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

Answer:

$\dfrac{5}{10}\ miles\ and\ \dfrac{6}{10}\ miles$

Step-by-step explanation:

Given:

The fractions are given as:

$\dfrac{1}{2}\ and\ \dfrac{3}{5}$

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,

$\dfrac{1}{2}=\dfrac{1\times 5}{2\times 5}=\dfrac{5}{10}$

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,

$\dfrac{3}{5}=\dfrac{3\times 2}{5\times 2}=\dfrac{6}{10}$

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

$\dfrac{5}{10}\ and\ \dfrac{6}{10}$

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

$\dfrac{5}{10}\ miles\ and\ \dfrac{6}{10}\ miles$