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. \( \begin{array}{l}\text { l. } \\ \text { m. } \\ \begin{array}{l}\text { n. }\end{array} \\ \begin{array}{ll}\text { n. } & 4-(-3) \cdot(6) \\ \text { o. } & 10+(-2)-7 \\ \text { p. } & (3-3)\left(10^{2}-11\right)\end{array}\end{array} \).

Calculate the value by following steps: - step0: Calculate: \(10+\left(-2\right)-7\) - step1: Remove the parentheses: \(10-2-7\) - step2: Subtract the numbers: \(1\) Calculate or simplify the expression \( (3-3)*(10^2-11) \). Calculate the value by following steps: - step0: Calculate: \(\left(3-3\right)\left(10^{2}-11\right)\) - step1: Subtract the terms: \(0\times \left(10^{2}-11\right)\) - step2: Multiply the numbers: \(0\) Calculate or simplify the expression \( 4-(-3)*(6) \). Calculate the value by following steps: - step0: Calculate: \(4-\left(-3\right)\times 6\) - step1: Remove the parentheses: \(4-\left(-3\times 6\right)\) - step2: Multiply the numbers: \(4-\left(-18\right)\) - step3: Remove the parentheses: \(4+18\) - step4: Add the numbers: \(22\) Calculate or simplify the expression \( (4/5)*(1/3) \). Calculate the value by following steps: - step0: Calculate: \(\frac{4}{5}\times \frac{1}{3}\) - step1: Multiply the fractions: \(\frac{4}{5\times 3}\) - step2: Multiply: \(\frac{4}{15}\) Let's solve the problems step by step. ### Problem 4-100: Multiply \( \frac{4}{5} \cdot \frac{1}{3} \) To multiply two fractions, you multiply the numerators together and the denominators together: \[ \frac{4}{5} \cdot \frac{1}{3} = \frac{4 \cdot 1}{5 \cdot 3} = \frac{4}{15} \] So, the result of \( \frac{4}{5} \cdot \frac{1}{3} \) is \( \frac{4}{15} \). ### Problem 4-101: Simplify each expression 1. **Expression n: \( 4 - (-3) \cdot (6) \)** First, calculate \( -(-3) \cdot 6 \): \[ -(-3) \cdot 6 = 3 \cdot 6 = 18 \] Now substitute back into the expression: \[ 4 + 18 = 22 \] 2. **Expression o: \( 10 + (-2) - 7 \)** Combine the terms: \[ 10 - 2 - 7 = 8 - 7 = 1 \] 3. **Expression p: \( (3 - 3)(10^2 - 11) \)** First, calculate \( 3 - 3 \): \[ 3 - 3 = 0 \] Now substitute back into the expression: \[ 0 \cdot (10^2 - 11) = 0 \cdot (100 - 11) = 0 \cdot 89 = 0 \] ### Summary of Results - For \( \frac{4}{5} \cdot \frac{1}{3} \): \( \frac{4}{15} \) - For \( 4 - (-3) \cdot (6) \): \( 22 \) - For \( 10 + (-2) - 7 \): \( 1 \) - For \( (3 - 3)(10^2 - 11) \): \( 0 \)