4-100. Multiply \( { }^{\frac{4}{5} \cdot \frac{1}{3}} \). You may want to show your thinking with a diagram. 4-101. Copy and simplify each expression. k. \( -2+5 \) 1. \( (-4) \cdot(6) \) m. \( \quad 4-(-3) \) n. \( \quad 10+(-2)-7 \) e. \( -5-3(2-6) \) p. \( \quad(3-3)\left(10^{2}-11\right) \)

### 4-100. We are asked to multiply \[ \frac{4}{5} \cdot \frac{1}{3}. \] **Step 1. Multiply the numerators:** \[ 4 \times 1 = 4. \] **Step 2. Multiply the denominators:** \[ 5 \times 3 = 15. \] **Step 3. Write the result as a fraction:** \[ \frac{4}{15}. \] A simple diagram of the multiplication process: ``` 4/5 × 1/3 ------ Numerators: 4 * 1 = 4 Denom.: 5 * 3 = 15 ------ Result: 4/15 ``` --- ### 4-101. Copy and simplify each expression. **k. \( -2+5 \)** \[ -2+5=3. \] **1. \( (-4) \cdot (6) \)** \[ (-4) \cdot (6) = -24. \] **m. \( 4-(-3) \)** \[ 4-(-3)=4+3=7. \] **n. \( 10+(-2)-7 \)** \[ 10+(-2)-7 = 10-2-7=1. \] **e. \( -5-3(2-6) \)** 1. First, simplify inside the parentheses: \[ 2-6=-4. \] 2. Then multiply: \[ -3 \times (-4)=12. \] 3. Finally, add: \[ -5+12=7. \] **p. \( (3-3)\left(10^{2}-11\right) \)** 1. Simplify the first factor: \[ 3-3=0. \] 2. Simplify the second factor: \[ 10^2-11=100-11=89. \] 3. Multiply: \[ 0 \times 89=0. \] --- **Final Answers:** - 4-100: \(\frac{4}{15}\) - k. \(3\) - 1. \(-24\) - m. \(7\) - n. \(1\) - e. \(7\) - p. \(0\)