Question
Subtract as indicated. Write all answers in lowest terms \[ \frac{5}{7 w}-\frac{2}{3 w} \]
Ask by Savage Chang. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The answer is \(\frac{1}{21w}\).
Solution
Calculate or simplify the expression \( \frac{5}{7w}-\frac{2}{3w} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{5}{7w}-\frac{2}{3w}\)
- step1: Reduce fractions to a common denominator:
\(\frac{5\times 3}{7w\times 3}-\frac{2\times 7}{3w\times 7}\)
- step2: Multiply the numbers:
\(\frac{5\times 3}{21w}-\frac{2\times 7}{3w\times 7}\)
- step3: Multiply the numbers:
\(\frac{5\times 3}{21w}-\frac{2\times 7}{21w}\)
- step4: Transform the expression:
\(\frac{5\times 3-2\times 7}{21w}\)
- step5: Multiply the numbers:
\(\frac{15-2\times 7}{21w}\)
- step6: Multiply the numbers:
\(\frac{15-14}{21w}\)
- step7: Subtract the numbers:
\(\frac{1}{21w}\)
The result of subtracting as indicated is \(\frac{1}{21w}\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To perform the subtraction, we first need a common denominator. The denominators here are \(7w\) and \(3w\). The least common denominator (LCD) will be \(21w\). Now, we convert each fraction: \[ \frac{5}{7w} = \frac{5 \cdot 3}{7w \cdot 3} = \frac{15}{21w} \] \[ \frac{2}{3w} = \frac{2 \cdot 7}{3w \cdot 7} = \frac{14}{21w} \] Now we can subtract the two fractions: \[ \frac{15}{21w} - \frac{14}{21w} = \frac{15 - 14}{21w} = \frac{1}{21w} \] Thus, the final answer is: \[ \frac{1}{21w} \]
