1. Simplify the following: a) $$ 6\left(\frac{1}{2}+\frac{1}{3}\right) $$ c) $$ 12(13-8)-11(22-17) $$

Question

UpStudy AI · Accepted Answer

Let's simplify each of the given expressions step by step.

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### Problem 1.a)
Simplify:
$$ 6\left(\frac{1}{2} + \frac{1}{3}\right) $$

**Step 1:** Add the fractions inside the parentheses.

To add $$\frac{1}{2}$$ and $$\frac{1}{3}$$, find a common denominator. The least common denominator (LCD) of 2 and 3 is 6.

$$
\frac{1}{2} = \frac{3}{6} \quad \text{and} \quad \frac{1}{3} = \frac{2}{6}
$$

$$
\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}
$$

**Step 2:** Multiply by 6.

$$
6 \times \frac{5}{6} = \frac{6 \times 5}{6} = \frac{30}{6} = 5
$$

**Final Answer:**  
$$
6\left(\frac{1}{2} + \frac{1}{3}\right) = 5
$$

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### Problem 1.c)
Simplify:
$$ 12(13 - 8) - 11(22 - 17) $$

**Step 1:** Calculate the expressions inside the parentheses.

$$
13 - 8 = 5 \quad \text{and} \quad 22 - 17 = 5
$$

**Step 2:** Multiply the results by their respective coefficients.

$$
12 \times 5 = 60 \quad \text{and} \quad 11 \times 5 = 55
$$

**Step 3:** Subtract the second product from the first.

$$
60 - 55 = 5
$$

**Final Answer:**  
$$
12(13 - 8) - 11(22 - 17) = 5
$$

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Both expressions simplify to **5**.
Both expressions simplify to 5.

1. Simplify the following: a) \( 6\left(\frac{1}{2}+\frac{1}{3}\right) \) c) \( 12(13-8)-11(22-17) \)