Question
Subtract. \[ \frac{7}{2}-\frac{9}{5 d} \] Simplify your answer as much as possible. \( \square \)
Ask by Rogers Vargas. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified answer is \( \frac{35d - 18}{10d} \).
Solution
Calculate or simplify the expression \( \frac{7}{2}-\frac{9}{5d} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{7}{2}-\frac{9}{5d}\)
- step1: Reduce fractions to a common denominator:
\(\frac{7\times 5d}{2\times 5d}-\frac{9\times 2}{5d\times 2}\)
- step2: Multiply the numbers:
\(\frac{7\times 5d}{10d}-\frac{9\times 2}{5d\times 2}\)
- step3: Multiply the numbers:
\(\frac{7\times 5d}{10d}-\frac{9\times 2}{10d}\)
- step4: Transform the expression:
\(\frac{7\times 5d-9\times 2}{10d}\)
- step5: Multiply the terms:
\(\frac{35d-9\times 2}{10d}\)
- step6: Multiply the numbers:
\(\frac{35d-18}{10d}\)
The result of subtracting \( \frac{7}{2} \) from \( \frac{9}{5d} \) is \( \frac{35d-18}{10d} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To subtract the fractions \( \frac{7}{2} \) and \( \frac{9}{5d} \), we need a common denominator. The least common denominator for 2 and \( 5d \) is \( 10d \). Now, let's rewrite each fraction with the common denominator: \[ \frac{7}{2} = \frac{7 \times 5d}{2 \times 5d} = \frac{35d}{10d} \] \[ \frac{9}{5d} = \frac{9 \times 2}{5d \times 2} = \frac{18}{10d} \] Now we can subtract: \[ \frac{35d}{10d} - \frac{18}{10d} = \frac{35d - 18}{10d} \] Thus, the simplified result of the subtraction is: \[ \frac{35d - 18}{10d} \] So, the final answer is \( \frac{35d - 18}{10d} \).
