Question
Find equivalent fractions to compare. Then, write \( >,< \), or \( = \). \( \frac{7}{10} ? \frac{4}{6} \) \( \frac{7}{10} \frac{4}{6} \)
Ask by Bright Dickson. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{7}{10} > \frac{4}{6} \)
Solution
To compare 7/10 and 4/6, we can find equivalent fractions with a common denominator.
Step 1: Choose a common denominator. One simple choice is 30.
Step 2: Convert each fraction:
• For 7/10, multiply the numerator and denominator by 3:
7/10 = (7×3)/(10×3) = 21/30.
• For 4/6, multiply the numerator and denominator by 5:
4/6 = (4×5)/(6×5) = 20/30.
Step 3: Compare the equivalent fractions:
21/30 is greater than 20/30, so we have
7/10 > 4/6.
Thus, the comparison is:
7/10 > 4/6.
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Simplify this solution Beyond the Answer
To find equivalent fractions, we can turn \( \frac{4}{6} \) into a fraction with a denominator of 10. To do that, we can simplify \( \frac{4}{6} \) to \( \frac{2}{3} \) and then multiply the numerator and denominator by 10 to get \( \frac{20}{30} \). Now, we compare \( \frac{7}{10} \) and \( \frac{20}{30} \). Next, we convert \( \frac{7}{10} \) into a fraction with a denominator of 30 as well. We multiply both the numerator and the denominator by 3, giving us \( \frac{21}{30} \). Now we can see that \( \frac{21}{30} > \frac{20}{30} \). Thus, \( \frac{7}{10} > \frac{4}{6} \). In conclusion: \( \frac{7}{10} > \frac{4}{6} \)
