Question

Find a common denominator:
Determine which fraction is larger: start fraction, 3, divided by, 8, end fraction
8
3
​
or one fifth
5
1
​

Answer 1

To compare the fractions \(\frac{3}{8}\) and \(\frac{1}{5}\), we need to find a common denominator.

The denominators are 8 and 5. The least common multiple (LCM) of 8 and 5 can be found as follows:

- The multiples of 8 are: 8, 16, 24, 32, 40, ...
- The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, ...

The smallest common multiple is 40.

Now, we will convert each fraction to have a denominator of 40.

1. For \(\frac{3}{8}\):
\[
\frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40}
\]

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

Now we compare \(\frac{15}{40}\) and \(\frac{8}{40}\).

Since \(15 > 8\), we see that:

\[
\frac{3}{8} > \frac{1}{5}
\]

Thus, \(\frac{3}{8}\) is the larger fraction.