In comparing ratios we will learn how to arrange the ratios.
How to Compare Ratios?
To compare two ratios, follow these steps:
Step I: Make the second term of both the ratios equal.
For this, determine the LCM of the second terms of the ratios. Divide the LCM by the second term of each ratio. Multiply the numerator and the denominator of each ratio by the quotient.
Step II: Compare the first terms (numerators) of the new ratios.
1. Which of the following ratios is grater?
Compare the ratios 3 : 4 and 1 : 2.
LCM of the second terms, i.e., 4 and 2 = 4
Now, dividing the LCM by the second term of each ratio, we get 4 ÷ 4 = 1, and 4 ÷ 2 = 2
Therefore, 34 = 3∗14∗1 = 34
12 = 1∗22∗2 = 24
As 3 > 2, 34 > 24, i.e., 3 : 4 > 1 : 2
Therefore the ratio 3:4 is greater than the ratio 1:2 according to the ratio comparison rules.
2. Which of the following ratios is grater?
Compare the ratios 3 : 5 and 2 : 11.
LCM of the second terms, i.e., 5 and 11 = 55
Now, dividing the LCM by the second term of each ratio, we get 55 ÷ 5 = 11, and 55 ÷ 11 = 5
Therefore, 35 = 3∗115∗11 = 3355
211 = 2∗511∗5 = 1055
As 33 > 10, 35 > 211, i.e., 3 : 5 > 2 : 11.
Therefore the ratio 3 : 5 is greater than the ratio 2 : 11 according to the ratio comparison rules.
To compare two or more given ratios, follow the steps given below:
Step I: Write each one of the given ratios in the form of a fraction in the simplest form.
Step II: Convert these fractions into like fractions and then compare.
3. Compare the ratios 4 : 7 and 5 : 8.
Solution:
4 : 7 = 47 and 5 : 8 = 58
LCM of 7 and 8 is 56.
47 = 4×87×8 = 3256 and 58 = 5×78×7 = 3556
Clearly, 3556 > 3256
⟹ 58 > 47
⟹ 5 : 8 > 4 : 7
Hence, 5 : 8 > 4 : 7
4. Write the following ratios in ascending order 4 : 3, 7 : 10, 4 : 7.
Solution:
4 : 3 = 43; 7 : 10 = 710 and 4 : 7 = 47.
LCM of 3, 7 and 10 = 210
43 = 4×703×70 = 280210
710 = 7×2110×21 = 147210
47 = 4×307×30 = 120210
Now 120210 < 147210 < 280210
⟹ 47 < 710 < 43
⟹ 4 : 7 < 7 : 10 < 4 : 3
Hence, 4 : 7 < 7 : 10 < 4 : 3
1. Which of the following ratio is larger?
(i) 3 : 4 or 9 : 16
(ii) 15 : 16 or 24 : 25
(iii) 4 : 7 or 5 : 8
(iv) 9 : 20 or 8 : 13
(v) 1 : 2 or 13 : 27
Answer:
1. (i) 3 : 4 > 9 : 16
(ii) 15 : 16 < 24 : 25
(iii) 4 : 7 < 5 : 8
(iv) 9 : 20 < 8 : 13
(v) 1 : 2 > 13 : 27
● Ratio and proportion
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