Write each improper fraction as a mixed number

We explain what improper fractions and mixed numbers are and how the relationship between them can be taught to primary-school children.

What are improper fractions and mixed numbers?

A mixed number is made up of a whole number and a fraction. For example:

An improper fraction is one that is 'top-heavy' so the numerator is bigger than the denominator. For example: 

The relationship between mixed numbers and improper fractions can be best explained through the diagram above. These two shapes have been cut into four pieces. We can either express the amount of the shape we have as a mixed number: (1 3/4) or as an improper fraction (7/4).
 

Working with mixed numbers and improper fractions in KS2

In Years 5 and 6 children need to start to be able to see equivalence between mixed numbers and improper fractions.

In the diagram above 10/3 is equivalent to 3 1/3.

Converting improper fractions into mixed numbers

What is 16/5 as a mixed number?

• Divide the numerator by the denominator (16 ÷ 5 = 3 R 1).
• Your answer is the whole number and your remainder becomes the numerator of the fraction next to the whole number, so your answer is 3 1/5.

Converting mixed numbers into improper fractions

What is 2 7/8 as an improper fraction?

• Multiply the whole number by the denominator (2 x 8 = 16) and then add the numerator (16 + 7 = 23).
• This answer becomes the numerator; the denominator stays the same: 23/8.

Improper Fractions to Mixed Numbers Conversion

Converting improper fractions to mixed numbers

Here, you can convert an improper fraction into mixed numbers. Enter the fraction numerator and denominator in the spaces above and press "To Mixed Numbers". You may enter values between -2147483648 and 2147483647.

What is an improper fraction

A fraction is improper when its numerator is greater than its denominator. When a fraction is 'improper' it can be expressed as a whole number plus a proper fraction. A proper fraction is a fraction that has a numerator smaller than its denominator, a fraction that has a value less than 1.

The mixed numbers form shows the whole portion followed by the proper fraction.

For example, 1.25 can be expressed as 5/4, or 1 and 1/4. 5/4 is an improper fraction, 1 1/4 is its mixed numbers representation.

How to convert a fraction to mixed numbers

The fraction is first reduced to its lowest terms (see simplify fractions for more information).

If the fraction's numerator is greater than the denominator (an improper fraction), then the whole portion is obtained by dividing the numerator by the denominator. The numerator of the proper fraction is the remainder of the division. The denominator is the same as the denominator of the original fraction.

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In math, improper fractions are fractions where the numerator (the top half) is a number that is bigger than or equal to the denominator (the bottom half). To convert an improper fraction to a mixed number (which is made from a fraction and a whole number, like 2 & 3/4), divide the numerator by the denominator. Write the whole number answer next to a fraction with the remainder in the numerator and the original denominator — you now have a mixed fraction!

1. 

   1

   Divide the numerator by the denominator. Start by writing your improper fraction. Then, divide the numerator by the denominator — in other words, just do the division problem that the fraction is already set up for. Don't forget to include the remainder.[1]

   • Let's follow along with an example. Let's say that we need to turn the fraction 7/5 into a mixed number. We'll start by dividing 7 by 5, like this:
   • 7/5 → 7 ÷ 5 = 1 R2

2. 

   2

   Write the whole number answer. The whole number part of your mixed number (the big number to the left of your fraction) is the whole number answer of your division problem. In other words, just write the answer of the division problem without the remainder.[2]

   • In our example, since our answer is 1 R2, we would leave off the remainder and just write 1.

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3. 

   3

   Make a fraction from the remainder and the original denominator. Now, we need to find the fraction part of the mixed number. Put the remainder from your division problem in the numerator and use the same denominator from your original improper fraction. Put this fraction next to your whole number and you have your mixed number![3]

   • In our example, our remainder is 2. Putting this over our original denominator (5), we get 2/5. We put this next to our whole number answer (1) to get our final mixed number, like this:
   • 1 2/5.

4. 

