6 / 7 E-1
There are very simple SHORTCUTS for multiplying any number by 10, 100, or 1,000:
There are very simple 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.
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.
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 b. 20 × 5 c. 200 × 8 d. 200 × 25
= ______ × 2 × 7 =
______ × 2 × 5 =
______ × 2 × 8 =
______ × 2 × 25
= 10 × ______ =
10 × ______ =
________ =
100 × ______
= ________ =
________ = 100 × ______ = ________
4. Word problem:
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? SHOW YOUR WORK
SHORTCUT for multiplying by whole tens , whole hundreds and
whole thousands
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
5. Multiply.
40 × 3 = ______ 8
× 20 = ______ 70
× 6 = _______ 50 × 11 = ______
80 × 9 = _______ 30
× 15 = _______ 60
× 11 = _______ 12 × 40 = _______
2000 × 9 = _____ 7
× 400 = ______ 700
× 6 = ______ 600 ×
11 = ______
200 × 12 = ______ 15
× 300 = ______ 3
× 1100 = ______
8 × 900 = ______
11 × 120 = ______
8 × 300 = ______ 8
x 4000 = ______ 5 x 1000 = ______
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
6. Multiply.
20 × 90 = _________ 70 × 300 = ________ 60 × 80 = ________
30 × 900 = ________ 400 × 50 = ________ 200 × 200 = ________
80 × 800 = ________ 200 × 500 = ________ 100 × 100 = _______
40 × 30 = ________ 800 × 300 = ________ 90 × 1100 = ________
Application.
Write a number sentence for each question.
7. One hour has ______ minutes.
How many minutes
are in 12 hours?
How many minutes
are in 24 hours?
8. One hour has ______ minutes, and one minute has ______
seconds.
How many seconds
are there in one hour?
9. 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?
10. Find the missing factor. Think “backwards”! How many
zeros do you need?
_______ × 3 = 360 _______ × 50 = 450 40 × _______ = 320 5 × ________= 600
________ × 40 = 400 ________ × 2 = 180 _______ × 30 = 4,800 _______ ×
200 = 1,800
40 × ________ = 2,000 6 × _________= 4,200 ______ × 800 = 56,000 _______
× 20 = 12,000
