Question

David is comparing the fractions 2/3 & 3/5. Which shows the fractions correctly rewritten and compared with the same numerator?

A: 6/9 > 6/10

B: 6/9 > 6/15

C: 10/15 < 9/15

D: 5/6 < 5/7

Answer 1

First off we need to find the least common multiple of 2 and 3, the numerators. That would 6. Next multiply 2/3 by 3/3 so that the numerator can equal 6 and the value of the fraction will not change. Applying the same rule, multiply 3/5 by 2/2. The final fractions should be:

6/9 and 6/10

To figure out which fraction is greater visualize it. A pizza with 10 slices would have more slices, but thinner pieces than a pizza with 9 slices. Therefore, 6 slices from the pizza with 9 slices would be greater than 6 slices from the pizza with 10 slices.

Final answer: A) 6/9 > 6/10
Hope this helps!

Answer 2

Start by getting a common denominator for both the fractions. You can only compare two fractions when they have the same denominator. When they do, the one with the bigger numerator will be bigger.

You have 2/3 and 3/5. 15 will be your lowest common denominator. Multiply 2/3 by 5/5. Multiply 3/5 by 3/3.
$\frac{2}{3} * \frac{5}{5} = \frac{10}{15}$
$\frac{3}{5} * \frac{3}{3} = \frac{9}{15}$

Since 10/15 > 9/15, 2/3 is larger than 3/5.

Now you just have to multiply 2/3 by 3/3 and 3/5 by 2/2 to get a common numerator like the question asks.
$\frac{2}{3} * \frac{3}{3} = \frac{6}{9}$
$\frac{3}{5} * \frac{2}{2} = \frac{6}{10}$

You final answer should be: A) 6/9 > 6/10