Compare the following fractions: rac{3}{8} and rac{11}{12}
Understand the Problem
The question asks to compare two fractions, rac{3}{8} and rac{11}{12}, and determine which is larger, smaller, or if they are equal.
Answer
$\frac{3}{8} < \frac{11}{12}$
Answer for screen readers
$\frac{3}{8} < \frac{11}{12}$
Steps to Solve
- Find a common denominator
To compare $\frac{3}{8}$ and $\frac{11}{12}$, we need to find a common denominator. The least common multiple (LCM) of 8 and 12 is 24.
- Convert both fractions to equivalent fractions with the common denominator
Convert $\frac{3}{8}$ to a fraction with a denominator of 24: $\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}$
Convert $\frac{11}{12}$ to a fraction with a denominator of 24: $\frac{11}{12} = \frac{11 \times 2}{12 \times 2} = \frac{22}{24}$
- Compare the fractions
Now we can easily compare the fractions since they have the same denominator: $\frac{9}{24}$ and $\frac{22}{24}$
Since $9 < 22$, we know that $\frac{9}{24} < \frac{22}{24}$.
- State the relationship between the original fractions
Therefore, $\frac{3}{8} < \frac{11}{12}$.
$\frac{3}{8} < \frac{11}{12}$
More Information
The least common multiple (LCM) is the smallest multiple that two or more numbers have in common. In this case, the LCM of 8 and 12 is 24.
Tips
A common mistake is to directly compare the numerators or denominators without finding a common denominator. This will lead to an incorrect comparison. For example, one might incorrectly assume that $\frac{11}{12}$ is smaller than $\frac{3}{8}$ because $11 < 3$ and $12 < 8$, which is wrong.
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