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| In the previous
lesson, you learned one way to solve equations with a variable. |
 |
For 5 + n = 12, you can say "What
number plus 5 equals 12"? |
| From your "fact family"
knowledge, you know that 5 + 7 equals 12, so n = 7 |
|
Now you will learn another method of solving equations.
But first we need to review
Fact Families!
|
|
Given
the numbers 8, 2 ,10,
write four equations. |
8 + 2 = 10 |
| 2 + 8 =
10 |
| 10 - 8 =
2 |
| 10 - 2 =
8 |
Yes, for those three numbers,
you would use addition and subtraction
to make fact families.
Those two operations
(addition and subtraction) are called INVERSE operations.
|
Given
the numbers 7, 2, 14
write four equations. |
7 x 2 = 14 |
|
2 x 7 = 14 |
|
14 ÷ 2 = 7 |
|
14 ÷ 7 = 2 |
Yes, for those three numbers,
you would use multiplication and division to make fact families.
Those two operations
(multiplication and division) are also called INVERSE operations.
Remember: addition and
subtraction are inverse operations, and multiplication and
division are also inverse operations.
So let's see how this inverse
operation relationship can help you solve equations. Let's take the
above equation , n + 5 = 12 as an example. You knew, because
of mental math, that n
must equal 7, so now think of the fact families to see how you could use
5, 12, and get 7.
| 5 + 7 = 12 |
Yes,
to solve the original equation that used addition, you have to
use the inverse operation, subtraction. |
| 7 + 5 = 12 |
| 12 - 5 = 7 |
| 12 - 7 = 5 |
|
Let's try another one: Solve y + 3 = 11 (addition!)
|
| You know "8" + 3 = 11, and
also 11 - 3 = "8" |
So you can solve the addition
problem by subtracting!
y = 11 - 3 |
|
Let's try another one: Solve 9 + m = 15 (addition)
|
| You know 9 + "6" = 15, and
also 15 - 9 = "6" |
So you can solve the addition
problem by subtracting!
m = 15 - 9 |
|
Let's try another one: 8 x n = 16 (8n = 16)
(multiplication)
|
| You know
8 times "2" = 16, and also 16 ÷ 8 = "2" |
So you
can solve the multiplication problem by dividing!
n = 16 ÷ 8 |
|
Another one?: n ÷ 5 = 6 (division)
|
| You know
5 x 6 = "30", and also "30" ÷ 5 = 6 |
So you
can solve the division problem by multiplying!
n = 5 times 6 |
|
One more?: t - 9 = 10 (subtraction) |
| You know
10 + 9 = "19", and also "19" - 9 = 10 |
So you
can solve the subtraction problem by adding!
t = 9 + 10 |
|
So you ask yourself, "Does this
work every time?" "Can I always use the inverse operation
to solve an equation with a variable?" |
The
answer is almost always "YES"!
(One exception is in subtraction with the variable in the second
position e.g. 8 - t = 3; you wouldn't add to find the value of
t.
The other exception is in division with the variable in the
denominator. More about those later. ) |
|
equations with variables
and: |
example |
Solve and Explain. |
|
addition |
k + 9 = 16 |
by using inverse operation
(subtraction)
16 - 9 = k
7 = k |
|
subtraction |
m - 7 = 20 |
by using inverse operation
(addition)
20 + 7 = m
27 = m |
|
multiplication |
5g =20 |
by using inverse operation
(division)
20 ÷ 5 = g
4 = g |
|
division |
n ÷ 5 = 12 |
by using inverse operation
(multiplication)
12 x 5 = n
60 = n |
Review: Solve simple
one-step equations using inverse operations.
Let's Practice!
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