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# Lesson 9: Dividing Fractions.

### RECIPROCALS

When you turn the fraction upside down you have a RECIPROCAL of the
original fraction.

Turning fraction upside down is also called inverting.

#### Examples

 A reciprocal of 3 is 4 = 1 1 4 3 3
 A reciprocal of  1 2 = 7 is 5 5 5 7
 A reciprocal of  3 = 3 is 1 1 3

### HOW TO DIVIDE FRACTIONS

Do you know how we call the numbers in division?

 12 4 = 3 DIVIDEND DIVISOR QUOTIENT

To divide 2 fractions multiply the dividend by the reciprocal of the divisor.

You can do this by following few simple steps:

• Change all mixed fractions ( if any) to improper fractions.
• Turn the second fraction (divisor) upside down.
• Change the divide sign to multiply sign and multiply the fractions.

### DIVIDING SIMPLE FRACTIONS

#### Example

 Find 1 2 2 5

Solution:

 1 2 = 1 x 5 Change the sign to x. 2 5 2 2 Invert (turn upside down) the divisor.

 = 1 x 5 = 5 Multiply the numerators. 2 x 2 4 Multiply the denominators.

 = 1 1 Change the result to a mixed fraction. 4

#### Example

 Find 2 2 3

Solution:

 2 2 = 2 x 3 Write 2 as 2 , invert  the divisor and change the sign to x. 3 1 2 1

 = 2 x 3 = 6 Multiply the numerators. 1 x 2 2 Multiply the denominators.

 = 3 = 3 Simplify the result. 1

#### Example

 Find 3 6 8

Solution:

 3 6 = 3 6 Write  6 as 6 . 8 8 1 1

 = 3 x 1 Invert  the divisor and change the sign to x. 8 6

 = 3 x 1 = 1 x 1 = 1 Multiply the numerators and the denominators. 8 x 6 8 x 2 16 Simplify before multiplying (divide 3 and 6 by 3).

### DIVIDING MIXED FRACTIONS

#### Example

 Find 2 1 1 1 2 10

 = 2 1 1 1 = 5 11 Convert mixed fractions to 2 10 2 10 improper fractions.

 = 5 x 10 Invert  the divisor and change the sign to x 2 11

 = 5 x 10 = 5 x 5 Simplify before multiplying 2 x 11 1 x11 (divide 10 and 2 by 2)

 = 25 = 2 3 Change the result to a mixed fraction. 11 11

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