# COMPARE FRACTIONS AND DECIMALS

To compare two quantities, they should be in the same kind.

Fraction with another fraction can be compared easily. Decimal with another decimal can be compared easily.

If we want to compare fraction and decimal, first let us check whether it is simple to make the fraction as decimal without performing long division.

If we have 10, 100, 1000, ....... at the denominator, we can simply change it as decimal.

Some times it will be very simple to convert fraction as decimal by making the denominator as multiple of 10's.

For example,

Problem 1 :

1/4 __ 0.4

Solution :

1/4 = 0.25

Comparing the decimals,

0.25 < 0.4

Substitute the corresponding original fraction

1/4 < 0.4

1/4 is lesser than 0.4

## Converting as 10's, 100's ....etc

To make it as multiple of 10.

4 x 25 = 100

8 x 125 = 1000

5 x 2 =10

To convert the decimal as fraction, we have to observe that the number of digits after the decimal.

• If we have one digit after the decimal, we have to multiply it by (10/10)
• If we have two digits after the decimal, we have to multiply it by (100/100)

In the following exercises, order each pair of numbers, using < or >.

Problem 2 :

1/8 __ 0.8

Solution :

It is hard to convert 8 as a multiple of 10. Doing long division, we get

1/8 = 0.125

Compare the decimals

0.125 < 0.8

Substitute the corresponding original fraction

1/8 < 0.8

1/8 is less than 0.8

Problem 3 :

2/5 __ 0.25

Solution :

2/5 = 0.4

Compare the decimals

0.4 > 0.25

Substitute the corresponding original fraction

2/5 > 0.25

2/5 is greater than 0.25

Problem 4 :

3/5 __ 0.35

Solution :

(3/5) ⋅ (20/20) = 60/100 = 0.6

Comparing the decimals

0.6 > 0.35

Substitute the corresponding original fraction

3/5 > 0.35

3/5 is greater than 0.35

Problem 5 :

0.725 __ 3/4

Solution  :

3/4

Converting 4 as 100, we have to multiply and divide 3/4 by 25.

= 0.75

Compare the decimals

0.725 < 0.75

Substitute the corresponding original fraction

0.725 < 3/4

0.725 is less than 3/4

Problem 6 :

0.92 __ 7/8

Solution :

Let us change 7/8 to a decimal.

7/8 = 0.875

Compare the decimals

0.92 > 0.875

Substitute the corresponding original fraction

0.92 > 7/8

0.92 is greater than 7/8

Problem 7 :

0.66 __ 2/3

Solution :

Doing long division, we can convert 2/3 as decimal.

2/3 = 0.667

Compare the decimals

0.66 < 0.667

Substitute the corresponding original fraction

0.66 < 2/3

0.66 is less than 2/3

Problem 8 :

0.83 __ 5/6

Solution :

Let us change 5/6 to a decimal.

5/6 = 0.833

Compare the decimals

0.83 < 0.833

Substitute the corresponding original fraction

0.83 < 5/6

0.83 is less than 5/6

Problem 9 :

-0.75 __ -4/5

Solution :

Let us change -4/5 to a decimal.

(-4/5) ⋅ (20/20) = -80/100 ==> -0.8

Compare the decimals

-0.75 > -0.8

Substitute the corresponding original fraction

-0.75 > -4/5

-0.75 is greater than -4/5

Problem 10 :

-0.44 __ -9/20

Solution :

Let us change -9/20 to a decimal.

-9/20 = -0.45

Compare the decimals

-0.44 > - 0.45

Substitute the corresponding original fraction

- 0.44 > - 9/20

- 0.44 is greater than - 9/20

Problem 11 :

-3/4 __ - 0.925

Solution :

Let us change -3/4 to a decimal.

(-3/4) ⋅ (25/25) = -75/100 = - 0.75

Compare the decimals

-0.75 > - 0.925

Substitute the corresponding original fraction

- 3/4 > - 0.925

- 3/4 is greater than - 0.925

Problem 12 :

-2/3 __ - 0.632

Solution :

Let us change -2/3 to a decimal.

-2/3 = - 0.66

Compare the decimals

-0.66 < - 0.632

Substitute the corresponding original fraction

- 2/3 < - 0.632

- 2/3 is less than - 0.632

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