# Multiplying by Whole Tens and Hundreds

This is a complete lesson with instruction and exercises for fourth grade about multiplying by whole tens and hundreds. The lesson explains the shortcut, and also explains why it works. It contains plenty of exercises for the students, including word problem.

 We have studied the SHORTCUTS for multiplying any number by 10, 100, or 1,000: To multiply any number by 10, just tag ONE zero on the end. To multiply any number by 100, just tag TWO zeros on the end. To multiply any number by 1,000, just tag THREE zeros on the end. 10 × 481 = 4,810 100 × 47 = 4,700 1000 × 578 = 578,000 Note especially what happens when the number you multiply already ends in a zero or zeros. The rule works the same; you still have to tag the zero or zeros. 10 × 800 = 8000 100 × 6,600 = 660,000 1000 × 40 = 40,000

1. Multiply.

 a.  10 × 315 = _______     3,560 × 10 = _______     35 × 100 = _______ b.  100 × 6,200 = _______     10 × 1,200 = _______     100 × 130 = _______ c.  1,000 × 250 = _______    38 × 1,000 = _______     10 × 5,000 = _______

 SHORTCUT for multiplying by 20 or 200     (You can probably guess this one!) What is 20 × 14? Imagine the problem without the zero. Then it becomes 2 × 14 = 28. Then, just tag a zero to the 28 you got, so it becomes 280. So, 20 × 14 = 280. What is 200 × 31? Imagine the problem without the zeros. Then it becomes 2 × 31 = 62. Then, just tag two zeros to the result you got, so you get 6,200.  In other words, 200 × 31 = 6,200.

2. Now try it! Multiply by 20 and 200.

 a. 20 × 8 = _______ 4 × 20 =_______ 20 × 5 = _______ b. 200 × 7 = ________ 5 × 200 = ________ 11 × 200 = ________ c. 20 × 12 = _______ 35 × 20 = _______ 200 × 9 = _______ d. 20 × 16 = _________ 42 × 200 = ________ 54 × 20 = _________

 Why does the shortcut work? It is based on the fact that you can multiply in any order. When multiplying by 20, we can change the 20 into 10 × 2. For example: 20 × 14 = 10 × 2 × 14 In that problem, first multiply 2 × 14 = 28. Then the problem becomes 10 × 28, which we know is 280. 20 × 14 = 10 ×  2 × 14 = 10 × 28 = 280 That's it! Let's try the same with 200. For example, 200 × 31 = 100 × 2 × 31 In that problem, first multiply 2 × 31 = 62. The problem now becomes 100 × 62, which is 6,200: 100 × 2 × 31 = 100 × 62 = 6,200

3. Try it yourself! Fill in.

 a.      20 × 7 = ______ × 2 × 7 = 10 × ______ = ________ b.      20 × 5 = ______ × 2 × 5 = 10 × ______ = ________ c.      200 × 8 = ______ × 2 × 8 = 100 × ______ = ________ d.      200 × 25 = ______ × 2 × 25 = 100 × ______ = ________

4. Mark's shed measures 20 ft by 15 ft. What is its area? Write a number sentence.
"A" means area.

A = __________________________________ 5. Write a number sentence, and find
the area of Mark's driveway.

A = __________________________________

6. Mark was told he needed four truckloads of gravel to cover his driveway.
One truckload costs 5 × \$20 plus \$30 for the delivery. How much will
it cost him to cover the driveway with gravel?

 SHORTCUT for multiplying by whole tens and whole hundreds The same principle works if you multiply by whole tens (30, 40, 50, 60, 70, 80, or 90): simply multiply 2, 3, 4, 5, 6, 7, 8, or 9, and then tag a zero to the end result. Similarly, if you multiply by some whole hundred, FIRST multiply without those two zeros, and then tag the two zeros to the end result. 50 × 8 = 400 90 × 11 = 990 300 × 8 = 2,400 12 × 800 = 9,600

7. Multiply.

 a.  40 × 3 = ______     8 × 20 = ______ b.  70 × 6 = _______     50 × 11 = ______ c.  80 × 9 = _______    30 × 15 = _______ d.  60 × 11 = _______     12 × 40 = _______ e.  200 × 9 = ______    7 × 400 = ______ f.  700 × 6 = ______  600 × 11 = ______ g.  200 × 12 = ______     15 × 300 = ______ h.  3 × 1100 = ______     8 × 900 = ______ i.  11 × 120 = ______     8 × 300 = ______

 It even works this way: To multiply 40 × 70, simply multiply 4 × 7, and tag two zeros to the result:  40 × 70 = 2,800 To multiply 600 × 40, simply multiply 6 × 4, and tag three zeros to the result: 600 × 40 = 24,000 To multiply 700 × 800, simply multiply 7 × 8, and tag four zeros to the result. 700 × 800 = 560,000

8. Multiply.

 a.  20 × 90 = _________     70 × 300 = ________ b.  60 × 80 = ________     30 × 900 = ________ c.  400 × 50 = ________     200 × 200 = ________ d.  80 × 800 = ________    200 × 500 = ________ e.  100 × 100 = _______     40 × 30 = ________ f.  800 × 300 = ________     90 × 1100 = ________

Write a number sentence for each question.

9. One hour has ______ minutes.
How many minutes are in 12 hours?

How many minutes are in 24 hours?

10. One hour has ______ minutes, and one minute has ______ seconds.

How many seconds are there in one hour?

11. Ed earns \$30 per hour.

a. How much will he earn in a 8-hour workday?

b. How much will he earn in a 40-hour workweek?

c. How many days will he need to work in order to earn more than \$1,000?

12. Find the missing factor. Think “backwards”! How many zeros do you need?

 a. _______ × 3 = 360     _______ × 50 = 450 b. 40 × _______ = 320    5 × ________= 600 c. ________ × 40 = 400    ________ × 2 = 180 d. _______ × 30 = 4,800    _______ × 200 = 1,800 e. 40 × ________ = 2,000    6 × _________= 4,200 f. ______ × 800 = 56,000    _______ × 20 = 12,000 John wanted to prove that 40 × 70 is indeed 2,800 by    breaking the multiplication into smaller parts. He wrote 40 as   4 × 10 and 70 as 7 × 10, and then multiplied in a different order: 40 × 70  =  4 × 10 × 7 × 10 = 10 × 10 × (4 × 7)  =  100 × 28  =  2,800. You do the same, and prove that 600 × 50 is indeed 30,000.

This lesson is taken from Maria Miller's book Math Mammoth Multiplication 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

#### Math Mammoth Multiplication 2

A self-teaching worktext for 4th grade that covers multiplying by whole tens and hundreds, multi-digit multiplication in columns, order of operations, word problems, scales problems, and money problems.