Determine which fraction is larger: start fraction, 4, divided by, 5, end fraction

Question

5
4
​
or start fraction, 5, divided by, 8, end fraction
8
5
​
Find a common denominator:

Answer 1

To compare the two fractions \( \frac{4}{5} \) and \( \frac{5}{8} \), we can find a common denominator.

The denominators are 5 and 8. The least common multiple (LCM) of 5 and 8 is 40.

Next, we will convert each fraction to have this common denominator of 40:

1. For \( \frac{4}{5} \): \[ \frac{4}{5} = \frac{4 \times 8}{5 \times 8} = \frac{32}{40} \]

2. For \( \frac{5}{8} \): \[ \frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40} \]

Now we can compare the two fractions \( \frac{32}{40} \) and \( \frac{25}{40} \).

Since \( 32 > 25 \), it follows that: \[ \frac{32}{40} > \frac{25}{40} \]

Therefore: \[ \frac{4}{5} > \frac{5}{8} \]

So, the larger fraction is \( \frac{4}{5} \).