# Multiply And Divide Fractions

## Multiplying Fractions:

**Real life applications** where common fractions are multiplied or divided include:

- image reduction
- adapting recipes for larger groups of people.

**Steps to multiply fractions** are:

- Step 1 - Change mixed numbers to improper fractions
- Step 2 - Multiply the numerators(top numbers) and multiply the denominators (bottom numbers)
- Step 3 - Simplify if needed.

**The extra step to divide fractions is to multiply by the reciprocal of the second fraction** (that is, turn the second fraction upside and then multiply).

## Example One - Image Reduction

An image is reduced to one half of its original size. If the original measurement is ^{3}⁄_{4} cm, what is the new reduced measurement?

**Answer:**
^{1}⁄_{2} × ^{3}⁄_{4}

= ^{3}⁄_{8} cm

## Example Two - Adapting Recipes for Large Groups

A risotto recipe for 5 people uses 2 ^{1}⁄_{2} cups of rice. How many cups of rice are required to feed 20 people?

**Answer:**

Multiplier

= 20 ÷ 5

= 4

No. of cups of rice

= 2 ^{1}⁄_{2} × 4

= 10 cups

## Questions

**Q1.** ^{1}⁄_{3} × ^{2}⁄_{5}
**Q2.** ^{3}⁄_{8} × ^{4}⁄_{5}
**Q3.** 2 ^{1}⁄_{4} × 3 ^{2}⁄_{3}

**Answers**
**A1.** ^{2}⁄_{15}
**A2.** ^{3}⁄_{10}
**A3.** 8 ^{1}⁄_{4}

## Dividing Fractions:

## Example Three - Gym Training

In a gym the whole 2 ^{1}⁄_{2} hour training session is divided into ^{1}⁄_{4} hour parts. How many parts is this?

**Answer:**

2 ^{1}⁄_{2} ÷ ^{1}⁄_{4}

= ^{5}⁄_{2} ÷ ^{1}⁄_{4}

= ^{5}⁄_{2} × ^{4}⁄_{1}

= ^{20}⁄_{2}

= 10 parts

## Questions

**Q1.** ^{6}⁄_{7} ÷ ^{1}⁄_{4}
**Q2.** ^{3}⁄_{8} ÷ ^{1}⁄_{2}
**Q3.** 2 ^{4}⁄_{5} ÷ ^{1}⁄_{10}

**Answers**
**A1.** 3 ^{3}⁄_{7}
**A2.** ^{3}⁄_{4}
**A3.** 28