Multiplying and Dividing Fractions in an easy and fun ways

One of the complicated topic in elementary mathematics is the multiplication and division of  fractions so here are some easy ways on how to multiply and divide fractions!

How to Multiply Fractions With Whole Numbers

STEP 1

Rewrite the whole number as a fraction. To rewrite a whole number as a fraction, simply place the whole number over 1.

• To rewrite 5 as a fraction, just write 5/1. 5 becomes the numerator, while 1 is the denominator; but the value remains the same.

STEP 2

Multiply the numerators of the two fractions. To get the numerator of your answer, you simply have to multiply the numerator of the first fraction with the numerator of the second fraction.

STEP 3

Multiply the denominators of the two fractions. To get the denominator of your answer, you simply have to multiply the denominator of the first fraction with the denominator of the second fraction.

• Multiply the denominators of 5/1 and 8/10 by multiplying 1 * 10. The answer is 10, so your new denominator will be 10.
• After multiplying the numerators and denominators of your fractions, your answer will be in fraction form, with the new numerator over the new denominator. The answer is 40/10.

STEP 4

Simplify. To simplify a fraction, you have to write it in its lowest terms. You can do this by dividing the numerator and denominator by the same factor. In this case, both 40 and 10 are divisible by 10. 40/10 = 4 and 10/10 = 1, so your new answer is 4/1, or just 4.

• If your answer is 4/6, for example, you can simplify the fraction by dividing both the numerator and denominator by 2 to get 2/3.

Here are the the step by step process on how to multiply fractions

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Dividing Fractions

Division of Fractions:

 

Here are some videos about division of fractions:

Understanding division of fractions

dividing 2/5 and 7/3

dividing 3/5 and 1/2

 

Dividing Fractions is Fun!!

One way to make you divide fractions easily is to remember and master the steps by steps process on how to do it so here are some fun ways to do it. 

To help you remember:

♫ “Dividing fractions, as easy as pie,
Flip the second fraction, then multiply.
And don’t forget to simplify,
Before it’s time to say goodbye” ♫

Now that you remember all the steps let us have some exercises to test your skills.

1. How Many?

20 divided by 5 is asking “how many 5s in 20?” (=4) and so:

1/2  ÷  1/6 is really asking: how many 16s in 12 ?

Now look at the pizzas below … how many “1/6th slices” fit into a “1/2 slice”?

How many

in

?

Answer: 3

So now you can see why 1/2  ÷  1/6 = 3

2. 1/8  ÷  1/4

Step 1. Turn the second fraction upside down (the reciprocal):

1/4  becomes  4/1

Step 2. Multiply the first fraction by that reciprocal:

1/8  ×  4/1 = 1 × 4/8 × 1 = 4/8

Step 3. Simplify the fraction:

4/8  =  1/2

Fractions and Whole Numbers
What about division with fractions and whole numbers?

Make the whole number a fraction, by putting it over 1.

Example: 5 is also 5/1
Then continue as before.

Example:
2/3  ÷  5

Make 5 into 511 :

2/3  ÷  5/1

Then continue as before.

Step 1. Turn the second fraction upside down (the reciprocal):

5/1 becomes 1/5

Step 2. Multiply the first fraction by that reciprocal:

2/3 × 1/5 = 2 × 1/3 × 5 = 215

Step 3. Simplify the fraction:

The fraction is already as simple as it can be.

Answer = 2 1/5
Example:
3  ÷  1/4

Make 3 into 3/1 :

31  ÷  1/4

Then continue as before.

Step 1. Turn the second fraction upside down (the reciprocal):

1/4 becomes 4/1

Step 2. Multiply the first fraction by that reciprocal:

3/1 × 4/1 = 3 × 4/1 × 1 = 12/1

Step 3. Simplify the fraction:

12/1 = 12

And Remember …
You can rewrite a question like “20 divided by 5” into “how many 5s in 20″So you can also rewrite “3 divided by ¼” into “how many ¼s in 3” (=12)

Why Turn the Fraction Upside Down?
Because dividing is the opposite of multiplying!

A fraction says to:

•  multiply by the top number
• divide by the bottom number

But for DIVISION we:

divide by the top number
multiply by the bottom number
Example: dividing by 5/2 is the same as multiplying by 2/5

So instead of dividing by a fraction, it is easier to turn that fraction upside down, then do a multiply.

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