Question
Find equivalent fractions to compare. Then, write \( >,< \), or \( = \). \[ \begin{array}{l}\frac{3}{10} ? \frac{4}{5} \\ \quad< \\ \quad=\end{array} \]
Ask by Hobbs King. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
3/10 < 4/5
Solution
To compare 3/10 and 4/5, we can find equivalent fractions with a common denominator. Notice that 10 is a common denominator for both fractions.
Convert 4/5 to an equivalent fraction with denominator 10 by multiplying the numerator and the denominator by 2:
4/5 = (4 × 2)/(5 × 2) = 8/10.
Now compare:
3/10 ? 8/10
Since 3/10 is less than 8/10, we conclude:
3/10 < 4/5.
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Simplify this solution Beyond the Answer
To compare the fractions \(\frac{3}{10}\) and \(\frac{4}{5}\), we can find a common denominator. The least common denominator (LCD) for 10 and 5 is 10. We can rewrite \(\frac{4}{5}\) as \(\frac{8}{10}\) (since \(4 \times 2 = 8\) and \(5 \times 2 = 10\)). Now we can compare: \[ \frac{3}{10} \quad \text{and} \quad \frac{8}{10} \] Since \(3 < 8\), it follows that: \[ \frac{3}{10} < \frac{4}{5} \] So, the final answer is: \[ \begin{array}{l}\frac{3}{10} < \frac{4}{5} \\ \quad< \\ \quad=\end{array} \]
