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Which fraction is bigger, [tex]\frac{7}{8}[/tex] or [tex]\frac{14}{15}[/tex]? Use the least common multiple (LCM) to compare them.

Answer :

Final answer:

To compare 7/8 and 14/15 using the LCM, both fractions are converted to have a common denominator of 120. The equivalent fractions are 105/120 and 112/120, respectively. Since 112/120 is greater than 105/120, the fraction 14/15 is larger than 7/8.

Explanation:

To compare the fractions 7/8 and 14/15 using the least common multiple (LCM), we first need to find the LCM of their denominators, which are 8 and 15. The LCM of 8 and 15 is 120, as it is the smallest number that both 8 and 15 can divide into without leaving a remainder.

Next, we convert each fraction to an equivalent fraction with a denominator of 120. To convert 7/8, we multiply the numerator and denominator by 15 (since 120 ÷ 8 = 15), which gives us 105/120. Similarly, to convert 14/15, we multiply the numerator and denominator by 8 (since 120 ÷ 15 = 8), resulting in 112/120.

Now that both fractions have the same denominator, we can easily compare the numerators to determine which fraction is larger. Because 112/120 (from 14/15) is greater than 105/120 (from 7/8), 14/15 is the larger fraction.

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