Question
Multiply the fractions. Simplify if possible. \[ \frac{8 x+8 y}{5} \cdot \frac{10}{x+y} \]
Ask by Davies Murphy. in the United States
Nov 03,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The product is 16.
Solution
Calculate or simplify the expression \( (8x+8y)/5 * 10/(x+y) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\frac{\left(8x+8y\right)}{5}\times 10}{\left(x+y\right)}\)
- step1: Remove the parentheses:
\(\frac{\frac{8x+8y}{5}\times 10}{x+y}\)
- step2: Multiply the terms:
\(\frac{2\left(8x+8y\right)}{x+y}\)
- step3: Factor the expression:
\(\frac{2\times 8\left(x+y\right)}{x+y}\)
- step4: Reduce the fraction:
\(2\times 8\)
- step5: Calculate:
\(16\)
The product of the fractions \(\frac{8x+8y}{5} \cdot \frac{10}{x+y}\) simplifies to 16.
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Simplify this solution Bonus Knowledge
To multiply the fractions, we multiply the numerators together and the denominators together: \[ \frac{(8x + 8y) \cdot 10}{5 \cdot (x + y)} \] Now we can simplify the expression. First, notice that \(8x + 8y\) can be factored: \[ 8(x + y) \] So, our expression becomes: \[ \frac{8(x + y) \cdot 10}{5 \cdot (x + y)} \] Next, we can cancel out \(x + y\) from the numerator and the denominator, assuming \(x + y \neq 0\): \[ \frac{8 \cdot 10}{5} = \frac{80}{5} \] Dividing \(80\) by \(5\) gives: \[ 16 \] Therefore, the simplified result of the multiplication is: \[ \boxed{16} \]
