Question

1. draw an area model, and then solve using the standard algorithm. a) 24×21 = b) 242×21 = 2. solve using the standard algorithm. a. 314×22 = b. 413×22 =

Explanation:

Step1: Rewrite numbers for 242×21

Rewrite 242 as 200 + 40+ 2 and 21 as 20 + 1.

Step2: Calculate partial - products

\[

$$\begin{align*} 200\times20&=4000\\ 200\times1&= 200\\ 40\times20&=800\\ 40\times1&=40\\ 2\times20&=40\\ 2\times1&=2 \end{align*}$$

\]

Step3: Sum up partial - products

\[4000 + 200+800 + 40+40+2=5082\]

For 314×22

Step1: Rewrite numbers

Rewrite 314 as 300 + 10+ 4 and 22 as 20 + 2.

Step2: Calculate partial - products

\[

$$\begin{align*} 300\times20&=6000\\ 300\times2&=600\\ 10\times20&=200\\ 10\times2&=20\\ 4\times20&=80\\ 4\times2&=8 \end{align*}$$

\]

Step3: Sum up partial - products

\[6000+600 + 200+20+80+8 = 6908\]

For 413×22

Step1: Rewrite numbers

Rewrite 413 as 400+10 + 3 and 22 as 20 + 2.

Step2: Calculate partial - products

\[

$$\begin{align*} 400\times20&=8000\\ 400\times2&=800\\ 10\times20&=200\\ 10\times2&=20\\ 3\times20&=60\\ 3\times2&=6 \end{align*}$$

\]

Step3: Sum up partial - products

\[8000+800+200 + 20+60+6=9086\]

Answer:

b. \(242\times21 = 5082\)
a. \(314\times22=6908\)
b. \(413\times22 = 9086\)