Question

Compare the ratios 3:8 and 1
2
.

1. Write ratios as fractions.

3
8
and 1
2

2. Find a common denominator.

2 is a factor of 8, so the common
denominator is 8.

Which comparison correctly compares the ratios 3:8 and 1
2
?

mc001-1.jpg
mc001-2.jpg
mc001-3.jpg

Answer 1

To compare the ratios 3:8 and 1/2, let's follow the steps you've outlined:

1. Write the ratios as fractions:
- The ratio 3:8 can be written as the fraction \( \frac{3}{8} \).
- The ratio 1/2 is already in fraction form.

2. Find a common denominator:
- The fractions are \( \frac{3}{8} \) and \( \frac{1}{2} \).
- The common denominator between 8 and 2 is 8.

Now we convert \( \frac{1}{2} \) to have a denominator of 8:
\[
\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}
\]

3. Now we compare the two fractions:
- \( \frac{3}{8} \) and \( \frac{4}{8} \).

Since \( \frac{3}{8} < \frac{4}{8} \), we can conclude that:
\[
3:8 < 1:2
\]

So, to summarize, the comparison that accurately compares the ratios 3:8 and 1/2 is:
\[
3:8 < 1:2
\]