Multiplying Fractions

• Math

Multiplying Fractions

Today we will learn how to multiply two or more fractions.

Multiplying fractions can be divided into 3 steps

1. Multiply the numerators
2. Multiply the denominators
3. Simply the new fraction
   

Multiplying fractions can be divided into 3 steps

1. Multiply the numerators
2. Multiply the denominators
3. Simply the new fraction
   

Unlike adding or subtracting fractions, we do not have to find a common denominator when multiplying.

Let's look at an example.

   Solve :

Step 1. Multiply the numerators

​3​​1​​⋅​4​​3​​

What part of the fraction is the numerator?

Step 1. Multiply the numerators

Solve:

Our numerators are 3 and 1.

So, we have:

​3​​1​​⋅​4​​3​​

1⋅3=3

​3​​1​​⋅​4​​3​​=​[?]​​3​​

Step 2. Multiply the denominators

Solve:

Our denominators are 3 and 4.

​3​​1​​⋅​4​​3​​

What is 3 4?

⋅

1. 20
2. 16
3. 12
4. 17

Step 2. Multiply the denominators

Solve:

Our denominators are 4 and 4.

So now we have the fraction:

​3​​1​​⋅​4​​3​​

3⋅4=12

​3​​1​​⋅​4​​3​​=​12​​3​​

Solve:

Step 1. Multiply the numerators:

Step 2. Multiply the denominators:

This gives us the fractions:

​3​​1​​⋅​4​​3​​

1⋅3=3

3⋅4=12

​12​​3​​

Step 3. Simply the new fraction

To simplify          we need to find the largest common factor of 3 and 12.

​12​​3​​

What is the largest common factor of 3 and 12?

1. 1
2. 3
3. 36
4. No common factors

Factors of 3

Factors of 12

1

2

3

1

3

4

6

12

7

9

8

Step 3. Simply the new fraction

To simplify         we must find the largest common factor of 3 and 12.

Their largest common factor is 3:                       and

This gives us the fraction

​12​​3​​

3÷3=1

12÷3=4

​4​​1​​

So this means that

Let's review:
Step 1. Multiply the numerators:  

Step 2. Multiply the denominators:

Step 3. Simply the new fraction: 

​3​​1​​⋅​4​​3​​=​4​​1​​

1⋅3=3

3⋅4=12

​12​​3​​÷3=​4​​1​​

Solve:

​3​​2​​⋅​6​​2​​

1. ​18​​8​​
2. ​9​​4​​
3. ​12​​1​​
4. ​9​​2​​

Now let's solve it together!

Step 1: Multiply the numerators:

Step 2: Multiply the denominators:

Step 3: Simply the new fraction: 

​3​​2​​⋅​6​​2​​

2⋅2=4

3⋅6=18

​18​​4​​

Step 3. Simplify the new fraction:

Let's list the factors of 4 and 18

• Factors of 4: 1, 2, 4

• Factors of 18: 1, 2, 3, 6, 9, 18
  

There largest common factor is: 2 2

​18​​4​​

Step 3: Simply the new fraction:

Now we divide 4 and 18 by 2:

​18​​4​​

4÷2=2

18÷2=?

Step 3: Simply the new fraction:

Now we divide 4 and 18 by 2:

                          and

This gives us:

So,

​18​​4​​

4÷2=2

18÷2=9

​9​​2​​

​3​​2​​⋅​6​​2​​=​9​​2​​