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

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

Problem 13 :

A butcher has four turkey left to sell. The butcher decides to display their weights in fractions of a kilograms

4   3/10  kg, 22/5 kg, 4  1/4 kg, 13/3 kg

Order the turkeys from lightest to heaviest ?

Solution :

4   3/10 = 43/10 ==> 4.3 kg

22/5 =  4.4 kg

4  1/4 ==> 17/4 ==> 4.25 kg

13/3 ==> 4.33 kg

4.25, 4.33, 4.3, 4.4

4  1/4 kg, 13/3 kg, 4  3/10 kg, 22/5 kg

Problem 14 :

A farmer has to deliver two different weights of vegetables. There are 63 bags of carrots weighting 1/4 kg and 39 bags weighing 2/3 kg. Which set of boxes is heavier ?

Solution :

63 bags of carrots of weighting = 1/4 kg

1 bag of carrots of weighting = 1/(4x63)

= (1/252) kg

= 0.0039 kg

39 bags of carrots of weighting = 2/3 kg

1 bag of carrots of weighting = 2/(3x39)

= (2/117) kg

= 0.017 kg

 0.017 kg > 0.0039 kg

39 bags is weighing more.

Problem 14 :

A shop sells three different packs of Christmas cards.

a)  12 cards with 25% extra free $2.99

b)  Eight cards $1.80, 1/5 off marked price.

c) Eight cards $1.96, buy one, get the second half price.

What is the cheapest way to buy 16 chirstmas cards

Solution :

a)  12 cards with 25% extra free $2.99

25% of 12

= (25/100) x 12

= 1/4 x 12

= 3 cards

Cost of 12 + 3 ==> 15 cards ==> 2.99

Cost of 1 card = 2.99/15

= 0.1933

Cost of 16 cards = 16(0.1933)

= 3.0928

b)  Eight cards $1.80, 1/5 off marked price.

Cost of eight cards = 1.80 - 1/5 of 1.80

= 1.80 - (1/5) x 1.80

= 1.80 - 0.36

= 1.44

Cost of 8 cards = 1.44

Cost of 1 card = 1.44/8

= 0.18

Cost of 16 cards = 16(0.18)

= 2.88

c) Eight cards $1.96, buy one, get the second half price.

Eight cards = 1.96

Half of the price = 1.96/2

= 0.98

Cost of 16 cards = 1.96 + 0.98

= 2.94

Option B is the cheapest.