Which sign makes the statement true? 1/5 5/16

1 answer

It seems like you're trying to compare the two fractions \( \frac{1}{5} \) and \( \frac{5}{16} \) to determine which is greater or if they are equal.

To compare the two fractions, you can convert them to a common denominator or convert them to decimal form.

  1. Finding a common denominator:
    • The least common multiple of 5 and 16 is 80.
    • Convert \( \frac{1}{5} \) to have a denominator of 80: \[ \frac{1}{5} = \frac{1 \times 16}{5 \times 16} = \frac{16}{80} \]
    • Convert \( \frac{5}{16} \) to have a denominator of 80: \[ \frac{5}{16} = \frac{5 \times 5}{16 \times 5} = \frac{25}{80} \]

Now we can compare \( \frac{16}{80} \) and \( \frac{25}{80} \). Since 16 is less than 25, we have: \[ \frac{1}{5} < \frac{5}{16} \]

  1. Converting to decimal:
    • \( \frac{1}{5} = 0.2 \)
    • \( \frac{5}{16} \approx 0.3125 \)

Again, it is clear that \( 0.2 < 0.3125 \).

Thus, the correct statement is: \[ \frac{1}{5} < \frac{5}{16} \]