CONNECTING FRACTIONS AND PERCENTS

In this section, we will learn the connection between fractions and percents using models.

We can use a percent bar model to model a ratio expressed as a fraction and to find an equivalent percent.

Problem 1 : 

Use a percent bar model to find an equivalent percent for 1/4 .

Solution :

Draw a model to represent 100 and divide it into fourths.

Shading 1/4, we get

Problem 2 : 

If 1/4 of 100 is 25, what is 1/4 of 100% ?

Solution :

Given : 1/4 of 100  =  25

Then, we have 

1/4 of 100%  =  25%

Problem 3 : 

Tell which operation you can use to find 1/4 of 100. Then find 1/4 of 100%. 

Solution :

In math, always the word "of" is translated to

"Multiplication"

So, we have

1/4 of 100  =  (1/4) x 100  =  25

Since we have 1/4 of 100  =  25, we have

1/4 of 100%  =  25%

Problem 4 : 

Use a percent bar model to find an equivalent percent for 1/3 .

Solution :

Draw a model to represent 100 and divide it into thirds.

Shading 1/3, we get

Problem 5 : 

Tell which operation you can use to find 1/3 of 100. Then find 1/3 of 100%. 

Solution :

In math, always the word "of" is translated to

"Multiplication"

So, we have

1/3 of 100  =  (1/3) x 100  =  100/3  =  33 1/3

Since we have 1/3 of 100  =  33 1/3, we have

1/3 of 100%  =  33 1/3%

Problem 6 : 

Jo says she can find the percent equivalent of 3/4 by multiplying the percent equivalent of 1/4 by 3. How can we use a percent bar model to support this claim?

Solution :

Shade three 1/4 sections to show 3/4. 

Since 1/4  =  25%, we have

3/4  =  3 x 25%  =  75%

That is

Problem 7 : 

Tell which operation you can use to share $120 equally among four people. Find the percentage of $120 that each person gets. 

Solution :

If we want share a quantity into equal parts, we always have to use the operation

"Division"

Since we share $120 equally among four people, we have to divide $120 by 4. 

 $120 ÷ 4  =  $30

Percentage of $120 that each person gets is 

=  (30/120) x 100%

=  25%

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