Finding the part

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,

$60\mbox{%}=\frac{60}{100}=\frac{3}{5}=\frac{24}{40}$

Method 4

Put the information in a ratio table and manipulate it to find 60%.

Method 5

Use an equation to find the answer. The word "of" means "multiply".

Method 6

Use a ratio table to set up a proportion. Then cross-multiply.

Notice that all methods lead to the same answer: 24 students have green backpacks.

 


Example 2

In a room of 300 people, 12% of them are left-handed. How many people is this?

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.

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

Make a table and find that you can multiply the left column by 3 to get the right column.

Method 2

Make a table and manipulate the rows until you get 12% in the left column, resulting in 36 in the right column.

Method 3

 

Use an equation to find the part. The word "of" translates to "multiply".

Method 4

 

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]


 

 

 

 

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