<< Chapter < Page | Chapter >> Page > |
Multiplication is a description of repeated addition.
In the addition of
$5+5+5$
the number 5 is repeated 3 times. Therefore, we say we have three times five and describe it by writing
$3\times 5$
Thus,
$3\times 5=5+5+5$
Express each repeated addition as a multiplication. In each case, specify the multiplier and the multiplicand.
$7+7+7+7+7+7$
$6\times 7$ .
$\text{18}+\text{18}+\text{18}$
$3\times \text{18}$ .
Express each repeated addition as a multiplication. In each case, specify the multiplier and the multiplicand.
$\text{12}+\text{12}+\text{12}+\text{12}$
$4\times \text{12}$ . Multiplier is 4. Multiplicand is 12.
$\text{36}+\text{36}+\text{36}+\text{36}+\text{36}+\text{36}+\text{36}+\text{36}$
$8\times \text{36}$ . Multiplier is 8. Multiplicand is 36.
$0+0+0+0+0$
$5\times 0$ . Multiplier is 5. Multiplicand is 0.
$\begin{array}{c}\underbrace{1847+1847+...+1847}\\ \mathrm{12,000}\phantom{\rule{5pt}{0ex}}\text{times}\end{array}$
$\text{12},\text{000}\times \mathrm{1,}\text{847}$ . Multiplier is 12,000. Multiplicand is 1,847.
$3\times 5$ ,
all represent the same product.
Since multiplication is repeated addition, we should not be surprised to notice that carrying can occur. Carrying occurs when we find the product of 38 and 7:
First, we compute $7\times 8=\text{56}$ . Write the 6 in the ones column. Carry the 5. Then take $7\times 3=\text{21}$ . Add to 21 the 5 that was carried: $\text{21}+5=\text{26}$ . The product is 266.
Find the following products.
$\begin{array}{ccc}3\times 4=12& & \text{Write the 2, carry the 1.}\hfill \\ 3\times 6=18& & \text{Add to 18 the 1 that was carried:}\phantom{\rule{2px}{0ex}}18+1=19\text{.}\hfill \end{array}$
The product is 192.
$\begin{array}{ccc}5\times 6=30& & \text{Write the 0, carry the 3.}\hfill \\ 5\times 2=10& & \text{Add to 10 the 3 that was carried:}\phantom{\rule{2px}{0ex}}10+3=13\text{. Write the 3, carry the 1.}\hfill \\ 5\times 5=25& & \text{Add to 25 the 1 that was carried:}\phantom{\rule{2px}{0ex}}25+1=6\text{.}\hfill \end{array}$
The product is 2,630.
Notification Switch
Would you like to follow the 'Contemporary math applications' conversation and receive update notifications?