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2.1 Multiplication of whole numbers

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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.

In the addition of

5 + 5 + 5 size 12{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 size 12{3 times 5} {}

Thus,

3 × 5 = 5 + 5 + 5 size 12{3 times 5=5+5+5} {}

Multiplicand

In a multiplication, the repeated addend (number being added) is called the multi­plicand . In 3 × 5 size 12{3 times 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 size 12{3 times 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 size 12{7+7+7+7+7+7} {}

6 × 7 size 12{6 times 7} {} . Multiplier is 6. Multiplicand is 7.

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18 + 18 + 18 size 12{"18"+"18"+"18"} {}

3 × 18 size 12{3 times "18"} {} . Multiplier is 3. Multiplicand is 18.

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Practice set a

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

12 + 12 + 12 + 12 size 12{"12"+"12"+"12"+"12"} {}

. Multiplier is . Multiplicand is .

4 × 12 size 12{4 times "12"} {} . Multiplier is 4. Multiplicand is 12.

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36 + 36 + 36 + 36 + 36 + 36 + 36 + 36 size 12{"36"+"36"+"36"+"36"+"36"+"36"+"36"+"36"} {}

. Multiplier is . Multiplicand is .

8 × 36 size 12{8 times "36"} {} . Multiplier is 8. Multiplicand is 36.

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0 + 0 + 0 + 0 + 0 size 12{0+0+0+0+0} {}

. Multiplier is . Multiplicand is .

5 × 0 size 12{5 times 0} {} . Multiplier is 5. Multiplicand is 0.

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1847 + 1847 + ... + 1847 ︸ 12,000 times

. Multiplier is . Multiplicand is .

12 , 000 × 1, 847 size 12{"12","000" times 1,"847"} {} . Multiplier is 12,000. Multiplicand is 1,847.

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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 = 15 size 12{3 times 5="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 size 12{3 times 5} {} , 3 ⋅ 5 size 12{3 cdot 5} {} , 3 ( 5 ) size 12{3 \( 5 \) } {} , ( 3 ) 5 size 12{ \( 3 \) 5} {} , ( 3 ) ( 5 ) size 12{ \( 3 \) \( 5 \) } {}

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:

Vertical multiplication. 38 times 7 is 266. The 5 is carried on top of the 3.

First, we compute 7 × 8 = 56 size 12{7 times 8="56"} {} . Write the 6 in the ones column. Carry the 5. Then take 7 × 3 = 21 size 12{7 times 3="21"} {} . Add to 21 the 5 that was carried: 21 + 5 = 26 size 12{"21"+5="26"} {} . The product is 266.

Sample set b

Find the following products.

Vertical multiplication. 64 times 3 is 192. The 1 is carried on top of the 6.

3 × 4 = 12 Write the 2, carry the 1. 3 × 6 = 18 Add to 18 the 1 that was carried: 18 + 1 = 19 .

The product is 192.

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Vertical multiplication. 526 times 5 is 2,630. The 2 is carried on top of the 2, and the 1 is carried on top of the 5.

5 × 6 = 30 Write the 0, carry the 3. 5 × 2 = 10 Add to 10 the 3 that was carried: 10 + 3 = 13 . Write the 3, carry the 1. 5 × 5 = 25 Add to 25 the 1 that was carried: 25 + 1 = 6 .

The product is 2,630.

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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