Question

2 - 61. draw generic rectangles to help you multiply the following numbers without a calculator. show the place value of each part of the rectangle. write it as a product and as a total sum.
a) 25·18
b) 153·25
c) 472·57
d) 289·77

Explanation:

Step1: Multiply \(25\times18\)

$$\begin{align*} 25\times18&=(20 + 5)\times(10+8)\\ &=20\times10+20\times8+5\times10+5\times8\\ &=200+160+50+40\\ &=450 \end{align*}$$

Step2: Multiply \(153\times25\)

$$\begin{align*} 153\times25&=(100 + 50+3)\times25\\ &=100\times25+50\times25+3\times25\\ &=2500+1250 + 75\\ &=3825 \end{align*}$$

Step3: Multiply \(472\times57\)

$$\begin{align*} 472\times57&=(400+70 + 2)\times(50+7)\\ &=400\times50+400\times7+70\times50+70\times7+2\times50+2\times7\\ &=20000+2800+3500+490+100+14\\ &=26904 \end{align*}$$

Step4: Multiply \(289\times77\)

$$\begin{align*} 289\times77&=(200+80 + 9)\times(70+7)\\ &=200\times70+200\times7+80\times70+80\times7+9\times70+9\times7\\ &=14000+1400+5600+560+630+63\\ &=22253 \end{align*}$$

Answer:

a) \(450\)
b) \(3825\)
c) \(26904\)
d) \(22253\)