Question
Find equivalent fractions to compare. Then, write \( >,< \), or \( = \). \( \frac{3}{5} ? \frac{5}{10} \) \( \frac{3}{5} \frac{5}{10} \)
Ask by Stuart Newton. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{3}{5} > \frac{5}{10} \)
Solution
To compare 3/5 and 5/10, first find equivalent fractions with a common denominator. One easy way is to convert both fractions to tenths.
• Convert 3/5 to an equivalent fraction with denominator 10:
Multiply the numerator and denominator by 2:
3/5 = (3×2)/(5×2) = 6/10
• Notice that 5/10 is already in tenths.
Now compare 6/10 and 5/10. Since 6 is greater than 5, we have:
6/10 > 5/10
Therefore, 3/5 > 5/10.
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Simplify this solution The Deep Dive
To compare the fractions \( \frac{3}{5} \) and \( \frac{5}{10} \), we can convert \( \frac{5}{10} \) into an equivalent fraction with the same denominator as \( \frac{3}{5} \). Since \( \frac{5}{10} \) simplifies to \( \frac{1}{2} \), we can rewrite it as \( \frac{3}{5} \) with a common denominator. Next, we multiply both the numerator and denominator of \( \frac{3}{5} \) by 2: \[ \frac{3 \times 2}{5 \times 2} = \frac{6}{10} \] Now we can compare \( \frac{6}{10} \) and \( \frac{5}{10} \). Clearly, \( \frac{6}{10} > \frac{5}{10} \). Thus, we have: \[ \frac{3}{5} > \frac{5}{10} \]
