ratio is same if you convert it to the smallest form then like first you have to divide it by 50 then you will find get the same ratio that is 3:1:2. 

You can also find the value of variables if two ratios are equal. Let’s take an example to understand it better. Suppose you have one ratio 3:2 and other ratio 5:x and these two ratios are equal and now you are required to find the value of x song the equation will be 

3 / 4 = 3/X

3 x X = 3 x 2 

Ratios are the mathematical expressions used to compare two or more numbers having common factors. We also use ratios one daily basis. Although ratio is a simple mathematical concept still many people ask how to solve ratios . So we have written this article in the simplest language and steps wise with examples to solve ratios. Get the best help for math homework from the leading experts.

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Ratio Questions And Practice Problems (KS3 & KS4): Harder GCSE Exam Style Questions Included

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Ratio questions appear throughout KS3 and KS4 building on what students have learnt in primary school. Here we provide a range of ratio questions and practice problems of varying complexity to use with your own students in class or as inspiration for creating your own. 

KS3 ratio questions

Ks4 ratio questions.

Free GCSE maths revision resources for schools As part of the Third Space Learning offer to schools, the personalised online GCSE maths tuition can be supplemented by hundreds of free GCSE maths revision resources from the secondary maths resources library including: – GCSE maths past papers – GCSE maths worksheets – GCSE maths questions – GCSE maths topic list

What is ratio?

Ratio is used to compare the size of different parts of a whole. For example, in a whole class of 30 students there are 10 girls and 20 boys. The ratio of girls:boys is 10:20 or 1:2. For every one girl there are two boys. 

Uses of ratio

You might see ratios written on maps to show the scale of the map or telling you the currency exchange rate if you are going on holiday.

Ratio will be seen as a topic in its own right as well as appearing within other topics. An example of this might be the area of two shapes being in a given ratio or the angles of a shape being in a given ratio.

Ratio in KS3 and KS4

In KS3, ratio questions will involve writing and simplifying ratios, using equivalent ratios, dividing quantities into a given ratio and will begin to look at solving problems involving ratio. In KS4 these skills are recapped and the focus will be more on problem solving questions using your knowledge of ratio.

Download this 15 Ratio Questions And Practice Problems (KS3 & KS4) Worksheet

Help your students prepare for their Maths GSCE with this free Ratio worksheet of 15 multiple choice questions and answers.

Proportion and ratio

Ratio often appears alongside proportion and the two topics are related. Whereas ratio compares the size of different parts of a whole, proportion compares the size of one part with the whole. Given a ratio, we can find a proportion and vice versa.

Take the example of a box containing 7 counters; 3 red counters and 4 blue counters:

The ratio of red counters:blue counters is 3:4.

For every 3 red counters there are four blue counters.

The proportion of red counters is \frac{3}{7} and the proportion of blue counters is \frac{4}{7}

3 out of every 7 counters are red and 4 out of every 7 counters are blue.

Direct proportion and inverse proportion

In KS4, we learn about direct proportion and inverse proportion. When two things are directly proportional to each other, one can be written as a multiple of the other and therefore they increase at a fixed ratio. 

How to solve a ratio problem

When looking at a ratio problem, the key pieces of information that you need are what the ratio is, whether you have been given the whole amount or a part of the whole and what you are trying to work out. 

If you have been given the whole amount you can follow these steps to answer the question:

  • Add together the parts of the ratio to find the total number of shares
  • Divide the total amount by the total number of shares
  • Multiply by the number of shares required

If you have been been given a part of the whole you can follow these steps:

  • Identify which part you have been given and how many shares it is worth
  • Use equivalent ratios to find the other parts
  • Use the values you have to answer your problem

Ratio tables are another technique for solving ratio problems.

How to solve a proportion problem

As we have seen, ratio and proportion are strongly linked. If we are asked to find what proportion something is of a total, we need to identify the amount in question and the total amount. We can then write this as a fraction:

Proportion problems can often be solved using scaling. To do this you can follow these steps:

  • Identify the values that you have been given which are proportional to each other
  • Use division to find an equivalent relationship
  • Use multiplication to find the required relationship

Real life ratio problems and proportion problems

Ratio is all around us. Let’s look at some examples of where we may see ratio and proportion:

Cooking ratio question

When making yoghurt, the ratio of starter yogurt to milk should be 1:9. I want to make 1000ml of yoghurt. How much milk should I use?

