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
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.
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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