Question
a) \( \frac{32 a b c}{64 a c} \times \frac{8 h c}{4 b^{2}} \)
Ask by Herrera Love. in South Africa
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form of the expression is \( \frac{hc}{b} \).
Solution
Calculate or simplify the expression \( \frac{32a*b*c}{64a*c} \times \frac{8h*c}{4b^{2}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{32abc}{64ac}\times \frac{8hc}{4b^{2}}\)
- step1: Divide the terms:
\(\frac{b}{2}\times \frac{8hc}{4b^{2}}\)
- step2: Divide the terms:
\(\frac{b}{2}\times \frac{2hc}{b^{2}}\)
- step3: Reduce the fraction:
\(1\times \frac{hc}{b}\)
- step4: Multiply the terms:
\(\frac{hc}{b}\)
The simplified form of the expression \( \frac{32 a b c}{64 a c} \times \frac{8 h c}{4 b^{2}} \) is \( \frac{hc}{b} \).
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Simplify this solution Extra Insights
First, we simplify the expression step by step. Start with the first fraction: \[ \frac{32 a b c}{64 a c} = \frac{32 b}{64} = \frac{1}{2} b \quad \text{(since } a \text{ and } c \text{ cancel out)} \] Next, simplify the second fraction: \[ \frac{8 h c}{4 b^{2}} = \frac{2 h c}{b^{2}} \quad \text{(dividing both the numerator and the denominator by 4)} \] Now, multiply these simplified fractions: \[ \frac{1}{2} b \times \frac{2 h c}{b^{2}} = \frac{1}{2} \times \frac{2 h c b}{b^{2}} = \frac{h c}{b} \] Thus, the final simplified expression is: \[ \frac{h c}{b} \]