Here we know the full amount – 1000ml.

The ratio is 1:9 and we want to find the amount of milk.

  • Total number of shares = 1 + 9 = 10
  • Value of each share: 1000 ÷ 10 = 100
  • The milk is 9 shares so 9 × 100 = 900

I need to use 900ml of milk.

Maps ratio question

The scale on a map is 1:10000. What distance would 3.5cm on the map represent in real life?

Here we know one part is 3.5. We can use equivalent ratios to find the other part.

The distance in real life would be 35000cm or 350m.

Speed proportion question

I travelled 60 miles in 2 hours. Assuming my speed doesn’t change, how far will I travel in 3 hours?

This is a proportion question.

  • I travelled 60 miles in 2 hours.
  • Dividing by 2, I travelled 30 miles in one hour
  • Multiplying by 3, I would travel 90 miles in 3 hours

KS2 ratio questions

Ratio is introduced in KS2. Writing and simplifying ratios is explored and the idea of dividing quantities in a given ratio is introduced using word problems such as the question below, before being linked with the mathematical notation of ratio.

Example KS2 worded question

Richard has a bag of 30 sweets. Richard shares the sweets with a friend. For every 3 sweets Richard eats, he gives his friend 2 sweets. How many sweets do they each eat?

In KS3 ratio questions ask you to write and simplify a ratio, to divide quantities into a given ratio and to solve problems using equivalent ratios.

You may also like:

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Ratio questions year 7

1. In Lucy’s class there are 12 boys and 18 girls. Write the ratio of girls:boys in its simplest form.

The question asks for the ratio girls:boys so girls must be first and boys second. It also asks for the answer in its simplest form.

2. Gertie has two grandchildren, Jasmine, aged 2, and Holly, aged 4. Gertie divides £30 between them in the ratio of their ages. How much do they each get?

Jasmine £15, Holly £15

Jasmine £15, Holly £7.50

Jasmine £10, Holly £20

Jasmine £2, Holly £4

£30 is the whole amount.

Gertie divides £30 in the ratio 2:4.

The total number of shares is 2 + 4 = 6.

Each share is worth £30 ÷ 6 = £5.

Jasmine gets 2 shares, 2 x £5 = £10.

Holly gets 4 shares, 4 x £5 = £20.

Ratio questions year 8

3. The ratio of men:women working in a company is 3:5. What proportion of the employees are women?

In this company, the ratio of men:women is 3:5 so for every 3 men there are 5 women.

This means that for every 8 employees, 5 of them are women.

Therefore \frac{5}{8} of the employees are women.

4. The ratio of cups of flour:cups of water in a pizza dough recipe is 9:4. A pizza restaurant makes a large quantity of dough, using 36 cups of flour. How much water should they use?

The ratio of cups of flour:cups of water is 9:4. We have been given one part so we can work this out using equivalent ratios.

Ratio questions year 9

5. The angles in a triangle are in the ratio 3:4:5. Work out the size of each angle.

30^{\circ} , 40^{\circ} and 50^{\circ}

22.5^{\circ},  30^{\circ} and 37.5^{\circ}

60^{\circ} , 60^{\circ} and 60^{\circ}

45^{\circ} , 60^{\circ} and 75^{\circ}

The angles in a triangle add up to 180 ^{\circ} . Therefore 180 ^{\circ} is the whole and we need to divide 180 ^{\circ} in the ratio 3:4:5.

The total number of shares is 3 + 4 + 5 = 12.

Each share is worth 180 ÷ 12 = 15 ^{\circ} .

3 shares is 3 x 15 = 45 ^{\circ} .

4 shares is 4 x 15 = 60 ^{\circ} .

5 shares is 5 x 15 = 75 ^{\circ} .

6. Paint Pro makes pink paint by mixing red paint and white paint in the ratio 3:4.

Colour Co makes pink paint by mixing red paint and white paint in the ratio 5:7. 

Which company uses a higher proportion of red paint in their mixture?

