Question

Which fraction is greater than 1/2 and less than 3/4 ?
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Answer 1

Answer:

a. $\frac{2}{3}$

Step-by-step explanation:

The fraction, $\frac{2}{3}$ is greater than $\frac{1}{2}$ and less than $\frac{3}{4}$.

How do we know this? See below how the fractions are compared together.

First, compare $\frac{2}{3}$ and $\frac{1}{2}$.

Find a common denominator for both fractions:

Common denominator of 2 and 3 would be 6. Therefore, multiply as follows:

$\frac{2 \times 2}{3 \times 2} = \frac{4}{6}$ and

$\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$.

Compare the numerators. Which one is greater?

Form the calculation above:

$\frac{2}{3} = \frac{4}{6}$ has a numerator of 4.

.

$\frac{1}{2} = \frac{3}{6}$ has a numerator of 3.

Since 4 is greater than 3, therefore, the fraction, $\frac{2}{3}$ is greater than $\frac{1}{2}$.

✍️Compare $\frac{2}{3}$ and $\frac{3}{4}$.

Find a common denominator for both fractions

$\frac{2 \times 4}{3 \times 4} = \frac{8}{12}$ and

$\frac{3 \times 3}{4 \times 3} = \frac{9}{12}$

Comparing their numerator, 8 is less than 9, therefore:

$\frac{2}{3}$ is less than $\frac{3}{4}$.

✔️We can conclude that:

$\frac{2}{3}$ is greater than $\frac{1}{2}$, and less than $\frac{3}{4}$.