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. \( \begin{array}{ll}\text { 1. } & (-4) \cdot(6) \\ \text { m. } & 4-(-3) \\ \text { n. } & 10+(-2)-7 \\ \text { o. } & -5-3(2-6) \\ \text { p. } & (3-3)\left(10^{2}-11\right)\end{array} \)

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 \( (4/5)*(1/3) \). 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: \(\frac{4}{15}\) Calculate or simplify the expression \( 4-(-3) \). Calculate the value by following steps: - step0: Calculate: \(4-\left(-3\right)\) - step1: Remove the parentheses: \(4+3\) - step2: Add the numbers: \(7\) Calculate or simplify the expression \( (-4)*(6) \). Calculate the value by following steps: - step0: Calculate: \(\left(-4\right)\times 6\) - step1: Remove the parentheses: \(-4\times 6\) - step2: Multiply the numbers: \(-24\) Calculate or simplify the expression \( 10+(-2)-7 \). 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 \( -5-3*(2-6) \). Calculate the value by following steps: - step0: Calculate: \(-5-3\left(2-6\right)\) - step1: Subtract the numbers: \(-5-3\left(-4\right)\) - step2: Multiply the numbers: \(-5+12\) - step3: Add the numbers: \(7\) 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 m: \( (-4) \cdot (6) \)** \[ (-4) \cdot (6) = -24 \] 2. **Expression n: \( 4 - (-3) \)** \[ 4 - (-3) = 4 + 3 = 7 \] 3. **Expression o: \( 10 + (-2) - 7 \)** \[ 10 + (-2) - 7 = 10 - 2 - 7 = 8 - 7 = 1 \] 4. **Expression p: \( -5 - 3(2 - 6) \)** First, calculate \( 2 - 6 \): \[ 2 - 6 = -4 \] Now substitute back: \[ -5 - 3(-4) = -5 + 12 = 7 \] 5. **Expression q: \( (3 - 3)(10^2 - 11) \)** Since \( 3 - 3 = 0 \): \[ (3 - 3)(10^2 - 11) = 0 \cdot (100 - 11) = 0 \cdot 89 = 0 \] ### Summary of Results - \( \frac{4}{5} \cdot \frac{1}{3} = \frac{4}{15} \) - \( (-4) \cdot (6) = -24 \) - \( 4 - (-3) = 7 \) - \( 10 + (-2) - 7 = 1 \) - \( -5 - 3(2 - 6) = 7 \) - \( (3 - 3)(10^2 - 11) = 0 \)