Which fraction is larger

Explanation

We will express each fraction as an equivalent fraction that has the LCD for its denominator. Then we will compare their numerators.  We cannot compare the fractions as given. They are not similar objects.

five-sixths is not the same as seven-eighths

Since the smallest number the denominators will divide exactly is 24, the LCD for \(\frac56\) and \(\frac78\) is 24

To build \(\frac56\) and \(\frac78\) so that their denominators are 24, multiply each by a form of 1

\(\frac56 = \frac56 \cdot \frac44\) and \(\frac78 = \frac78 \cdot \frac33\)

Multiply the numerators.  Multiply the denominators.

= \(\frac{20}{24}\) and = \(\frac{21}{24}\)

Next, we compare the numerators.  Since 21 \(>\) 20, it follows that \(\frac{21}{24}\) is greater than \(\frac{20}{24}\), Thus \(\frac78 > \frac56\)