Question

maths
compare the following ratios:
3:4 , 5:6 , 3:8​

Answer 1

Answer:

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Comparison of Ratios

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In comparison of ratios, we first need to convert them into like fractions by using the following steps and then compare them.

Step I: Obtain the given ratios.

Step II: Now we express each of the given ratios as a fraction in the simplest form.

Step III: Find the L.C.M (least common multiple) of the denominators of the fractions obtained in the above step (Step II).

Step IV: Obtain the first fraction and its denominator. Divide the L.C.M (least common multiple) obtained in the above step (Step III) by the denominator to get a number z (say).

Now, multiply the numerator and denominator of the fraction by the z (L.C.M). Similarly apply the same procedure to the all other fraction.

In other words convert each fraction to its equivalent fractions with denominator equal to the L.C.M (least common multiple).

Thus, the denominators of all the fractions are be same.

Answer 2

Given: Ratios 3/4, 5/6 and 3/8

To find: Order of these ratios

Solution: Given ratios are 3/4, 5/6 and 3/8

To compare these ratios, first we need to convert these to like fractions.

Converting to like fractions

Step 1: Find L.C.M. of the denominators

L.C.M. of 4, 6 and 8 is 24

Step 2: Multiply the fractions with such numbers so that the resulting denominator becomes 24. The resultant fractions would be equivalent fractions to these fractions. (Equivalent fractions have different numerator and denominator but same in value as of initial fraction)

To find such number, divide the L.C.M. by the denominator

For 3/4, divide 24 by 4. The result is 6.

$\frac{3}{4}$ × $\frac{6}{6}$ = $\frac{18}{24}$

For 5/6, divide 24 by 6. The result is 4.

$\frac{5}{6}$ × $\frac{4}{4}$ = $\frac{20}{24}$

For 3/8, divide 24 by 8. The result is 3.

$\frac{3}{8}$ × $\frac{3}{3}$ = $\frac{9}{24}$

On comparing the fractions

20/24 > 18/24 > 9/24   OR   5/6 > 3/4 > 3/8