## How to Multiply and Divide Fractions

Fractions are generally used to define any whole number into equal parts. While writing a fraction, there are two numbers involved. The number at the top is called the numerator, while that at the bottom is called a denominator. There are three types of fractions. They are:

Proper Fractions: In proper fractions, the denominator is greater than the numerator. For ex: $$\frac{3}{4} \ , \ \frac{1}{3}$$
Improper Fraction: As the name suggests, these fractions are “top-heavy” or the numerator is greater than the denominator. For ex: $$\frac{7}{8} \ , \ \frac{5}{2}$$
Mixed-Fraction: Mixed fractions are another type of improper fractions where there is a whole number as well as a fraction part. For ex: $$1\frac{1}{3} \ , \ 2\frac{3}{7}$$

To multiply or divide two fractions, we will follow the steps mentioned below.

Multiplication of 2 Fractions

Let’s take the example of two fractions $$\frac{a}{b}$$ and $$\frac{c}{d}$$
Now, $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} = \frac{ac}{bd}$$
So, multiplication is pretty simple. Just multiply the two numerators and write the answer over the multiplication result of the two denominators.
Note: Before directly multiplying fractions, you can convert each one of them into their simplest forms. Also, you can even cross out equal factors to make each number as small as possible.

Division of 2 Fractions

Let’s take the example of two fractions $$\frac{a}{b}$$ and $$\frac{c}{d}$$
Now, $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}= \frac{ad}{bc}$$
Division too, is pretty simple. Just write the first fraction as it is, and then flip the second fraction. Once flipped, change the sign from division to multiplication. Now proceed as normal.

Finally, you may have a fraction that can be reduced to a simpler fraction. it's always best to reduce simplest form when you can. Learn more

### Exercises for Multiplying and Dividing Fractions

1) $${2 \over 3} \ \times \ {17 \over 15} =$$

2) $${3 \over 8} \ \times \ {10 \over 16} =$$

3) $${4 \over 6} \ \times \ {18 \over 17} =$$

4) $${7 \over 10} \ \times \ {7 \over 8} =$$

5) $${7 \over 3} \ \times \ {1 \over 5} =$$

6) $${9 \over 7} \ \times \ {6 \over 5} =$$

7) $${10 \over 5} \ \div \ {8 \over 3} =$$

8) $${6 \over 3} \ \div \ {14 \over 18} =$$

9) $${6\over 10} \ \div \ {16 \over 17} =$$

10) $${8\over 7} \ \div \ {15 \over 20} =$$

11) $${2\over 5} \ \div \ {3 \over 2} =$$

12) $${1\over 6} \ \div \ {3 \over 6} =$$

1)$${2 \over 3} \ \times \ {17 \over 15} =$$$$\ \color{red}{{2 \times 17 \over 3\times15} = }$$ $$\color{red}{{34 \over 45}}$$
Solution:
Multiply the top numbers, and then multiply the bottom numbers.
$${2 \over 3} \ \times \ {17 \over 15} =$$$${2 \times 17 \over 3\times15} =$$ $${34 \over 45}$$
2)$${3 \over 8} \ \times \ {10 \over 16} =$$$$\ \color{red}{{3 \times 10 \over 8\times16} = }$$ $$\color{red}{{30 \over 128}}$$$$\color{red}{ = {30 \div 2 \over 128 \div 2} = {15 \over 64}}$$

GCF(30,128) = 2

Solution:
Step1: Multiply the top numbers, and then multiply the bottom numbers.
$${3 \over 8} \ \times \ {10 \over 16} =$$$${3 \times 10 \over 8\times16} =$$ $${30 \over 128}$$
Step 2: Simplify your answer. $${30 \over 128}$$$$= {30 \div 2 \over 128 \div 2} = {15 \over 64}$$
3)$${4 \over 6} \ \times \ {18 \over 17} =$$$$\ \color{red}{{4 \times 18 \over 6\times17} = }$$ $$\color{red}{{72 \over 102}}$$$$\color{red}{ = {72 \div 6 \over 102 \div 6} = {12 \over 17}}$$

GCF(72,102) = 6

Solution:
Step1: Multiply the top numbers, and then multiply the bottom numbers.
$${3 \over 8} \ \times \ {10 \over 16} =$$$${3 \times 10 \over 8\times16} =$$ $${30 \over 128}$$
Step 2: Simplify your answer. $${72 \over 102}$$$$= {72 \div 6 \over 102 \div 6} = {12 \over 17}$$
4)$${7 \over 10} \ \times \ {7 \over 8} =$$$$\ \color{red}{{7 \times 7 \over 10\times8} = }$$ $$\color{red}{{49 \over 80}}$$
Solution:
Step1: Multiply the top numbers, and then multiply the bottom numbers.
$${7 \over 10} \ \times \ {7 \over 8} =$$$${7 \times 7 \over 10\times8} =$$ $${49 \over 80}$$
5)$${7 \over 3} \ \times \ {1 \over 5} =$$$$\ \color{red}{{7 \times 1 \over 3\times5} = }$$ $$\color{red}{{7 \over 5}}$$
Solution:
Step1: Multiply the top numbers, and then multiply the bottom numbers.
$${7 \over 3} \ \times \ {1 \over 5} =$$$${7 \times 1 \over 3\times5} =$$ $${7 \over 5}$$
6)$${9 \over 7} \ \times \ {6 \over 5} =$$$$\ \color{red}{{9 \times 6 \over 7\times5} = }$$ $$\color{red}{{54 \over 35}}$$
Solution:
Step1: Multiply the top numbers, and then multiply the bottom numbers.
$${9 \over 7} \ \times \ {6 \over 5} =$$$${9 \times 6 \over 7\times5} =$$ $${54 \over 35}$$
7)$${10 \over 5} \ \div \ {8 \over 3} =$$$${10 \over 5} \ \times \ {3 \over 8} =$$$$\ \color{red}{{10 \times 3 \over 5\times8} = }$$ $$\color{red}{{30 \over 40}}$$$$\color{red}{ = {30 \div 10 \over 40 \div 10} = {3 \over 4}}$$

