# 7.4 Whole numbers: multiplication

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to multiply whole numbers. By the end of the module students should be able to understand the process of multiplication, multiply whole numbers, simplify multiplications with numbers ending in zero, and use a calculator to multiply one whole number by another.

## Section overview

• Multiplication
• The Multiplication Process With a Single Digit Multiplier
• The Multiplication Process With a Multiple Digit Multiplier
• Multiplication With Numbers Ending in Zero
• Calculators

## Multiplication

Multiplication is a description of repeated addition.

$5+5+5$

the number 5 is repeated 3 times. Therefore, we say we have three times five and describe it by writing

$3×5$

Thus,

$3×5=5+5+5$

## Multiplicand

In a multiplication, the repeated addend (number being added) is called the multi­plicand . In $3×5$ , the 5 is the multiplicand.

## Multiplier

Also, in a multiplication, the number that records the number of times the multiplicand is used is called the multiplier . In $3×5$ , the 3 is the multiplier.

## Sample set a

Express each repeated addition as a multiplication. In each case, specify the multiplier and the multiplicand.

$7+7+7+7+7+7$

$6×7$ . Multiplier is 6. Multiplicand is 7.

$\text{18}+\text{18}+\text{18}$

$3×\text{18}$ . Multiplier is 3. Multiplicand is 18.

## Practice set a

Express each repeated addition as a multiplication. In each case, specify the multiplier and the multiplicand.

$\text{12}+\text{12}+\text{12}+\text{12}$

. Multiplier is . Multiplicand is .

$4×\text{12}$ . Multiplier is 4. Multiplicand is 12.

$\text{36}+\text{36}+\text{36}+\text{36}+\text{36}+\text{36}+\text{36}+\text{36}$

. Multiplier is . Multiplicand is .

$8×\text{36}$ . Multiplier is 8. Multiplicand is 36.

$0+0+0+0+0$

. Multiplier is . Multiplicand is .

$5×0$ . Multiplier is 5. Multiplicand is 0.

$\begin{array}{c}\underbrace{1847+1847+...+1847}\\ 12,000\phantom{\rule{5pt}{0ex}}\text{times}\end{array}$

. Multiplier is . Multiplicand is .

$\text{12},\text{000}×1,\text{847}$ . Multiplier is 12,000. Multiplicand is 1,847.

## Factors

In a multiplication, the numbers being multiplied are also called factors .

## Products

The result of a multiplication is called the product . In $3×5=\text{15}$ , the 3 and 5 are not only called the multiplier and multiplicand, but they are also called factors. The product is 15.

## Indicators of multiplication $×$ ,⋅,( )

The multiplication symbol ( $×$ ) is not the only symbol used to indicate multiplication. Other symbols include the dot ( ⋅ ) and pairs of parentheses ( ). The expressions

$3×5$ , $3\cdot 5$ , $3\left(5\right)$ , $\left(3\right)5$ , $\left(3\right)\left(5\right)$

all represent the same product.

## The multiplication process with a single digit multiplier

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 $7×8=\text{56}$ . Write the 6 in the ones column. Carry the 5. Then take $7×3=\text{21}$ . Add to 21 the 5 that was carried: $\text{21}+5=\text{26}$ . The product is 266.

## Sample set b

Find the following products.

$\begin{array}{ccc}3×4=12& & \text{Write the 2, carry the 1.}\hfill \\ 3×6=18& & \text{Add to 18 the 1 that was carried:}\phantom{\rule{2px}{0ex}}18+1=19\text{.}\hfill \end{array}$

The product is 192.

$\begin{array}{ccc}5×6=30& & \text{Write the 0, carry the 3.}\hfill \\ 5×2=10& & \text{Add to 10 the 3 that was carried:}\phantom{\rule{2px}{0ex}}10+3=13\text{. Write the 3, carry the 1.}\hfill \\ 5×5=25& & \text{Add to 25 the 1 that was carried:}\phantom{\rule{2px}{0ex}}25+1=6\text{.}\hfill \end{array}$

The product is 2,630.

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