Is 7/8 greater than 5/6?

Understand the Problem

The question is asking to compare the fractions 7/8 and 5/6 to determine which one is greater.

Answer

$ \frac{7}{8} > \frac{5}{6} $

Steps to Solve

Find a common denominator To compare the fractions $ \frac{7}{8} $ and $ \frac{5}{6} $, we need to find a common denominator. The least common multiple (LCM) of the denominators 8 and 6 is 24.
Convert fractions to have the same denominator Now, we convert each fraction to have the common denominator of 24:

For $ \frac{7}{8} $: $$ \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} $$

For $ \frac{5}{6} $: $$ \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} $$

Compare the converted fractions Now we compare the two fractions: $$ \frac{21}{24} \text{ and } \frac{20}{24} $$

Since $ 21 > 20 $, we can conclude that $ \frac{7}{8} > \frac{5}{6} $.

The fraction $ \frac{7}{8} $ is greater than $ \frac{5}{6} $.

More Information

In this comparison, we used the least common multiple to create equivalent fractions. It’s a useful technique for comparing fractions with different denominators.

Tips

A common mistake is forgetting to find a common denominator before comparing fractions.
Another mistake is incorrectly multiplying to convert fractions. Always double-check your multiplication.

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