They are the same

It is impossible to tell

The proportion of red paint for Paint Pro is \frac{3}{7}

The proportion of red paint for Colour Co is \frac{5}{12}

We can compare fractions by putting them over a common denominator using equivalent fractions

\frac{3}{7} = \frac{36}{84} \hspace{3cm} \frac{5}{12}=\frac{35}{84}

\frac{3}{7} is a bigger fraction so Paint Pro uses a higher proportion of red paint. 

In KS4 we apply the knowledge that we have of ratios to solve different problems. Ratio is an important topic in all exam boards, including Edexcel, AQA and OCR. Ratio questions can be linked with many different topics, for example similar shapes and probability, as well as appearing as problems in their own right.

Read more: Question Level Analysis Of Edexcel Maths Past Papers (Foundation)

Ratio GCSE exam questions foundation

7. The students in Ellie’s class walk, cycle or drive to school in the ratio 2:1:4. If 8 students walk, how many students are there in Ellie’s class altogether?

We have been given one part so we can work this out using equivalent ratios.

The total number of students is 8 + 4 + 16 = 28

8. A bag contains counters. 40% of the counters are red and the rest are yellow.

Write down the ratio of red counters:yellow counters. Give your answer in the form 1:n.

If 40% of the counters are red, 60% must be yellow and therefore the ratio of red counters:yellow counters is 40:60. Dividing both sides by 40 to get one on the left gives us

Since the question has asked for the ratio in the form 1:n, it is fine to have decimals in the ratio.

9. Rosie and Jim share some sweets in the ratio 5:7. If Jim gets 12 sweets more than Rosie, work out the number of sweets that Rosie gets.

Jim receives 2 shares more than Rosie, so 2 shares is equal to 12.

Therefore 1 share is equal to 6. Rosie receives 5 shares: 5 × 6 = 30.

10. Rahim is saving for a new bike which will cost £480. Rahim earns £1500 per month. Rahim spends his money on bills, food and extras in the ratio 8:3:4. Of the money he spends on extras, he spends 80% and puts 20% into his savings account.

How long will it take Rahim to save for his new bike?

Rahim’s earnings of £1500 are divided in the ratio of 8:3:4.

The total number of shares is 8 + 3 + 4 = 15.

Each share is worth £1500 ÷ 15 = £100 .

Rahim spends 4 shares on extras so 4 × £100 = £400 .

20% of £400 is £80.

The number of months it will take Rahim is £480 ÷ £80 = 6

Ratio GCSE exam questions higher

11. The ratio of milk chocolates:white chocolates in a box is 5:2. The ratio of milk chocolates:dark chocolates in the same box is 4:1.

If I choose one chocolate at random, what is the probability that that chocolate will be a milk chocolate?

To find the probability, we need to find the fraction of chocolates that are milk chocolates. We can look at this using equivalent ratios.

To make the ratios comparable, we need to make the number of shares of milk chocolate the same in both ratios. Since 20 is the LCM of 4 and 5 we will make them both into 20 parts.

We can now say that milk:white:dark is 20:8:5. The proportion of milk chocolates is \frac{20}{33} so the probability of choosing a milk chocolate is \frac{20}{33} .

12. In a school the ratio of girls:boys is 2:3. 

25% of the girls have school dinners.

30% of the boys have school dinners.

What  is the total percentage of students at the school who have school dinners?

In this question you are not given the number of students so it is best to think about it using percentages, starting with 100%.

100% in the ratio 2:3 is 40%:60% so 40% of the students are girls and 60% are boys.

25% of 40% is 10%.

30% of 60% is 18%.

The total percentage of students who have school dinners is 10 + 18 = 28%.

13. For the cuboid below, a:b = 3:1 and a:c = 1:2.

Find an expression for the volume of the cuboid in terms of a.

If a:b = 3:1 then b=\frac{1}{3}a

If a:c = 1:2 then c=2a.

Difficult ratio GCSE questions

14. Bill and Ben win some money in their local lottery. They share the money in the ratio 3:4. Ben decides to give £40 to his sister. The amount that Bill and Ben have is now in the ratio 6:7.

Calculate the total amount of money won by Bill and Ben.

Initially the ratio was 3:4 so Bill got £3a and Ben got £4a. Ben then gave away £40 so he had £(4a-40).

The new ratio is 3a:4a-40 and this is equal to the ratio 6:7.

Since 3a:4a-40 is equivalent to 6:7, 7 lots of 3a must be equal to 6 lots of 4a-40.

