Question
Find equivalent fractions to compare. Then, write \( >,< \), or \( = \). \( \begin{array}{l}\frac{1}{5} ? \frac{3}{8} \\ \quad< \\ =\end{array} \)
Ask by Olson Willis. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{1}{5} < \frac{3}{8} \)
Solution
To compare 1/5 and 3/8, we can use equivalent fractions with a common denominator.
Step 1: Find a common denominator.
A common denominator for 5 and 8 is 40.
Step 2: Convert each fraction to an equivalent fraction with denominator 40.
– For 1/5, multiply both numerator and denominator by 8:
1/5 = (1×8)/(5×8) = 8/40.
– For 3/8, multiply both numerator and denominator by 5:
3/8 = (3×5)/(8×5) = 15/40.
Step 3: Compare the fractions.
Since 8/40 < 15/40, we have
1/5 < 3/8.
The final answer is: 1/5 < 3/8.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Bonus Knowledge
To compare \( \frac{1}{5} \) and \( \frac{3}{8} \), we can find a common denominator. The least common multiple of 5 and 8 is 40. Convert \( \frac{1}{5} \): \[ \frac{1 \times 8}{5 \times 8} = \frac{8}{40} \] Convert \( \frac{3}{8} \): \[ \frac{3 \times 5}{8 \times 5} = \frac{15}{40} \] Now, we can compare \( \frac{8}{40} \) and \( \frac{15}{40} \). Since 8 is less than 15, we can say: \[ \frac{1}{5} < \frac{3}{8} \] So the answer is: \( \frac{1}{5} < \frac{3}{8} \)