Compare the following pairs of ratios.

i.ii.

iii. iv.

v.

(i)

Given ratios are

Step I: Make the second term of both the ratios equal.

Multiply and divide first ratio by √7:

Multiply and divide second ratio by 3:

Step II: Compare the first terms (numerators) of the new ratios.

Since the denominators of new ratios are equal, compare the numerators of the new ratios:

Since, 9>√35, therefore .

Therefore the second ratio is greater than the first ratio according to the ratio comparison rules.

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(ii)

Given ratios are

Step I: Make the second term of both the ratios equal.

Multiply and divide first ratio by √5:

Multiply and divide second ratio by √7:

Step II: Compare the first terms (numerators) of the new ratios.

Since the denominators of new ratios are equal, compare the numerators of the new ratios:

Since, 21>15, therefore .

Therefore the second ratio is greater than the first ratio according to the ratio comparison rules.

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(iii)

Given ratios are

Step I: Make the second term of both the ratios equal.

Multiply and divide first ratio by 121:

Multiply and divide second ratio by 18:

Step II: Compare the first terms (numerators) of the new ratios.

Since the denominators of new ratios are equal, compare the numerators of the new ratios:

Since, 605 <306, therefore .

Therefore, the first ratio is greater than the second ratio according to the ratio comparison rules.

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(iv)

Given ratios are

Simplifying the ratios, we get:

Since, the denominators of both the terms are same; compare the first terms (numerators) of the new ratios.

Since the denominators of new ratios are equal, compare the numerators of the new ratios:

Since, √5 = √5, therefore .

Therefore, both the ratios are equal, according to the ratio comparison rules.

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(v)

Given ratios are

Simplifying the ratios, we get:

(Multiply the numerator and denominator of both the ratios by 10)

Step I: Make the second term of both the ratios equal.

Multiply and divide first ratio by 71:

Multiply and divide second ratio by 51:

Step II: Compare the first terms (numerators) of the new ratios.

Since the denominators of new ratios are equal, compare the numerators of the new ratios:

Since, 6532 > 1734, therefore .

Therefore the first ratio is greater than the second ratio according to the ratio comparison rules.

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