USING A GRID TO MODEL PERCENTS

Percent is comparing a number to 100. 

In other words, percent of a number is the ratio between the number and 100.

For example, 13% is equivalent to the following.

13 / 100     (or)     13 to 100     (or)     13 : 100   

Let us see, how to use grids to model percents in the following example. 

The free-throw ratios for three basketball players are shown.

Player 1 :  17/25

Player 2 :  33/50

Player 3 :  14/20

Question (i) :

Rewrite each ratio as a number compared to 100. Then shade the grid to represent the free-throw ratio.

Answer : 

The ratio for player 1 is 17/25.

Since we have to write each ratio as a number compared to 100, we have to make the second quantity 25 in the above ratio as 100 using multiplication. 

Then, we have

17 / 25  =  (17x4) / (25x4)  =  68 / 100

Similarly for player 2, we have 

33 / 50  =  (33x2) / (50x2)  =  66 / 100

For player 3, we have 

14 / 20  =  (14x5) / (20x5)  =  70/100

Therefore, we have

Each grid has been divided into 100 equal parts. 

For player 1, we have to shade 68 parts of the grid to represent 68/100 

For player 2, we have to shade 66 parts of the grid to represent 66/100. 

For player 3, we have to shade 70 parts of the grid to represent 70/100. 

Then, we have

Question (ii) :

Which player has the greatest free-throw ratio ?

Answer : 

When we write the free throw ratios of all three players as a number compared to 100,  we get

Player 1 :  68/100

Player 2 :  66/100

Player 3 :  70/100

In all the above three ratios, the second quantity is same.

Now, we have to compare the first quantities in all the three ratios.

In the third ratio, the first quantity is greater than the first quantity in the first two ratios. 

Player 3 has the greatest free-throw ratio. 

Question (iii) :

Use a percent to describe each player’s free-throw ratio. Write the percents in order from least to greatest.

Answer :

Player 1 :  68/100  =  68 %

Player 2 :  66/100  =  66%

Player 3 :  70/100  =  70%

The percents in order from least to greatest :

66%,  68%,  70%

(Player 2,  Player 1,  Player 3)

Question (iv) :

How did you determine how many squares to shade on each grid ?

Answer :

Write equivalent ratios whose second term is 100.

The first term tells how many squares to shade out of 100.

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