How to Turn an Improper Fraction into a Mixed Number

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How to Turn an Improper Fraction into a Mixed Number
How to Turn an Improper Fraction into a Mixed Number
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An improper fraction is one with a numerator (top number) greater than the denominator (bottom number), such as 5/2. Mixed numbers are whole numbers with a fraction, such as 21/2. It is usually easier to imagine 21/2 pizzas than "five halves" of a pizza, so it might be useful to be able to convert between these two number types. Splitting is the easiest way to do this, but there is an easier way if you have difficulty with the first method.

Steps

Method 1 of 2: Using Division

Turn an Improper Fraction Into a Mixed Number Step 01

Step 1. Start with an improper fraction

We will use the number 15/4 for example. This is an improper fraction because the numerator (15) is greater than the denominator (4).

If you're still not comfortable with fractions or division, start with the example below

Turn an Improper Fraction Into a Mixed Number Step 02

Step 2. Rewrite the fraction as a division problem

Write the fraction as a long division problem. Always write the numerator divided by the denominator. In the example used, 15 ÷ 4.

Turn an Improper Fraction Into a Mixed Number Step 03

Step 3. Start solving the division problem

Review this article if you don't know what to do. This example will be easier to follow if you write the long division problem as you read it:

  • Compare the number 4 to the first digit, 1. The 4 doesn't fit into the number 1, so we need to include the next digit.
  • Compare the number 4 to the first two digits, 15. How many times does the number 4 fit within the number 15? If you're not sure, take a guess and see if you got it right using multiplication.
  • The answer is 3, so write the number 3 on the answer line above the number 5.
Turn an Improper Fraction Into a Mixed Number Step 04

Step 4. Find the rest

Unless the division is exact, there will be a remainder. Here's how to find the rest in a long division problem:

  • Multiply the answer by the divisor (the number on the left). In the example used, 3 x 4.
  • Write the result below the dividend (the number below the division sign). In the example used, 3 x 4 = 12, so write 12 under the number 15.
  • Subtract the result of the dividend: 15 - 12 =

    Step 3.. Number 3 is the rest.

Turn an Improper Fraction Into a Mixed Number Step 05

Step 5. Write the mixed number using the results

A mixed number is an integer together with a fraction of its own. After calculating the division, you will have everything you need to write the mixed number:

  • The integer is the answer to the division problem. In this case, the

    Step 3..

  • The fraction numerator is the remainder. In this case, also the number

    Step 3..

  • The denominator of the fraction is the same as the denominator in the original fraction (the

    Step 4.).

  • Write it as a mixed number: 33/4.

Method 2 of 2: Without using division

Turn an Improper Fraction Into a Mixed Number Step 06

Step 1. Write the fraction

An improper fraction is one where the top number is greater than the bottom number. For example, 3/2 is an improper fraction, as 3 is greater than 2.

  • The top number is called numerator. The bottom number is called denominator.

  • This method will take a long time on larger fractions. If the numerator is much larger than the denominator, the division method above works much faster.
Turn an Improper Fraction Into a Mixed Number Step 07

Step 2. Remember the fractions that equal 1

Did you know that 2 ÷ 2 = 1? Or that 4 ÷ 4 = 1? In fact, any number divided by itself equals 1. Fractions work that way too. 2/2 = 1 and 4/4 = 1, and even 397/397 equals 1!

Turn an Improper Fraction Into a Mixed Number Step 08

Step 3. Divide the fraction into two parts

This is an easy way to turn a fraction into a whole number. Let's see if we can do this for part of the improper fraction:

  • in the fraction 3/2, the numerator is 2.
  • 2/2 it is an easy fraction to be simplified because the numerator and denominator are the same. It is necessary to remove this part of the fraction greater than to find the rest.
  • Write: 3/2 = 2/2 + ?/2.

Step 4. Find the second part

How can we turn that question mark into a number? If you don't know how to add and subtract fractions, don't worry. When the denominators are the same, you can ignore them and turn the problem into an ordinary addition operation. See a guide to the example used, 3/2 = 2/2 + ?/2:

Turn an Improper Fraction Into a Mixed Number Step 09
  • Just look at the numerators. They say 3 = 2 + "?". What number can be used in place of the question mark to solve the problem? Which number can be added to 2 to get the number 3?
  • The answer is 1 because 3 = 2 + 1.
  • When you get the answer, write the equation again, including the denominators: 3/2 = 2/2 + 1/2.
Turn an Improper Fraction Into a Mixed Number Step 10

Step 5. Simplify the fraction

Now, you know that the improper fraction equals 2/2 + 1/2. You also know that 2/2 = 1, as well as any fraction with equal number and denominator. That means you can cross out 2/2, and write 1 instead. Now you have it 1 + 1/2, that is, a mixed number! In this example, the issue is resolved.

  • After finding the solution, you no longer need to write the "+" symbol. just write 11/2.
  • A mixed number is an integer together with a fraction of its own.
Turn an Improper Fraction Into a Mixed Number Step 11

Step 6. Repeat these instructions if the fact remains inappropriate

Sometimes the fraction portion of the answer may remain inappropriate, with a numerator greater than the denominator. In this case, you can start all over again by turning it into a mixed number. Don't forget to add the number "1" when done. In the following example, the number 7/3 will be transformed into a mixed fraction:

  • 7/3 = 3/3 + ?/3
  • 7 = 3 + ?
  • 7 = 3 + 4
  • 7/3 = 3/3 + 4/3
  • 7/3 = 1 + 4/3
  • This fraction is improper, so ignore the number 1 and do the same thing: 4/3 = 3/3 + ?/3
  • 4 = 3 + ?
  • 4 = 3 + 1
  • 4/3 = 3/3 + 1/3
  • 4/3 = 1 + 1/3
  • That fraction is your own, so you're done. Remember to add the previously ignored number: 1 + 1 + 1/3 = 21/3.

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