Question
a) \( 6\left(\frac{1}{2}+\frac{1}{3}\right) \) c) \( 12(13-8)-11(22-17) \)
Ask by Sullivan Campbell. in South Africa
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Both expressions equal 5.
Solution
Let's solve the given expressions step-by-step.
---
### a) \( 6\left(\frac{1}{2} + \frac{1}{3}\right) \)
**Step 1:** Add the fractions inside the parentheses.
\[
\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}
\]
**Step 2:** Multiply the sum by 6.
\[
6 \times \frac{5}{6} = 5
\]
**Answer:** \(5\)
---
### c) \( 12(13 - 8) - 11(22 - 17) \)
**Step 1:** Simplify the expressions inside the parentheses.
\[
13 - 8 = 5 \quad \text{and} \quad 22 - 17 = 5
\]
**Step 2:** Substitute the simplified values back into the expression.
\[
12 \times 5 - 11 \times 5
\]
**Step 3:** Perform the multiplications.
\[
60 - 55
\]
**Step 4:** Subtract the results.
\[
60 - 55 = 5
\]
**Answer:** \(5\)
---
Both expressions **a)** and **c)** evaluate to **5**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve \( 6\left(\frac{1}{2}+\frac{1}{3}\right) \), first find a common denominator for the fractions. The least common multiple of 2 and 3 is 6. Thus, convert \(\frac{1}{2}=\frac{3}{6}\) and \(\frac{1}{3}=\frac{2}{6}\). Adding them gives \(\frac{3+2}{6}=\frac{5}{6}\). Now multiplying by 6 results in \(6 \times \frac{5}{6} = 5\). For \( 12(13-8)-11(22-17) \), start by simplifying the parentheses. \(13-8=5\) and \(22-17=5\). Therefore, you have \(12 \times 5 - 11 \times 5\), which simplifies to \(60 - 55 = 5\). So, you get the final answer for both parts as \(5\).
