Simplify the following: $$ \begin{array}{ll} ext { a ) } 6\left(\frac{1}{2}+\frac{1}{3} ight) & ext { b ) } \frac{1}{2}(18+36) \ ext { c) } 12(13-8)-11(22-17) & ext { d) } 1,5 imes 3+1,5 imes 4 \ ext { e ) } \frac{1}{8} imes 2 imes 8 & ext { f) } \frac{3}{4} imes \frac{4}{3} imes 12\end{array} $$

Question

Simplify the following: $$ \begin{array}{ll}	ext { a ) } 6\left(\frac{1}{2}+\frac{1}{3}ight) & 	ext { b ) } \frac{1}{2}(18+36) \ 	ext { c) } 12(13-8)-11(22-17) & 	ext { d) } 1,5 	imes 3+1,5 	imes 4 \ 	ext { e ) } \frac{1}{8} 	imes 2 	imes 8 & 	ext { f) } \frac{3}{4} 	imes \frac{4}{3} 	imes 12\end{array} $$

UpStudy AI · Accepted Answer

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

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

1. **Add the fractions inside the parentheses:**
   $$
   \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}
   $$
2. **Multiply by 6:**
   $$
   6 \times \frac{5}{6} = 5
   $$

**Simplified Answer:** $$ 5 $$

---

### b) $$ \frac{1}{2}(18 + 36) $$

1. **Add the numbers inside the parentheses:**
   $$
   18 + 36 = 54
   $$
2. **Multiply by $$\frac{1}{2}$$:**
   $$
   \frac{1}{2} \times 54 = 27
   $$

**Simplified Answer:** $$ 27 $$

---

### c) $$ 12(13 - 8) - 11(22 - 17) $$

1. **Calculate the differences:**
   $$
   13 - 8 = 5 \quad \text{and} \quad 22 - 17 = 5
   $$
2. **Perform the multiplications:**
   $$
   12 \times 5 = 60 \quad \text{and} \quad 11 \times 5 = 55
   $$
3. **Subtract the results:**
   $$
   60 - 55 = 5
   $$

**Simplified Answer:** $$ 5 $$

---

### d) $$ 1.5 \times 3 + 1.5 \times 4 $$

1. **Factor out 1.5:**
   $$
   1.5 \times (3 + 4) = 1.5 \times 7 = 10.5
   $$

*Alternatively:*
   
   $$
   1.5 \times 3 = 4.5 \quad \text{and} \quad 1.5 \times 4 = 6
   $$
   $$
   4.5 + 6 = 10.5
   $$

**Simplified Answer:** $$ 10.5 $$

---

### e) $$ \frac{1}{8} \times 2 \times 8 $$

1. **Multiply the numbers:**
   $$
   \frac{1}{8} \times 2 = \frac{2}{8} = \frac{1}{4}
   $$
2. **Multiply by 8:**
   $$
   \frac{1}{4} \times 8 = 2
   $$

*Alternatively:*
   
   $$
   \frac{1}{8} \times 2 \times 8 = \frac{2 \times 8}{8} = \frac{16}{8} = 2
   $$

**Simplified Answer:** $$ 2 $$

---

### f) $$ \frac{3}{4} \times \frac{4}{3} \times 12 $$

1. **Multiply the fractions:**
   $$
   \frac{3}{4} \times \frac{4}{3} = 1
   $$
2. **Multiply by 12:**
   $$
   1 \times 12 = 12
   $$

**Simplified Answer:** $$ 12 $$

---

**Summary of Simplified Expressions:**

- **a)** $$ 5 $$
- **b)** $$ 27 $$
- **c)** $$ 5 $$
- **d)** $$ 10.5 $$
- **e)** $$ 2 $$
- **f)** $$ 12 $$
- **a)** 5 - **b)** 27 - **c)** 5 - **d)** 10.5 - **e)** 2 - **f)** 12

Simplify the following:

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