|
In the previous
lesson, you learned two "tricks" for doing mental math. In this
lesson, you will learn the last two "tricks": using the
Distributive Property and finding patterns!
Remember the Distributive
Property "breaks down" the larger number into smaller, more manageable
numbers. Calculate in your head, using the smaller numbers, then
combine them again!
a x (b +
c) = (a x b) + (a x c)
|
First, let's practice
"breaking down" large numbers! |
|
large number |
"broken down" number |
|
29 |
20 + 9 |
|
82 |
80 + 2 |
|
57 |
50 + 7 |
|
Now let's break down 82 and
use the smaller numbers (80 + 2) to calculate this problem in our
head (mental math). |
| EXAMPLE |
82
x 5 = (80 + 2) x 5 = (80 x 5) + (2 x 5) = 400 + 10 = 410 |
|
See how easy
that was? You can do it all without pencil and paper or
calculator! |
Ready for some more examples?
|
problem |
use
Distributive Property on which number |
rewrite
problem |
solve |
|
28 x 7 |
28 = 20 + 8 |
28 x 7=(20 + 8) x
7 =
(20 x 7) + (8 x 7) |
140 + 56 =
196 |
|
104 x 9 |
104 = 100 + 4 |
104
x 9 = (100 + 4) x 9 =
(100 x 9) + (4 x 9) |
900+ 36 =
936 |
|
212 x 6 |
212 = 200 + 12 |
212 x 6 =
(200 + 12) x 6 =
(200 x 6) + (12 x 6) |
1200 + 72 =
1,272 |
|
4 x 3½ |
3½ = 3 + ½ |
4
x 3½ = (3 + ½) x 4 =
(3 x 4) + (4 x ½) |
12 + 2 = 14 |
In our Base 10 system, the
easiest patterns involve the numbers that end in 0s, such as 10 or 20 or
30 or 400 or 6000 etc. You need to know the pattern after you know
the math fact involved:
- if it is multiplication, add
the zeros
- if it is division, subtract
the zeros
|
examples |
|
answer |
|
30 x 400 |
Use the math fact: 3 x 4 =
12
and the pattern
(1 zero + 2 zeros = 3
zeros)
to get the answer mentally! |
12,000 |
|
2400 ÷
60 |
Use the math fact: 24
÷
6 = 4
(2 zeros - 1 zero =
1 zero) |
40 |
Here is
another pattern you can use to calculate "hard" problems in your
head.
| Did
you know that you can take half of one factor and double the second
factor, and the product is the same? Look at this! |
| problem |
half of first factor |
double the
second factor |
answer |
| 4
x 12 |
half of 4 is 2 |
double 12 is 24 |
24 x 2 = 48 (and so is 4
x 12)!! |
| 12
x 35 |
half of 12 is
6 |
double 35 is 70 |
6 x 70 is
420(now isn't that easier?) |
Ready to
Practice?
|
