Question

Miguel walked 1/2 mile to the library and then 3/5 mile to the post office.How can he write 1/2 and 3/5 as a pair of fractions with a common denominator?

Answer 1

`(5)/(10)\ miles\ and\ (6)/(10)\ miles`

Explanation:

Given:

The fractions are given as:

`(1)/(2)\ and\ (3)/(5)`

The denominators of the first fraction is 2 and that of the second fraction is 5.

In order to find the common denominator for 2 and 5, we have to find the least common multiple of each of the numbers.

Multiples of 2 = 2, 4, 6, 8, 10, 12,....

Multiples of 5 = 5, 10, 15, 20, 25, 30,....

Therefore, the least common multiple of 2 and 5 is 10. So, the common denominator is 10.

Now, multiply the numerator and denominator of each fraction by the same suitable number such that the denominator becomes 10.

So, for the first fraction, 2 is in the denominator.

So, 2 when multiplied by 5 gives 10.

So, we multiply the numerator and denominator of first fraction by 5. This gives,

`(1)/(2)=(1* 5)/(2* 5)=(5)/(10)`

Now, for the second fraction, 5 is in the denominator.

So, 5 when multiplied by 2 gives 10.

So, we multiply the numerator and denominator of first fraction by 2. This gives,

`(3)/(5)=(3* 2)/(5* 2)=(6)/(10)`

Therefore, the new fractions after making the denominators same are:

`(5)/(10)\ and\ (6)/(10)`

So, the miles covered in fraction with same denominators are:

`(5)/(10)\ miles\ and\ (6)/(10)\ miles`