   4

   To get back to an improper fractions, add the whole number to the numerator. Mixed numbers look good on paper and are easy to read, but they're not always the best choice. For example, if we're multiplying a fraction and a mixed number, our work will be a lot easier if we convert the mixed number back into an improper fraction. To do this, just multiply the whole number by the denominator and add it to the numerator.[4]

   • If we wanted to convert our example answer (1 2/5) back to an improper fraction, we would do it like this:[5]
   • 1 × 5 = 5 → (2 + 5)/5 = 7/5

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1. 

   1

   Convert 11/4 to a mixed number. This problem is easy — just solve exactly as above. See below for a step-by-step solution.

   • 11/4 — to start, we need to divide the numerator by the denominator.
   • 11 ÷ 4 = 2 R 3 — now, we need to make a fraction from the remainder and our original denominator.
   • 11/4 = 2 3/4

2. 

   2

   Convert 99/5 to a mixed number. We're dealing with a really big numerator here, but don't be intimidated — the process is exactly the same! See below:

   • 99/5 — how many times does 5 go into 99? Since 5 goes into 100 exactly 20 times, it's safe to say that 5 goes into 99 19 times.
   • 99 ÷ 5 = 19 R 4 — now, we just put the mixed number together like before.
   • 99/5 = 19 4/5

3. 

   3

   Convert 6/6 to a mixed number. Up until now, we've only dealt with improper fractions where the numerator is bigger than the denominator. But what happens when they're the same number? See below to find out.

   • 6/6 — six goes into six one time with no remainder, obviously.
   • 6 ÷ 6 = 1 R0. Since a fraction with 0 in the numerator is always equal to zero, we don't need to put a fraction next to our whole number.
   • 6/6 = 1

4. 

   4

   Convert 18/6 to a mixed number. If the numerator is a multiple of the denominator, you don't have to bother with the remainder — just do the division problem to get your answer. See below.

   • 18/6 — since we know that 18 is just 6 × 3, we know we'll have a remainder of 0, so we don't need to worry about the fraction part of our mixed number.
   • 18/6 = 3

5. 

   5

   Convert -10/3 to a mixed number. Negatives work exactly the same way as positive numbers do. See below:

   • -10/3
   • -10 ÷ 3 = -3 R1
   • -10/3 = -3 1/3

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Add New Question

• Question

  How do you convert 7/2 into a mixed number?

  

  Divide 2 into 7. You get 3 with a remainder of 1. 3 is the whole number of the mixed number, 1 is the numerator of the fraction, and 2 is the denominator.

• Question

  How do I convert 46/12 into a mixed number?

  

  Divide 12 into 46. You get 3 with a remainder of 10. 3 is the whole number of the mixed number, 10 is the numerator of the fraction, and 12 is the denominator. The fraction can be reduced to 5/6.

• Question

  What do I add to 19/4 to make 5?

  

  Find the answer by subtracting 19/4 from 5. Do this by converting 5 to 20/4 and then subtracting 19/4.

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• Improper fractions aren't necessarily bad to have. In fact, sometimes they're more useful than mixed numbers. For instance, if you're going to multiply two fractions, improper fractions are better because you just have to multiply across the numerator and the denominator to get your answer: e.g., 1/6 × 7/2 = 7/12. Now, try multiplying 1/6 × 3 1/2 — not so simple.

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• On the other hand, mixed numbers are usually best when you're describing something in real life. For instance, if a recipe calls for 4 1/2 cups of flour, you wouldn't say, "we need 9/2 cups of flour."

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To convert an improper fraction into a mixed number, start by writing the fraction as a division problem. Divide the numerator by the denominator. For instance, if the improper fraction is 7/5, write it out as 7 ÷ 5. Next, write out the whole number part of the answer. In our example, 5 divides into 7 one time, so the whole number is 1. This leaves us with a remainder of 2. The remainder will become the new numerator in the fraction, while the denominator remains the same. So, in the example of 7/5, you would get 7 ÷ 5 = 1 remainder 2. To express this as a fraction, write it as 1 and 2/5ths. If you want to turn it back into an improper fraction, multiply the whole number by the denominator and add the product to the numerator. The sum will become the new numerator in your improper fraction, while the denominator will remain the same. If you want to learn how to check your answer to make sure your mixed number is right, keep reading!

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