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improper fraction/mixed number word problems

improper fraction/mixed number word problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity


Last updated

20 January 2015

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terible word porblems becuse i dont like it

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Improper Fractions

An Improper Fraction has a top number larger than (or equal to) the bottom number. It is usually " top-heavy "

More Examples:

See how the top number is bigger than (or equal to) the bottom number? That makes it an Improper Fraction, (but there is nothing wrong about Improper Fractions ).

Three Types of Fractions

There are three types of fraction:

A Fraction (such as 7 / 4 ) has two numbers:

Numerator Denominator

The top number (the Numerator) is the number of parts we have . The bottom number (the Denominator) is the number of parts the whole is divided into .

Example: 7 / 4 means:

  • We have 7 parts
  • Each part is a quarter ( 1 / 4 ) of a whole

So we can define the three types of fractions like this:

Improper Fraction

So an improper fraction is a fraction where the top number (numerator) is greater than or equal to the bottom number (denominator): it is top-heavy .

Can be Equal

What about when the numerator equals the denominator? Such as 4 4 ?

Well it is the same as a whole, but it is written as a fraction, so most people agree it is a type of improper fraction.

Improper Fractions or Mixed Fractions

We can use either an improper fraction or a mixed fraction to show the same amount.

For example 1 3 4 = 7 4 , as shown here:

Converting Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, follow these steps:

  • Divide the numerator by the denominator.
  • Write down the whole number answer
  • Then write down any remainder above the denominator.

Example: Convert 11 4 to a mixed fraction.

Write down the 2 and then write down the remainder (3) above the denominator (4).

That example can be written like this:

Example: Convert 10 3 to a mixed fraction.

Converting mixed fractions to improper fractions.

To convert a mixed fraction to an improper fraction, follow these steps:

  • Multiply the whole number part by the fraction's denominator.
  • Add that to the numerator
  • Then write the result on top of the denominator.

Example: Convert 3 2 5 to an improper fraction.

Multiply the whole number part by the denominator:

Add that to the numerator:

Then write that result above the denominator:

We can do the numerator in one go:

Example: Convert 2 1 9 to an improper fraction.

Are improper fractions bad .

NO, they aren't bad!

For mathematics they are actually better than mixed fractions. Because mixed fractions can be confusing when we write them in a formula: should the two parts be added or multiplied?

But, for everyday use , people understand mixed fractions better.

Example: It is easier to say "I ate 2 1 4 sausages", than "I ate 9 4 sausages"

We Recommend:

  • For Mathematics: Improper Fractions
  • For Everyday Use: Mixed Fractions

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How to Solve Improper Fraction Math Problems

Adding and subtracting fractions sometimes results in improper fractions.

How to Divide Radicals

Improper fractions contain a numerator that is equal to or greater than the denominator. These fractions are described as improper because a whole number can be pulled out from them, yielding a mixed number fraction. This mixed number fraction is a simplified version of the number and, therefore, is more desirable because it removes complexity in further operations that may be preformed. Performing operations on improper fractions is a pre-algebra exercise that allows students to become familiar with the concept of rational numbers.

Complete all operations indicated on an improper fraction as normal. For example, (3/2 ) * ( 5/2) = 15/4.

Divide the top number by the bottom number. If there is a remainder write it down for later use. In our example, 4 divides into 15 three times. This yields 3 with a remainder of 3.

Write down the whole number.

Create a fraction beside the whole number with the original denominator value. Continuing from above, 3 ( /4).

Place the remainder from above into the blank numerator. In conclusion, 15 / 4 = 3 3/4.

Check your work by multiplying the denominator by the whole number portion of the mixed number and adding the product to the numerator. Checking the above yields ((4 * 3) + 3)) / 4 = 15 / 4. This check proves the operation was a success and that the improper fraction was simplified properly.

Related Articles

How to check multiplication, how to multiply 3 fractions, multiplying fractions, how to write an equivalent fraction with a given denominator, how to convert a fraction to a ratio, how to divide rational numbers, how to write the remainder as a whole number, how to type a mixed fraction in a ti-83 plus, how to: improper fractions into proper fractions, how to add & subtract radical expressions with fractions, how to get a remainder in your calculator, how to square a fraction with a variable, how to find the x intercept of a function, how to get rid of a variable that is cubed, how to subtract mixed numbers with regrouping, how to do fractions on a ti-30x iis, how to do exponents outside of the parenthesis, how to simplify algebraic expressions.

  • "Introductory and Intermediate Algebra"; Marvin L. Bittinger and Judith A. Beecher; 2007
  • Purplemath; Fractions Review - Mixed Numbers and Improper Fractions; Elizabeth Stapel; 2000

About the Author

Gabriel Dockery began writing in 2009, with his work published on various websites. He is working toward a Bachelor of Science in neuroscience in a transfer program between Ivy Tech College and Indiana State University.

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Understand Improper Fractions – Reasoning and Problem Solving

Understand Improper Fractions

Understand Improper Fractions - Reasoning and Problem Solving

This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of understanding improper fractions.

problem solving improper fractions

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problem solving improper fractions


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