Question
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Tutor-Verified Answer
Answer
The sum is \(\frac{41}{48}\) or approximately 0.8541.
Solution
Calculate or simplify the expression \( \frac{5}{12}+\frac{7}{16} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{5}{12}+\frac{7}{16}\)
- step1: Reduce fractions to a common denominator:
\(\frac{5\times 4}{12\times 4}+\frac{7\times 3}{16\times 3}\)
- step2: Multiply the numbers:
\(\frac{5\times 4}{48}+\frac{7\times 3}{16\times 3}\)
- step3: Multiply the numbers:
\(\frac{5\times 4}{48}+\frac{7\times 3}{48}\)
- step4: Transform the expression:
\(\frac{5\times 4+7\times 3}{48}\)
- step5: Multiply the numbers:
\(\frac{20+7\times 3}{48}\)
- step6: Multiply the numbers:
\(\frac{20+21}{48}\)
- step7: Add the numbers:
\(\frac{41}{48}\)
The sum of \(\frac{5}{12}\) and \(\frac{7}{16}\) is \(\frac{41}{48}\) or approximately 0.8541.
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Simplify this solution Beyond the Answer
To add the fractions \(\frac{5}{12}+\frac{7}{16}\), we first need a common denominator. The least common multiple of 12 and 16 is 48. Next, convert each fraction: \[ \frac{5}{12} = \frac{5 \times 4}{12 \times 4} = \frac{20}{48} \] \[ \frac{7}{16} = \frac{7 \times 3}{16 \times 3} = \frac{21}{48} \] Now, we can add them: \[ \frac{20}{48} + \frac{21}{48} = \frac{41}{48} \] So, \(\frac{5}{12}+\frac{7}{16} = \frac{41}{48}\).
