Page 68 - Start Up Mathematics_5

Example 2: Compare 5 and 9 using the LCM method.
7 11
Solution: LCM of 7 and 11 = 77 7 7 , 11

5 = 5 × 11 = 55 11 1 , 11
7 7 × 11 77 1 , 1

9 = 9 × 7 = 63 LCM = 7 × 11 = 77
11 11 × 7 77
55 < 63

So, 5 < 9 .
7 11
Cross-multiplication method

In this method, we do not find the LCM. We cross-multiply to compare the fractions.

Example 3: Compare 8 and 3 by cross-multiplication method.
15 25
3
8
Solution: Step 1: Write the two fractions side by side. 15 25
Step 2: Cross-multiply.
8 3
15 25
8 × 25 = 200 15 × 3 = 45 Remember
Step 3: Compare the first product with the Do not change the order.
second product. Always compare the first

200 > 45 fraction with the second
fraction and not vice versa.
So, 8 > 3 .
15 25

Example 4: Compare 2 and 6 by cross-multiplication method.
7 21

Solution: 2 6
7 21
2 × 21 = 42 7 × 6 = 42
2 × 21 = 7 × 6 = 42

So, 2 = 6 .
7 21

Example 5: Compare 6 and 13 by cross-multiplication method.
11 15

Solution: 6 13
11 15
6 × 15 = 90 11 × 13 = 143
90 < 143

So, 6 < 13 .
11 15

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