GCF(30,40) = 10

Solution:
Step1: Keep first fraction, change division sign to multiplication, and flip the numerator and denominator of the second fraction. Then multiply them.
$${10 \over 5} \ \div \ {8 \over 3} =$$$${10 \over 5} \ \times \ {3 \over 8} =$$$${10 \times 3 \over 5\times8} =$$ $${30 \over 40}$$
Step 2: Simplify your answer.  $${30 \over 40}$$$$= {30 \div 10 \over 40 \div 10} = {3 \over 4}$$
8)$${6 \over 3} \ \div \ {14 \over 18} =$$$${6 \over 3} \ \times \ {18 \over 14} =$$$$\ \color{red}{{6 \times 18 \over 3\times14} = }$$ $$\color{red}{{108 \over 42}}$$$$\color{red}{ = {108 \div 6 \over 42 \div 6} = {18 \over 7}}$$

GCF(108,42) = 6

Solution:
Step1: Keep first fraction, change division sign to multiplication, and flip the numerator and denominator of the second fraction. Then Multiply them:
$${6 \over 3} \ \div \ {14 \over 18} =$$$${6 \over 3} \ \times \ {18 \over 14} =$$$${6 \times 18 \over 3\times14} =$$ $${108 \over 42}$$
Step 2: Simplify your answer.  $${108 \over 42}$$$$= {108 \div 6 \over 42 \div 6} = {18 \over 7}$$
9)$${6\over 10} \ \div \ {16 \over 17} =$$$${6 \over 10} \ \times \ {17 \over 16} =$$$$\ \color{red}{{6 \times 17 \over 10\times 16} = }$$$$\color{red}{{102 \over 160}}$$$$\color{red}{ = {102 \div 2\over 160\div 2} = {51 \over 80}}$$

GCF(102,160) = 2

Solution:
Step1: Keep first fraction, change division sign to multiplication, and flip the numerator and denominator of the second fraction. Then Multiply them:
$${6\over 10} \ \div \ {16 \over 17} =$$$${6 \over 10} \ \times \ {17 \over 16} =$$$${6 \times 17 \over 10\times 16} =$$$${102 \over 160}$$
Step 2: Simplify your answer. $${102 \over 160}$$$$= {102 \div 2\over 160\div 2} = {51 \over 80}$$
10)$${8\over 7} \ \div \ {15 \over 20} =$$$${8 \over 7} \ \times \ {20 \over 15} =$$$$\ \color{red}{{8 \times 20 \over 7\times 15} = }$$$$\color{red}{{160 \over 105}}$$$$\color{red}{ = {160 \div 5\over 105\div 5} = {32 \over 21}}$$

GCF(160,105) = 5

Solution:
Step1: Keep first fraction, change division sign to multiplication, and flip the numerator and denominator of the second fraction. Then Multiply them:
$${8\over 7} \ \div \ {15 \over 20} =$$$${8 \over 7} \ \times \ {20 \over 15} =$$$${8 \times 20 \over 7\times 15= }$$$${160 \over 105}$$
Step 2: Simplify your answer. $${160 \over 105}$$$$= {160 \div 5\over 105\div 5} = {32 \over 21}$$
11)$${2\over 5} \ \div \ {3 \over 2} =$$$${2 \over 5} \ \times \ {2 \over 3} =$$$$\ \color{red}{{2 \times 2 \over 5\times3} = }$$$$\color{red}{{4 \over 15}}$$
Solution:
Step1: Keep first fraction, change division sign to multiplication, and flip the numerator and denominator of the second fraction. Then Multiply them:
$${2\over 5} \ \div \ {3 \over 2} =$$$${2 \over 5} \ \times \ {2 \over 3} =$$$${2 \times 2 \over 5\times3} =$$$${4 \over 15}$$
12)$${1\over 6} \ \div \ {3 \over 6} =$$$${1 \over 6} \ \times \ {6 \over 3} =$$$$\ \color{red}{{1 \times 6 \over 6\times 3} = }$$$$\color{red}{{6 \over 18}}$$$$\color{red}{ = {6 \div 6\over 18\div 6} = {1 \over 3}}$$

GCF(6,18) = 6

Solution:
Step1: Keep first fraction, change division sign to multiplication, and flip the numerator and denominator of the second fraction. Then Multiply them:
$${1\over 6} \ \div \ {3 \over 6} =$$$${1 \over 6} \ \times \ {6 \over 3} =$$$${1 \times 6 \over 6\times 3} =$$$${6 \over 18}$$
Step 2: Simplify your answer. $${6 \over 18}$$$$= {6 \div 6\over 18\div 6} = {1 \over 3}$$

## Multiply and Divide Fractions Quiz

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