The initial amounts were 3a:4a. a is 80 so Bill received £240 and Ben received £320.

The total amount won was £560.

15. On a farm the ratio of pigs:goats is 4:1. The ratio of pigs:piglets is 1:6 and the ratio of gots:kids is 1:2.

What fraction of the animals on the farm are babies?

The easiest way to solve this is to think about fractions.

\\ \frac{4}{5} of the animals are pigs, \frac{1}{5} of the animals are goats.

\frac{1}{7} of the pigs are adult pigs, so  \frac{1}{7}   of  \frac{4}{5} is  \frac{1}{7} \times \frac{4}{5} = \frac{4}{35}

\frac{6}{7} of the pigs are piglets, so \frac{6}{7} of \frac{4}{5} is \frac{6}{7} \times \frac{4}{5} = \frac{24}{35}

\frac{1}{3}   of the goats are adult goats, so \frac{1}{3} of \frac{1}{5} is \frac{1}{3} \times \frac{1}{5} = \frac{1}{15}

\frac{2}{3}   of the goats are kids, so \frac{2}{3} of \frac{1}{5} is \frac{2}{3} \times \frac{1}{5} = \frac{2}{15}

The total fraction of baby animals is \frac{24}{35} + \frac{2}{15} = \frac{72}{105} +\frac{14}{105} = \frac{86}{105}

Looking for more ratio questions and resources?

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ACT Math: How to Solve Ratio Problems

There are a few key concepts to get down in order to ace ACT Math ratios. Let’s go right into how the ACT will test you on ratios and break it down for you.

Ratio Basics

A ratio tells you the proportional quantity of one thing relative to another.

Make sure not to get ratios confused with fractions. Fractions tell you the proportional quantity of something relative to its whole. Ratios expressed as fractions do not tell you the whole. One instance where you need to use the concept of ratios involves baking. If you want to make double the amount of cookies that a recipe will yield, then you need to double the quantity of each ingredient.

ACT Math ratio

ACT Math: Dealing With Ratios

You might see ACT ratios written in fraction form, colon form, or in plain English. Whatever the case may be, you can treat them all the same way. In the case of the fraction form, do not get it confused with a regular fraction! The denominator of a ratio is not necessarily equivalent to the denominator of a ratio.

For example, the ratio 12/8, 12:8, and 12 to 8 are all the same. Like fractions, you should reduce ratios down to simplest terms – in this case, it is 3/2. Keep your numbers manageable, especially when you need to look for the lowest common multiple later on in the multi-step ratio section.

On the test, ratios will be clearly spelled out for you. If you are looking at a ratio problem, you’ll know it because the test makers will make it obvious.

The important part lies in knowing how to manipulate ratios to get to your answer. The two main things you need to know are proportions and multi-step ratios.

Proportions

You’ll find that these are very common on the ACT. Thankfully, they are also easy to solve.

You will usually be given a ratio along with a hypothetical quantity of one of the things on the original ratio. The key is to set up two ratios and cross-multiply as you would two fractions to solve for the missing fourth quantity.

If you have a ratio of 3 cats to 2 dogs, how many cats do you have if you have 20 dogs? You could use mental math or set up two fractions to get 30 cats as your answer.

Multi-Step Ratios

These are a little bit more involved, but shouldn’t pose much of a threat to your ACT Math score one you learn about how to go about solving them.

Here you’ll be given two ratios and three different types of quantities: a, b, and c. The two ratios given compare a to b and b to c. You’ll then be asked to figure out the ratio of a to c.

In order to solve, you need to figure out the least common multiple of the two b’s and multiply the respective a’s accordingly. Now with your b’s equal to each other, simply take the values of your a and c and create a new ratio.

For example, if a:b is 2:3 and b:c is 6:9, then what is a:c? Here we need to multiply our first ratio by 2 in order to get 4:6. Since our b from the first and second ratio match, we can take our a and c and form a new ratio.

Our answer is 4:9.

Minh Nguyen

Minh’s passion for helping students succeed grew during his time as a career counselor at the University of California, Irvine. Now, he’s helping students all over the world by spilling SAT/ACT secrets through blog posts on Magoosh. When he’s not busy tutoring or writing, he enjoys playing guitar, traveling, and talking about himself in third-person.

