How do you divide fractions and mixed numbers

When you divide a number by a mixed number, first rewrite the mixed number as an improper fractions . Then multiply the number by the  reciprocal of the improper fraction.

Example 1:

Find the quotient. Write in simplest form.

216÷115

First, write the mixed numbers as improper fractions.

216=136115=65

So, the expression becomes

136÷65

Multiply by the reciprocal of 65 , which is 56 .

136÷65=136⋅56

Multiply the numerators and multiply the denominators.

=6536

Write the improper fraction as a mixed number.

=12936

So,

216÷115=12936

Example 2:

Find the quotient. Write in simplest form.

712÷2110

First, write the mixed numbers as improper fractions.

712=1522110=2110

So, the expression becomes

152÷2110

Multiply by the reciprocal of 2110 , which is 1021 .

152÷2110=152⋅1021

The GCF of 15 and 21 is 3 . So, to simplify the fractions, divide 15 and 21 by 3 .

The GCF of 2 and 10 is 2 . So, to simplify the fractions, divide 2 and 10 by 2 .

=15521⋅105217=51⋅57

Multiply the numerators and multiply the denominators.

=257

Write the improper fraction as a mixed number.

=347

So,

712÷2110=347 .

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To divide mixed fractions, you could first convert each to an improper fraction. Then, switch to a multiplication problem by multiply by the reciprocal of the divisor. Simplify and convert your answer back to a mixed fraction to get your answer! This tutorial will show you how!

The easiest way to divide mixed fractions is to convert them into improper fractions first. Start by multiplying the whole number in each mixed fraction by its denominator. For example, if one of the fractions is 6 ½, multiply 6 x 2 to get 12. Then, add the product to the numerator. In this example, 12 + 1 = 13. This will become the new numerator of your fraction, giving you the improper fraction 13/2. Once you’ve converted all the mixed fractions into improper fractions, you can divide them. Let’s say you have to solve the problem 6 ½ ÷ 2 ¼. Written as improper fractions, this would be 13/2 ÷ 9/4. To do the division problem, find the reciprocal of the divisor by flipping the fraction over. Then, multiply the two fractions together. So, in our example, 13/2 ÷ 9/4 becomes 13/2 x 4/9. Now all you need to do is multiply the numerators and denominators of the fractions together. 13 x 4 = 52 and 2 x 9 = 18, so 13/2 ÷ 9/4 = 52/18. If you can, simplify your answer by dividing the numerator and denominator of the fraction by their greatest common factor. 52 and 18 both share the factor 2, so you can simplify the fraction to 26/9. Now, convert the fraction back to a mixed number by dividing the numerator by the denominator. The quotient is the whole number, while the remainder is the new numerator. 26 ÷ 9 = 2 with a remainder of 8. So, 26/9 becomes the mixed fraction 2 and eight ninths. If you want to learn how to convert your improper fractions back to mixed numbers, keep reading the article!

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The steps involved in dividing fractions and mixed numbers are similar, but an important step is required when dividing mixed numbers.

To divide fractions, invert (turn upside down) the second fraction (the one “divided by”) and multiply. Then simplify, if possible. Division of fractions can also be performed by multiplying the first fraction by the reciprocal of the second fraction.

Divide

Divide 

Divide 

Sometimes, a division of fractions problem may appear in the following form. These are called complex fractions.

The line separating the two fractions means “divided by.” Therefore, this problem may be rewritten as

Now follow the same procedure as shown in Example .

Divide = 

To divide mixed numbers, first change them to improper fractions (Example ). Then follow the rule for dividing fractions (Example ).

Divide

Notice that after you invert and have a multiplication of fractions problem, you may then cancel tops with bottoms when appropriate.

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