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

Question

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

UpStudy AI · Accepted Answer

$$ \textbf{a. } 266 \times 22 $$

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:

- $$266 \times 22 = 5852$$
- $$1550 \times 130 = 201500$$
- $$424 \times 18 = 7632$$
- $$622 \times 12 = 7464$$
$$ \textbf{a. } 266 \times 22 = 5852 $$ $$ \textbf{b. } 1550 \times 130 = 201500 $$ $$ \textbf{c. } 424 \times 18 = 7632 $$ $$ \textbf{d. } 622 \times 12 = 7464 $$

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.

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