Question

Rafiq exercised 3 by 6 of an hour, while Rohit, exercised for 3/4 of an hour.who exercised for a longer time and by what fraction of an hour.​

Answer 1

Rafiq exercised = 3 / 6 of an hour

Rohit exercised = 3 / 4 of a hour

3 / 6, 3 / 4

Convert these into like fractions

3 / 6 = (3 × 2) / (6 × 2)

= 6 / 12

3 / 4 = (3 × 3) / (4 × 3)

= 9 / 12

Clearly, 9 / 12 > 6 / 12

∴ 3 / 4 > 3 / 6

Therefore Rohit exercised for a longer time than Rafiq

hope it Helps^^

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Answer 2

Question:

Rafiq exercised 3 by 6 of an hour, while Rohit exercised for 3/4 of an hour. Who exercised for a longer time and by what fraction of an hour?

Answer:

Rohit exercised for a longer time by one-fourth of an hour.

Step-by-step explanation:

To compare fractions, we must convert the denominators of the fraction such that they are both equal. To do this, we should simply find the LCM of the two denominators, and then convert both the denominators into their LCM by multiplying a number which will give that answer, and multiplying the same number by the numerator. We can then compare the fractions- the bigger numerator will be the bigger fraction.

STEP 1: To find the LCM of the denominators (Least Common Multiple)

The denominators are 6 and 4.

Multiples of 6 --> 6, 12, 18...

Multiples of 4 --> 4, 8, 12, 16...

As you can see, the highest common multiple is 12.

LCM = 12

STEP 2: To make the denominators equal

$\frac{3}{6 * ? = 12}$ $\frac{3}{4*?=12}$

We can easily figure out that the question marks in the above figures represent 2 and 3 respectively. So, we will multiply that number by the numerator too. The resulting fractions:

$\frac{6}{12}$ _ $\frac{9}{12}$

STEP 3: Comparing

We can easily compare the two fractions now.

$\frac{6}{12}$ < $\frac{9}{12}$

Hence, Rohit exercised for a longer time.

STEP 4: By what fraction of an hour?

To find out what fraction of an hour did Rohit exercise more than Rafiq, we will subtract the first fraction from the second fraction.

$\frac{9}{12}$ - $\frac{6}{12}$ = $\frac{9-6}{12}$ = $\frac{3}{12}$ = $\frac{1}{4}$

Hence, Rohit exercised for a longer time by one-fourth of an hour.

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I hope it helps!