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How to Find Molar Ratio: Examples and Practice

  • The Albert Team
  • Last Updated On: February 12, 2024

How to find molar ratio: examples and practice problems

Chemistry isn’t just about mixing colorful liquids in beakers and waiting for an explosion—it’s a world of ratios, reactions, and relationships. At the heart of understanding this fascinating world lies the concept of the molar ratio, a key player in predicting the outcomes of chemical reactions. But what exactly is a molar ratio, and why is it so important? Simply put, it quantifies the proportions of reactants and products in a chemical equation, and accounts for every atom according to the law of conservation of mass. Remember learning about balanced equations? It’s time to put that knowledge into action. In this blog post, we’ll dive deep into the world of molar ratios, from what they are to how to find them using balanced equations. Whether you’re a budding chemist or just curious about the science behind the reactions, you’re in the right place to uncover the secrets of how to find the molar ratio.

What We Review

What is Molar Ratio?

Imagine you’re following a recipe to bake a cake. You wouldn’t just throw in random amounts of flour, sugar, and eggs, right? Just like in baking, chemistry requires precise measurements to get the desired outcome. This is where the concept of the molar ratio comes into play, acting as the “recipe” for chemical reactions.

In order to determine how much reactant must be used in an equation or how much product will be produced, molar ratio calculations are used. They are all based on the balanced equation.

A molar ratio is the proportion of moles of one substance to the moles of another substance in a chemical reaction. The coefficients of the substances in a balanced chemical equation show the molar ratio relationship. For example, in the reaction to produce water ( 2H_2 + O_2 \rightarrow 2H_2O ), the molar ratio of H_2 to O_2 is 2:1. This means that two moles of hydrogen gas react with one mole of oxygen gas to produce water.

So, why is this important? Chemists predict how much of each reactant they need to produce a certain amount of product without any waste by using molar ratio. It ensures that every atom of the reactants has a place in the products, adhering to the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.

Understanding molar ratios is crucial for anyone looking to delve into the world of chemistry, whether it’s synthesizing a new compound in a research lab or figuring out the right amount of baking soda to add to your volcano science project. By mastering this concept, you’ll unlock the ability to navigate through chemical equations with ease, paving the way for exciting experiments and discoveries.

Chemical plants and other factories use balanced equations and molar ratios to determine reactant amounts to create a certain amount of product.

How to Find Molar Ratio

In order to truly grasp the concept of molar ratio, let’s dive into some example problems that highlight how to use this tool in real chemical equations. Curious about how to find the molar ratio? These examples will show you step-by-step how to calculate molar ratios and apply them to predict the amounts of reactants and products in a chemical reaction.

Example 1: Combustion of Propane

The combustion of propane ( C_3H_8 ) in oxygen ( O_2 ) is a common reaction that produces carbon dioxide ( CO_2 ) and water ( H_2O ). The balanced chemical equation for this reaction is:

Question: What is the molar ratio of O_2 to CO_2 in the combustion of propane?

Solution: To find molar ratio, look at the coefficients in your balanced equation. By looking at the balanced equation, we can see that 5 moles of O_2 produce 3 moles of CO_2 . Therefore, the molar ratio of O_2 to CO_2 is 5:3.

Example 2: Formation of Ammonia

The Haber process combines nitrogen ( N_2 ) and hydrogen ( H_2 ) gas to form ammonia ( NH_3 ), a crucial component in fertilizers. The balanced equation for this reaction is:

Question: If you start with 4 moles of N_2 how many moles of H_2 are needed to react completely based on the molar ratio?

Solution: From the balanced equation, the molar ratio of N_2 to H_2 is 1:3. This means for every mole of N_2 , they require 3 moles of H_2 to react. For 4 moles of N_2 , we need:

Therefore, 12 moles of H_2 completely react with 4 moles of N_2 .

Practice Problems: Finding and Applying Molar Ratio

Now that you’ve seen how to find molar ratio and how to use them through example problems, it’s your turn to try solving some on your own. These practice problems will test your understanding of molar ratios and how to apply them to different chemical reactions. Work through these on your own, then scroll down for solutions.

Problem 1: Synthesis of Water

When hydrogen gas ( H_2 ) reacts with oxygen gas ( O_2 ) water ( H_2O ) forms. The balanced equation for this reaction is: 

If you have 6 moles of H_2 , how many moles of O_2 are needed to react completely, and how many moles of H_2O will be produced?

