MODELING DECIMALS

Using models can help us to understand how decimals, fractions, and percent are related.

Example 1 :

Model 0.78 by shading a 10-by-10 grid.

Solution :

Since there are two digits after the decimal point in 0.78, we can write 0.78 as a fraction 78/100.

0.78 = 78/100

0.78 = 78%

0.78 = 78 out of a hundred

In 10 by- 10 grid, there will be 100 equal parts.

Because 10 x 10 = 100.

Since 0.78 = 78 out of a hundred, we have to shade 78 out 100 parts in 10 by- 10 grid to model the decimal 0.78.

Example 2 :

Model 1.42 by shading a 10-by-10 grid.

Solution :

There are two digits after the decimal point in 1.42. So, we can write 1.42 as a fraction 142/100.

Here, the numerator 142 is greater than 100.

Since we are going to use 10 by 10- grid (100 equal parts), we can write the given decimal 1.42 as given below.

In 1.42 = 1 42/100 or 1 + 42/100, there are two parts.

They are 1 and 42/100.

So, we have to use two 10 by-10 grids to model the decimal 1.42.

Since we write 1.42 = 100/100 + 42/100, we have to shade all the 100 parts in the first grid and 42 parts in the second grid.

Example 3 :

Model 0.53 by shading a 10-by-10 grid.

Solution :

Since there are two digits after the decimal point in 0.53, we can write 0.53 as a fraction 53/100.

0.53 = 53/100 = 53%

0.53 = 53 out of a hundred

In 10-by- 10 grid, there will be 100 equal parts.

Because 10 x 10  = 100.

Since 0.53  =  53 out of a hundred, we have to shade 53 out 100 parts in 10 by- 10 grid to model the decimal 0.53.

That is,

Example 4 :

Model 1.07 by shading a 10-by-10 grid.

Solution :

There are two digits after the decimal point in 1.07. So, we can write 1.07 as a fraction 107/100.

Here, the numerator 107 is greater than 100.

Since we are going to use 10 by 10- grid (100 equal parts), we can write the given decimal 1.07 as given below.

1.07 = 1 + 0.07

1.07 = 100/100 + 7/100 = 1 7/100

In 1.07 = 1 7/100 or 1 + 7/100, there are two parts.

They are 1 and 7/100.

So, we have to use two 10 by-10 grids to model the decimal 1.07.

Since we write 1.07  =  100/100 + 7/100, we have to shade all the 100 parts in the first grid and 7 parts in the second grid.

Example 5 :

Model 125% by shading a 10-by-10 grid.

Solution : 

Percent means per hundred.

125% = 125/100

Here, the numerator 125 is greater than 100.

Since we are going to use 10 by 10- grid (100 equal parts), we can write 125% as given below.

125% = 1 + 25/100

Therefore, there are two parts in 125%.

They are 1 and 25/100.

So, we have to use two 10 by-10 grids to model 125%.

Since we write 125% = 100/100 + 25/100, we have to shade all the 100 parts in the first grid and 25 parts in the second grid.

Write the decimal and the fraction of each shaded part.

Example 6 :

Solution :

We have 2 wholes and 6 tenths. So, the decimal represented by the grid is 2.6

Converting it as fraction, out of 100 parts 26 grids has been shaded. Then the fraction is 26/100.

Example 7 :

Solution :

We have 4 wholes and there is no tenths. So, the decimal represented by the grid is 4

Converting it as fraction, 4/1.

Example 8 :

Solution :

We have 4 wholes and 5 tenths. So, the decimal represented by the grid is 4.5

Converting it as fraction, out of 100 parts 45 grids has been shaded. Then the fraction is 45/100. 45 tenths are here.

Example 9 :

Solution :

We have 4 wholes and there is no tenths. So, the decimal represented by the grid is 4

Converting it as fraction, out of 10 parts 4 grids has been shaded. Then the fraction is 4/10.

Example 10 :

Solution :

We have 6 wholes and there is 7 tenths. So, the decimal represented by the grid is 6.7

Converting it as fraction, out of 100 parts 67 grids has been shaded. Then the fraction is 67/100.

Example 11 :

Solution :

We have 3 wholes and there is 2 tenths. So, the decimal represented by the grid is 3.2

Converting it as fraction, out of 100 parts 32 grids has been shaded. Then the fraction is 32/100.

Subtract by crossing out the correct number of boxes. Give the answer as a fraction.

Example 12 :

50/100 - 30/100

Solution :

Given that, 50/100 - 30/100

Eliminating the 30 grids out of 50 grids, we get 20 grids.

Example 13 :

38/100 - 12/100

Solution :

Given that, 38/100 - 12/100

Eliminating the 38 grids out of 12 grids, we get 26 grids.

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