2.1 Multiplication of whole numbers

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.

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,

$3\times 5=5+5+5$

Multiplicand

Multiplier

Sample set a

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

Practice set a

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

Factors

Products

Indicators of multiplication $\times$ ,⋅,( )

$3\times 5$ , $3\cdot 5$ , $3(5)$ , $(3)5$ , $(3)(5)$

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 $7\times 8=\text{56}$ . 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.

Sample set b

Find the following products.