Is 3/32 smaller than 1/8?
Understand the Problem
The question is asking us to compare two fractions, 3/32 and 1/8, to determine which is smaller. This involves converting the fractions to a common denominator or comparing their decimal equivalents.
Answer
Yes, $ \frac{3}{32} < \frac{1}{8} $.
Answer for screen readers
Yes, $ \frac{3}{32} $ is smaller than $ \frac{1}{8} $.
Steps to Solve
- Convert the fractions to comparable forms
To compare the two fractions, we can find a common denominator. The denominators here are 32 and 8. The least common denominator (LCD) of 32 and 8 is 32.
- Rewrite the fractions with the common denominator
We need to express $1/8$ with a denominator of 32. To do this, we can multiply both the numerator and denominator of $1/8$ by 4:
$$ \frac{1}{8} \times \frac{4}{4} = \frac{4}{32} $$
Now we have:
- $3/32$ remains the same
- $1/8$ is now $4/32$
- Compare the numerators
Now that both fractions are expressed with the same denominator, we can compare their numerators:
- The numerator of $3/32$ is 3
- The numerator of $4/32$ is 4
Since $3 < 4$, it follows that:
$$ \frac{3}{32} < \frac{4}{32} $$
Thus, $3/32$ is smaller than $1/8$.
Yes, $ \frac{3}{32} $ is smaller than $ \frac{1}{8} $.
More Information
Comparing fractions involves finding a common denominator or converting them into decimals. In this case, converting to a common denominator helped us easily see that the fraction with the smaller numerator ($\frac{3}{32}$) is indeed less than $\frac{1}{8}$.
Tips
- Failing to find a common denominator may lead to inaccurate comparisons. Always ensure the fractions have the same denominator before comparing.
- Assuming the fractions are in the same form without checking can lead to incorrect conclusions. Always convert to a common form for comparison.
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