Video and Examples

Learn how to find the part of something when you are given the percent and the whole.

There are 40 kids riding on a bus. 60% of the students have green backpacks. How many students have green backpacks?

 To solve this problem you need to know that the 40 kids represents the 100%, since they are all the kids on the bus. The kids with green backpacks is the "part" of the bus, which is 60%.

There are many ways to solve this problem. Here are a few of the ways in no particular order. Make sure you understand at least a few of the methods.

Method 1

Since 60\mbox{%}=\frac{3}{5}, you can find \frac{3}{5}\,\mbox{ of 40}.

Method 2

40 students can be sorted into 10 groups of 4 students. Each group counts as 10%, so 60% equals 4 x 6.

Method 3

60% can be written as the fraction \frac{3}{5} and \frac{3}{5}=\frac{24}{40}. So,</p>
                <p>60\mbox{%}=\frac{60}{100}=\frac{3}{5}=\frac{24}{40}</p>
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                <p>Method 4</p>
                <p><img alt="" id="_x0000_i1087" src="http://www.mathvillage.info/sites/default/files/Percents/percents_set1/per_files/image063.png" width="156" height="137" border="0"></p>
                <p>Put the information in a ratio table and manipulate it to find 60%.</p>
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                <p>Method 5</p>
                <p><img alt="" id="_x0000_i1085" src="http://www.mathvillage.info/sites/default/files/Percents/percents_set1/per_files/image061.png" width="192" height="89" border="0"></p>
                <p>Use an equation to find the answer. The word "<em><strong>of</strong></em>" means "<em><strong>multiply</strong></em>".</p>
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                <p>Method 6</p>
                <p><img alt="" id="_x0000_i1088" src="http://www.mathvillage.info/sites/default/files/Percents/percents_set1/per_files/image064.jpg" width="122" height="194" border="0"></p>
                <p>Use a ratio table to set up a proportion. Then cross-multiply.</p>
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<p>Notice that all methods lead to the same answer: 24 students have green backpacks.</p>
<p> </p>
<hr>
<table style="" width="527" cellspacing="1" cellpadding="10" border="1">
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                <p><em><img alt="" id="_x0000_i1089" src="http://www.mathvillage.info/sites/default/files/Percents/percents_set1/per_files/image065.png" width="94" height="90" border="0" align="right"></em><strong>Example 2</strong></p>
                <p><em>In a room of 300 people, 12% of them are left-handed. How many people is this?</em></p>
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                <p>The important thing to know about this problem is the 300 people represent the 100%. We are to find the number of people that 12% represents.</p>
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<p>There are many ways to solve this problem. Here are a few of the ways in no particular order. Make sure you understand at least a few of the methods.</p>
<table style="" width="100%" cellspacing="1" cellpadding="10" border="1" align="center">
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                <p>Method 1</p>
                <p><img alt="" src="http://www.mathvillage.info/sites/default/files/Percents/percents_set1/per_files/Partex2a.png" width="150" height="199"></p>
                <p>Make a table and find that you can multiply the left column by 3 to get the right column.</p>
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                <p>Method 2</p>
                <p><img alt="" src="http://www.mathvillage.info/sites/default/files/Percents/percents_set1/per_files/Partex2b.png" width="150" height="186"></p>
                <p>Make a table and manipulate the rows until you get 12% in the left column, resulting in 36 in the right column.</p>
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                <p>Method 3</p>
                <p> <img alt="" src="http://www.mathvillage.info/sites/default/files/Percents/percents_set1/per_files/Partex2c.png" width="150" height="183"></p>
                <p>Use an equation to find the part. The word "of" translates to "multiply".</p>
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                <p>Method 4</p>
                <p> <img alt="" src="http://www.mathvillage.info/sites/default/files/Percents/percents_set1/per_files/Partex2d.png" width="150" height="182"></p>
                <p>Create a proportion using \frac{part}{whole}=\frac{part}{whole}$$.

Method 5

12% is turned into a fraction and then the fraction is renamed to have a denominator of 300.

 


   


 

Self-Check


Question 1

There are 35 people in a room. 20% of those people are left-handed. How many people are right-handed?

 

 

[show answer]

Question 2

James has 150 stamps. 45% of them are in excellent condition. How many stamps is this?

 

 

[show answer]

Question 3

 How much is 8% sales tax for a bicycle that costs $240?

 

[show answer]

 

Last modified: Sunday, 19 April 2020, 10:13 AM