Problem 2: Decomposition of Potassium Chlorate

Potassium chlorate ( KClO_3 ) decomposes upon heating to produce potassium chloride ( KCl ). The balanced equation for this reaction is:

How many moles of O_2 can be produced from the decomposition of 4 moles of KClO_3 ?

Problem 3: Combustion of Ethanol

Ethanol ( C_2H_5OH ) combusts in oxygen to produce carbon dioxide and water. The balanced chemical equation is:

If 2 moles of C_2H_5OH are combusted, how many moles of O_2 are required, and what amounts of CO_2 and H_2O are produced?

Problem 4: Production of Ammonium Nitrate

Ammonium nitrate ( NH_4NH_3 )is produced by the reaction of ammonia ( NH_4 ) with nitric acid ( HNO_3 ). The balanced chemical equation for this reaction is:

If a fertilizer company needs 5 moles of ammonium nitrate, how many moles of ammonia and nitric acid are required to achieve this?

Problem 5: Synthesis of Magnesium Oxide

Magnesium ( Mg ) reacts with oxygen ( O_2 ) to form magnesium oxide ( MgO ). The balanced equation for this reaction is:

During a lab experiment, a student reacts 6 moles of magnesium with excess oxygen. How many moles of magnesium oxide does the reaction produce, and how many moles of oxygen are consumed in the reaction?

Tips for Solving:

  • Start by identifying the molar ratios between the reactants and products from the balanced chemical equations.
  • Use the molar ratios to calculate the amounts of reactants or products as needed.
  • Remember to check your work and ensure that the law of conservation of mass is satisfied in your calculations.

Molar Ratio Practice Problem Solutions

Are you ready to see how you did? Review below to see the solutions for the molar ratio practice problems.

Remember, to find molar ratio, use the coefficients in the balanced equation. The molar ratio of H_2 to O_2 is 2:1, meaning 2 moles of H_2 react with 1 mole of O_2 . You will use this ratio to determine how many moles of O_2 are needed to react completely.

The molar ratio of H_2 to H_2O is 2:2, which can be simplified to 1:1. Therefore, if 6 moles of H_2 reacts, it produces 6 moles of H_2O .

The molar ratio of KClO_3 to O_2 is 2:3. Hence, 2 moles of KClO_3 react with 3 moles of O_2 . You will use this to determine how many moles of O_2 will be produced.

This question has three different parts. The first is determining how many moles of O_2 are needed to react completely with 2 moles of C_2H_5OH . Initially, you must find the molar ratio. The ratio of O_2 to  C_2H_5OH is 3:1.

The second part asks how much CO_2 is produced from 2 moles of C_2H_5OH . The ratio of CO_2 to C_2H_5OH is 2:1.

The third part asks how much H_2O the reaction produces from 2 moles of C_2H_5OH . The ratio of H_2O to  C_2H_5OH is 3:1.

If a fertilizer company needs to produce 5 moles of ammonium nitrate, how many moles of ammonia and nitric acid are required to achieve this?

This is a two-part problem, but solved the same way. This is because the balanced equation has a molar ratio of 1:1 for all reactants and products in the equation. Therefore, however many moles you put into the reaction, produces the same amount of moles as products. Therefore, if we want to produce 5 moles of NH_4NH_3 , we would need to put in 5 moles of NH_3 and 5 moles of HNO_3 .

During a lab experiment, a student reacts 6 moles of magnesium with excess oxygen. How many moles of magnesium oxide will be produced, and how many moles of oxygen are consumed in the reaction?

This is a two-part problem. The first part asks how many moles of Mg the reaction makes if 6 moles of Mg reacts. The molar ratio of MgO to Mg is 2:2, which can be simplified to 1:1. Therefore, if 6 moles of Mg reacts, 6 moles of MgO will be produced.

The second part of the problem asks how much excess O_2 the reaction uses if 6 moles of Mg reacted. The molar ratio of Mg to O_2 is 2:1. We use this to determine our answer.

Molar ratios aren't just something learned in chemistry class; they are used by companies across the world to make commercial products.

