a. 72 Use your factor knowledge to multiply the numbers below by breaking them us first. \( \begin{array}{ll}\text { a. } 266 \times 22 & \text { b. } 1550 \times 130 \\ \text { c. } 424 \times 18 & \text { d. } 622 \times 12\end{array} \) eck your answers by using a calculator.

\( \textbf{a. } 266 \times 22 \) 1. Notice that \(22 = 2 \times 11\). So, we can write: \[ 266 \times 22 = 266 \times (2 \times 11) = (266 \times 2) \times 11 \] 2. First, compute \(266 \times 2\): \[ 266 \times 2 = 532 \] 3. Next, multiply by 11: \[ 532 \times 11 = 532 \times 10 + 532 = 5320 + 532 = 5852 \] --- \( \textbf{b. } 1550 \times 130 \) 1. Express \(130\) as \(10 \times 13\): \[ 1550 \times 130 = 1550 \times (10 \times 13) = (1550 \times 10) \times 13 \] 2. Calculate \(1550 \times 10\): \[ 1550 \times 10 = 15500 \] 3. Multiply by 13: \[ 15500 \times 13 = 15500 \times 10 + 15500 \times 3 = 155000 + 46500 = 201500 \] --- \( \textbf{c. } 424 \times 18 \) 1. Write \(18\) as \(10 + 8\): \[ 424 \times 18 = 424 \times (10 + 8) = 424 \times 10 + 424 \times 8 \] 2. Compute each term: \[ 424 \times 10 = 4240 \] \[ 424 \times 8 = 3392 \quad \text{(since } 400 \times 8 = 3200 \text{ and } 24 \times 8 = 192\text{)} \] 3. Add the two results: \[ 4240 + 3392 = 7632 \] --- \( \textbf{d. } 622 \times 12 \) 1. Break \(12\) into \(10 + 2\): \[ 622 \times 12 = 622 \times (10 + 2) = 622 \times 10 + 622 \times 2 \] 2. Compute: \[ 622 \times 10 = 6220 \] \[ 622 \times 2 = 1244 \] 3. Sum the two products: \[ 6220 + 1244 = 7464 \] --- Final answers verified with a calculator: - \(266 \times 22 = 5852\) - \(1550 \times 130 = 201500\) - \(424 \times 18 = 7632\) - \(622 \times 12 = 7464\)