Dividing Fractions

For example, the reciprocal of ¾ is 4/3.

The reciprocal of 3 ¾ is 4/15.

$\frac{1}{2}$ + $\frac{1}{2}$   +

$\frac{1}{2}$ + $\frac{1}{2}$   +

$\frac{1}{2}$ + $\frac{1}{2}$   +

$\frac{1}{2}$ + $\frac{1}{2}$   +

$\frac{1}{2}$ + $\frac{1}{2}$

    1      + 

    1      + 

    1      + 

    1      + 

    1 

=   5

2. What is $\frac{10}{15}$ ÷ 5?

$\frac{10}{15}$ ÷ $\frac{5}{1}$

= $\frac{10}{15}$ × $\frac{1}{5}$

= $\frac{2 × \not 5 × 1}{3 × \not 5 × 5}$

= $\frac{2}{15}$

              10 = 2 × 5

              15 = 3 × 5

                5 = 1 × 5

Solution:

3/5 ÷ 12

= 3/5 ÷ 12/1

= 3/5 × 1/12

= (3 × 1)/(5 × 12)

= 3/60

= 1/20

Step I: Find the reciprocal of the whole number and multiply with the fractional number as usual.

Step II: Express the product in its lowest terms.

= 5/7 ÷ 10/1

= 5/7 × 1/10

= (5 × 1)/(7 × 10)

= 5/70

Step I: Find the reciprocal of the whole number and multiply with the fractional number as usual.

Step II: Express the product in its lowest terms.

Solution:

7/8 ÷ 1/5

= 7/8 × 5/1

= (7 × 5)/(8 × 1)

= 35/8

= 4 3/8

Step I: Find reciprocal of 1/5.

Step II: Multiply 7/8 by it.

Step III: Express the product in its simplest form.

Solution:

5/9 ÷ 10/18

= 5/9 × 18/10

= (5 × 18)/(9 × 10)

= 90/90

= 1

Step I: Find reciprocal of 1/5.

Step II: Multiply 7/8 by it.

Step III: Express the product in its simplest form.

4. Divide $\frac{16}{27}$ ÷ $\frac{4}{9}$

Therefore, $\frac{16}{27}$ ÷ $\frac{4}{9}$ = $\frac{16}{27}$ × $\frac{9}{4}$; [Reciprocal of $\frac{4}{9}$ = $\frac{9}{4}$]

                            = $\frac{\not 2 × \not 2 × 2 × 2 × \not 3 × \not 3}{\not 3 × \not 3 × 3 × \not 2 × \not 2}$

                            = $\frac{4}{3}$

                            = 1$\frac{1}{3}$

            16 = 2 × 2 × 2 × 2

            9 = 3 × 3

            27 = 3 × 3 × 3

            4 = 2 × 2

Solution:

2 ¾ ÷ 1 2/3

= 11/4 ÷ 5/3

= 11/4 × 3/5

= (11 × 3)/(4 × 5)

= 33/20

= 1 13/20

Express the mixed numbers as improper fractions and multiply as usual.

Solution:

2  4/17 ÷ 1  4/17

= 38/17 ÷ 21/17

= 38/17 × 17/21

= (38 × 17)/(17 × 21)

= 646/357

= 38/21

= 1 17/21

Express the mixed numbers as improper fractions and multiply as usual.