Embarking on the journey through the world of chemistry reveals the intricate dance of atoms and molecules, governed by fundamental principles such as the molar ratio. This concept, akin to the precise measurements in a recipe, ensures that chemical reactions proceed smoothly, with each reactant and product playing its part in the grand scheme of matter transformation.

Understanding molar ratios not only demystifies how substances react in specific proportions but also empowers us with the ability to predict the outcomes of these reactions. Whether it’s synthesizing a new compound in the lab, analyzing environmental samples, or simply marveling at the chemical reactions in everyday life, the knowledge of molar ratios serves as a crucial tool in the arsenal of any budding chemist.

In conclusion, we’ve explored how to find molar ratio and tackled practice problems to solidify our understanding. Remember, the beauty of chemistry lies not just in theoretical knowledge but in applying these concepts to solve real-world problems. So, I encourage you to continue exploring, questioning, and experimenting with the fascinating reactions that make up our world.

Chemistry continually challenges and inspires, and with tools like molar ratios, you can uncover the mysteries that lie in molecules and reactions. So, keep your curiosity alive, and let the molar ratio guide you as you journey through the incredible landscape of chemistry.

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  1. How to Solve Ratio Problems Easily: Try These Tricks!

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COMMENTS

  1. Ratio Problem Solving

    When problem solving with a ratio, the key facts that you need to know are: What is the ratio involved? What order are the quantities in the ratio? What is the total amount / what is the part of the total amount known? What are you trying to calculate? As with all problem solving, there is not one unique method to solve a problem.

  2. Ratios and proportions

    part: whole = part: sum of all parts To write a ratio: Determine whether the ratio is part to part or part to whole. Calculate the parts and the whole if needed. Plug values into the ratio. Simplify the ratio if needed. Integer-to-integer ratios are preferred. [Example: Part to whole] [Examples: Simplifying ratios]

  3. Ratio Problem Solving

    3 + 5 = 8 40 ÷ 8 = 5 Then we multiply each part of the ratio by 5. 3 x 5:5 x 5 = 15:25 This means that Charlie will get 15 sweets and David will get 25 sweets. Dividing ratios Step-by-step guide: Dividing ratios (coming soon) Ratios and fractions (proportion problems) We also need to consider problems involving fractions.

  4. Solving Ratio Problems

    Solving Ratio Problems We add the parts of the ratio to find the total number of parts. There are 2 + 3 = 5 parts in the ratio in total. To find the value of one part we divide the total amount by the total number of parts. 50 ÷ 5 = 10. We multiply the ratio by the value of each part. 2:3 multiplied by 10 gives us 20:30.

  5. How to Calculate Ratios: 9 Steps (with Pictures)

    1 Be aware of how ratios are used. Ratios are used in both academic settings and in the real world to compare multiple amounts or quantities to each other. The simplest ratios compare only two values, but ratios comparing three or more values are also possible.

  6. Ratio Word Problems (video lessons, examples and solutions)

    Step 1: Assign variables: Let x = number of red sweets. Write the items in the ratio as a fraction. Step 2: Solve the equation. Cross Multiply 3 × 120 = 4 × x 360 = 4 x Isolate variable x Answer: There are 90 red sweets. Example 2: John has 30 marbles, 18 of which are red and 12 of which are blue.

  7. Ratio

    When simplifying fractions, use the common factors to divide all the numbers in a ratio until they cannot be divided further to write the ratio in lowest terms. For example, The ratio of red counters to blue counters is 16 : 12. 16: 12.

  8. Part to whole ratio word problem using tables

    Discover how to solve ratio problems with a real-life example involving indoor and outdoor playtimes. Learn to use ratios to determine the number of indoor and outdoor playtimes in a class with a 2:3 ratio and 30 total playtimes. Created by Sal Khan. Questions Tips & Thanks Want to join the conversation? Sort by: Top Voted Annet Torres 6 years ago

  9. Ratio Math Problems

    Solution: Step 1: Assign variables: Let x = amount of corn. Write the items in the ratio as a fraction. Step 2: Solve the equation: Cross Multiply 2 × x = 3 × 5 2x = 15 Isolate variable x Answer: The mixture contains 7.5 pounds of corn. Example 2: Clothing store A sells T-shirts in only three colors: red, blue and green.

