Discover Mathematics P4: Term 2, Unit 10, Lessons 9–12
GoalCompare fractions and decimals with denominators 10 and 100 by renaming tenths as hundredths.
New words
like denominators · the same number below the line in both fractionsnumerator · the number above the line; it tells how many parts we haverename · write a number in a different but equal way, such as 3/10 = 30/100
Explanation
To compare fractions, first check the denominators. If they are the same, the fraction with the greater numerator is greater: 58/100 < 60/100. If one fraction has denominator 10 and the other has 100, rename the tenths as hundredths. Ten hundredths make one tenth, so we multiply the top and the bottom by 10: 3/10 = 30/100. Now the denominators match and we compare the numerators. Is 3/10 or 27/100 greater? 3/10 = 30/100 and 30 > 27, so 3/10 > 27/100. To compare a fraction with a decimal, write both as decimals or both as hundredths. Be careful when two fractions have the same numerator: 4/10 is much greater than 4/100, because a tenth is a bigger piece than a hundredth.
Fraction
3/10
27/100
As hundredths
30/100
27/100
As a decimal
0.30
0.27
Worked examples
Compare 3/10 and 27/100. The bars have the same length. 3/10 = 30/100. Compare 30 and 27: 30 > 27, so 3/10 > 27/100.
Number
0.58
6/10
As a decimal
0.58
0.60
As hundredths
58/100
60/100
Compare 0.58 and 6/10. Write 6/10 as a decimal: 6/10 = 0.6 = 0.60. Now 0.60 > 0.58, so 6/10 > 0.58. As hundredths it is 60/100 > 58/100.
Compare 4/10 and 4/100. The numerators are the same but the pieces are different. 4/10 = 40/100, and 40/100 > 4/100. So 4/10 > 4/100. Four tenths is ten times as much as four hundredths.
Class activity
Fraction duel. Make 12 cards with fractions and decimals such as 3/10, 0.35, 28/100, 5/10, 0.45 and 7/100. Each player turns over one card at a time. The player whose number is greater takes both cards. If you disagree, rename both numbers as hundredths and check.
Practice
1
Write <, > or =: 7/10 __ 65/100.
7/10 = 70/100, so 7/10 > 65/100.
2
Write <, > or =: 2/10 __ 30/100.
2/10 = 20/100, so 2/10 < 30/100.
3
Write <, > or =: 0.4 __ 41/100.
0.4 = 40/100, so 0.4 < 41/100.
4
Put 5/10, 49/100 and 0.51 in order from the smallest to the greatest.
As decimals: 0.50, 0.49, 0.51. The order is 49/100, 5/10, 0.51.
5
Karim says 9/100 > 8/10 because 9 is greater than 8. Is he right?
No. 8/10 = 80/100, and 9/100 is much less than 80/100. The denominators must match before we compare the numerators.
