1.3.1 COMPARISON OF FRACTIONS
Comparing Fractions
Comparing fractions means determining the larger and the smaller fraction between any two or more fractions.
Comparing Fractions with Same Denominators
When denominators are the same, the fraction with the larger numerator is greater. If both numerator and denominator are equal, the fractions are equal.
Example 1.11
Arrange the following fractions in ascending order:
49,
79,
29,
89
Solution: Ascending order:
29,
49,
79,
89
Comparing Fractions with Unlike Denominators
(I) Using LCM: Convert fractions to like denominators using LCM.
Example 1.12
Which is larger between
47 and
59?
Solution:
LCM of 7 and 9 = 63
4×9=3663 and
5×7=3563
36/63 > 35/63, so 47 is larger.
(II) Using Decimals: Convert fractions to decimals and compare.
Example 1.13
Arrange in descending order:
67,
811,
913,
1115
Solution (decimals):
6/7 = 0.8571, 8/11 = 0.7272, 9/13 = 0.6923, 11/15 = 0.7333
Descending order: 6/7, 11/15, 8/11, 9/13
(III) Using Cross-Multiplication
Example 1.14
Which is larger:
47 or
59?
Cross multiply: 4×9 = 36, 5×7 = 35 → 36 > 35 → 4/7 is larger.
Fraction Battle!
Click the fraction that is larger:
Exercise 1.8 – Comparing Fractions
1. Arrange the following fractions in descending order
(a)
47,
611,
34,
914
LCM method: Denominators 7,11,4,14 → LCM=308
4/7=176/308, 6/11=168/308, 3/4=231/308, 9/14=198/308
Descending order: 3/4, 9/14, 4/7, 6/11
(b)
56,
79,
23,
67
Cross-multiplication method:
5/6 vs 7/9 → 45>42 → 5/6>7/9
5/6 vs 2/3 → 15>12 → 5/6>2/3
5/6 vs 6/7 → 35<36 → 6/7>5/6
6/7 vs 7/9 → 54>49 → 6/7>7/9
7/9 vs 2/3 → 21>18 → 7/9>2/3
Descending order: 6/7, 5/6, 7/9, 2/3
(c)
911,
89,
56,
78
Decimal method:
9/11≈0.818, 8/9≈0.888, 5/6≈0.833, 7/8=0.875
Descending order: 8/9, 7/8, 5/6, 9/11
(d)
37,
511,
613,
917
LCM method: Denominators 7,11,13,17 → LCM=17017
3/7=7307/17017, 5/11=7735/17017, 6/13=7854/17017, 9/17=9009/17017
Descending order: 9/17, 6/13, 5/11, 3/7
2. Arrange the following fractions in ascending order
(a)
23,
67,
58
Cross-multiplication:
2/3 vs 6/7 → 14<18 → 2/3<6/7
2/3 vs 5/8 → 16>15 → 2/3>5/8
Ascending order: 5/8, 2/3, 6/7
(b)
47,
23,
58
LCM method: Denominators 7,3,8 → LCM=168
4/7=96/168, 2/3=112/168, 5/8=105/168
Ascending order: 4/7, 5/8, 2/3
(c)
35,
23,
56
Decimal method:
3/5=0.6, 2/3≈0.6667, 5/6≈0.8333
Ascending order: 3/5, 2/3, 5/6
(d)
25,
13,
58
Cross-multiplication:
2/5 vs 1/3 → 6>5 → 2/5>1/3
2/5 vs 5/8 → 16<25 → 2/5<5/8
Ascending order: 1/3, 2/5, 5/8