  10. Solving Ratios, Practice with SAT Problems

    How do we solve ratio problems? A comparison between quantities using division. 3:2 , 3:2:88, 3 to 2, 3 to 2 to 88 A 2 to 5 ratio can be represented as 2:5 A ration between X and Y can be written A bucket holds 4 quarts of popcorn.

  11. Ratios and rates

    Pre-algebra 15 units · 179 skills. Unit 1 Factors and multiples. Unit 2 Patterns. Unit 3 Ratios and rates. Unit 4 Percentages. Unit 5 Exponents intro and order of operations. Unit 6 Variables & expressions. Unit 7 Equations & inequalities introduction. Unit 8 Percent & rational number word problems.

  12. Solve Ratio Word Problems

    156 20K views 3 years ago Learn Algebra In this video I'll show you how to solve multiple types of Ratio Word Problems using 5 examples. We'll start simple and work up to solving the most...

  13. Ratios

    So the ratio of flour to milk is 3 : 2. To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4: 3 ×4 : 2 ×4 = 12 : 8. In other words, 12 cups of flour and 8 cups of milk. The ratio is still the same, so the pancakes should be just as yummy.

  14. Solving ratio problems

    Real-world maths Game - Divided Islands Key points Ratio problems take different forms, which may include: linking ratios and fractions part-part problems - where the value of one part of...

  15. Multi-Step Ratio Problems (Simplifying Math)

    This video shows how to calculate Ratios of a number and then use that to solve multi-step ratio problems. With examples and practice for you to try on your ...

  16. Solving Ratio Word Problems (the easy way!)

    1.4K 118K views 8 years ago This video focuses on how to solve ratio word problems. In particular, I show students the trick of multiplying each term in the ratio by x to help set up an...

  17. Solving Ratio Problems Involving Totals

    To solve ratio problems involving totals, we take these steps: Name the unknowns using variables. Set up a ratio box with totals using the given information. Use the ratio box to set up a...

  18. Ratio Questions And Problems: Differentiated Questions Included

    At this level, ratio questions ask you to write and simplify a ratio, to divide quantities into a given ratio and to solve problems using equivalent ratios. See below the example questions to support test prep. Ratio questions for 6th grade. 1. In Lucy's class there are 12 boys and 18 girls. Write the ratio of girls to boys in its simplest form.

  19. Solve Problems with Ratios and Proportions

    You can cross-multiply to solve ratios. A more efficient way to solve equivalent ratios is by cross-multiplying. Consider the short-haired versus long-haired problem above. You can write the ratios as fractions instead. 2:3 can be written as 2/3. 12:x can be written as [ggfrac]12/x[/ggfrac].

  20. How to Solve a One-Step Problem Involving Ratios

    It's similar to a rate, but whereas rates are often in terms of only one of a given quantity, ratios can be in terms of multiple units. For example, a ratio could be two pizzas for every five ...

  21. Video: Solving Ratio Problems With Tables, Tape Diagrams & Double

    A ratio problem involves finding out how two values are related to each other. In this lesson, we learned three different ways to solve these kinds of problems.

  22. Step by Step tutorial on How to Solve Ratios In Mathematics

    The first step on how to solve the ratio is to write the values you want to compare and you can write such values in any given form like using colon or through division sign or by writing isto. Let's understand the steps through an example. Suppose you want to take out the ratio of your maths and physics marks.

  23. 15 Ratio Questions & Practice Problems

    Ratio tables are another technique for solving ratio problems. How to solve a proportion problem. As we have seen, ratio and proportion are strongly linked. If we are asked to find what proportion something is of a total, we need to identify the amount in question and the total amount. We can then write this as a fraction:

  24. ACT Math: How to Solve Ratio Problems

    The two ratios given compare a to b and b to c. You'll then be asked to figure out the ratio of a to c. In order to solve, you need to figure out the least common multiple of the two b's and multiply the respective a's accordingly. Now with your b's equal to each other, simply take the values of your a and c and create a new ratio.

  25. How to Find Molar Ratio: Examples and Practice

    Review below to see the solutions for the molar ratio practice problems. Problem 1: Synthesis of Water. When hydrogen gas ... Remember, the beauty of chemistry lies not just in theoretical knowledge but in applying these concepts to solve real-world problems. So, I encourage you to continue exploring, questioning, and experimenting with the ...