Basic Mathematics for College Students

42 Chapter 1 Whole Numbers

EXAMPLE (^2) Multiply: a. b. c.
Strategy For each multiplication, we will identify the factor that ends in zeros and
count the number of zeros that it contains.
WHY Each product can then be found by attaching that number of zeros to the
other factor.
Solution
a. Since 1,000 has three zeros, attach three 0’s after 6.
b. Since 100 has two zeros, attach two 0’s after 45.
c.912(10,000)9,120,000 Since 10,000 has four zeros, attach four 0’s after 912.

45  100 4,500

6  1,0006,000

6 1,000 45  100 912(10,000)

Self Check 2

Multiply:

a.

b.

c.

Now TryProblems 23 and 25

875(1,000)

25  100

9  1,000

We can use an approach similar to that of Example 2 for multiplication involving

any whole numbers that end in zeros. For example, to find , we have

Write 2,000 as 2 1,000.

Working left to right, multiply 67 and 2 to get 134.

Since 1,000 has three zeros, attach three 0’s

after 134.

This example suggests that to find we simply multiply 67 and 2 and

attach three zeros to that product. This method can be extended to find products of

two factors that both end in zeros.

67 2,000

134,000

 134 1,000

67 2,000 67  2 1,000

67 2,000

EXAMPLE (^3) Multiply: a. b.
Strategy We will multiply the nonzero leading digits of each factor. To that
product, we will attach the sum of the number of trailing zeros in the factors.
WHY This method is faster than the standard vertical form multiplication of
factors that contain many zeros.
Solution
a. The factor 3 00 has two trailing zeros.
Attach two 0’s after 42.
Multiply 14 and 3
to get 42.
b. The factors 3,5 00 and 5 0 , 000 have a total of six trailing zeros.
Attach six 0’s after 175.
Multiply 35 and 5
to get 175.

3,50050,000175,000,000

14  300 4,200

14  300 3,50050,000

Self Check 3

Multiply:

a.

b.

Now TryProblems 29 and 33

3,1007,000

15  900

Success Tip Calculations that you cannot perform in your head should be

shown outside the steps of your solution.

3 Multiply whole numbers by two- (or more) digit numbers.

EXAMPLE (^4) Multiply:
Strategy We will write the multiplication in vertical form. Then we will multiply
436 by 3 and by 20, and add those products.
WHY Since , we can multiply 436 by 3 and by 20, and add those
products.

23  3  20

23  436

Self Check 4

Multiply:

Now TryProblem 37

36  334

1

1

4

 3

42

3

2

5

 5

(^175)