Compare the fractions 7/8 and 1/6.
Understand the Problem
The question is asking us to compare two fractions, 7/8 and 1/6, and determine which is larger or if they are equal. We need to place the correct inequality symbol (>, <, or =) in the circle between them.
Answer
$\frac{7}{8} > \frac{1}{6}$
Answer for screen readers
$\frac{7}{8} > \frac{1}{6}$
Steps to Solve
- Find a common denominator
To compare the fractions $\frac{7}{8}$ and $\frac{1}{6}$, we need to find a common denominator. The least common multiple (LCM) of 8 and 6 is 24.
- Convert each fraction to an equivalent fraction with the common denominator
Convert $\frac{7}{8}$ to have a denominator of 24: $\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}$
Convert $\frac{1}{6}$ to have a denominator of 24: $\frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24}$
- Compare the fractions
Now we can compare $\frac{21}{24}$ and $\frac{4}{24}$. Since $21 > 4$, we know that $\frac{21}{24} > \frac{4}{24}$.
- Write the inequality
Therefore, $\frac{7}{8} > \frac{1}{6}$.
$\frac{7}{8} > \frac{1}{6}$
More Information
The fraction $\frac{7}{8}$ is much larger than $\frac{1}{6}$. $\frac{7}{8}$ is close to 1, while $\frac{1}{6}$ is much smaller than 1.
Tips
A common mistake is to compare the denominators directly, assuming that a larger denominator always means a larger fraction, without considering the numerators. Another mistake is to make an error when finding the least common multiple or converting the fractions.
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