Compare the following fractions: 6/8 and 8/10. Which fraction is greater?
Understand the Problem
The question asks to compare two fractions: 6/8 and 8/10. We need to determine which fraction is greater or if they are equal.
Answer
$\frac{6}{8} < \frac{8}{10}$
Answer for screen readers
$\frac{6}{8} < \frac{8}{10}$
Steps to Solve
- Find a common denominator
To compare the two fractions $\frac{6}{8}$ and $\frac{8}{10}$, we first need to find a common denominator. The least common multiple (LCM) of 8 and 10 is 40.
- Convert both fractions to equivalent fractions with the common denominator
Convert $\frac{6}{8}$ to a fraction with a denominator of 40
$\frac{6}{8} = \frac{6 \times 5}{8 \times 5} = \frac{30}{40}$
Convert $\frac{8}{10}$ to a fraction with a denominator of 40
$\frac{8}{10} = \frac{8 \times 4}{10 \times 4} = \frac{32}{40}$
- Compare the fractions
Now we can compare the two fractions with the same denominator: $\frac{30}{40}$ and $\frac{32}{40}$
Since $30 < 32$, we have $\frac{30}{40} < \frac{32}{40}$.
- Determine the relationship between the original fractions
Therefore, $\frac{6}{8} < \frac{8}{10}$.
$\frac{6}{8} < \frac{8}{10}$
More Information
We can also reduce the fractions before comparing. $\frac{6}{8}$ simplifies to $\frac{3}{4}$, which is $0.75$. $\frac{8}{10}$ simplifies to $\frac{4}{5}$, which is $0.8$. $0.75 < 0.8$, so $\frac{6}{8} < \frac{8}{10}$.
Tips
A common mistake is to try to compare the numerators or denominators directly without finding a common denominator. For example, incorrectly assuming that since 8 > 6 and 10 > 8, then 8/10 must be greater than 6/8. To avoid this, always convert the fractions to equivalent fractions with a common denominator before making the comparison.
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