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Multiplying Fractions with Whole Numbers

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    Common Core
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CCSS.Math.Content.4.NF.B.4CCSS.Math.Content.5.NF.B.4

Multiplying fractions with whole numbers is much easier than adding fractions.

Let us learn this by following examples :

Example 1

 

If we have four children and each has two cookies, how many cookies are there in all?

1

If we multiply 4 x 2, we find that there are 8 cookies total.

But what if we have four children and each has
2
3
of a cookie? How many cookies are there in all?
 
Just like with whole numbers, we can use multiplication to solve a problem like this.

Multiply the numerator by the whole number, and leave the denominator the same.

We need to multiply 4 x
2
3
First, multiply the numerator by the whole number.

That's your new numerator!

4 x 2 = 8

Remember, the denominator stays the same, so our answer is:

 
8
3

Since the numerator is larger than the denominator, you can tell that this fraction is bigger than one.

You can restate it as 2
2
3
.
 

Here is how we did it. To change an improper fraction to a mixed number, you must divide the numerator by the denominator. Then, the mixed number takes the following form :

  • The answer becomes the whole number
  • The remainder becomes the numerator
  • The denominator stays the same

3

Example 2

 
There are three bowls of soup on a table. Each bowl is
1
5
full. How much soup is there in total?
 

2

We need to multiply 3 x
1
5
.
 
 
3 x 1
5
=
3
5
 
There is
3
5
of a bowl soup in total.
Summary
  • Fractions represent parts of whole numbers
  • Numerator (number on top) represents how many parts of the whole you have
  • Denominator (number on the bottom) represents how many equal parts the whole is divided into.
  • Multiplying Fractions by a Whole Number: Multiply the numerator by the whole number, and leave the denominator the same.

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