Math 6 H Periods 1, 6 & 7 (Wednesday)

Equations: Decimals and Fractions 8-4


You can use transformations to solve equations which involve decimals or fractions

Solve 0.42 x = 1.05
Divide both sides by 0.42
.42x/.42 = 1.05/.42

now, do side bar and actually divide carefully and you will arrive at
x = 2.5

Solve: n/.15 = 92
multiply both sides by .15 to undo the division

(n/.15)(.15) = 92 (.15)
Again, do a sidebar for your calculations and you will arrive at

n = 13.80

How would we solve the following: (2/3)x = 6?

Let’s look at 2x = 6. What do we do?
We divide both sides by 2—or multiply both sides by the reciprocal of 2—which is ½
Remember the product of a number and its reciprocal is 1

Reminder: the ultimate objective is applying transformations to an equation is to obtain an equivalent equation in the form x = c
(where c is a constant.) Also remember that the understood (invivisble) coefficient of x in the equation x = c is 1. [Can you picture the poster in the front of the room?]
So to solve (2/3)x = 6 you would divide both sides by 2/3 but that is the same as multiplying by the reciprocal of 2/3, which is 3/2.

If an equation has the form

(a/b)(x) = c,
where both a and c are nonzero,
multiply both sides by b/a, the reciprocal of a/b
Solve (1/3)y = 18

(3/1)(1/3)y = 18(3/1)

y =18(3)
y = 54

Solve the equation: (6/7)n = 8

(7/6)(6/7)n = 8(7/6)

n = 8(7/6)

simplify first , then multiply
n = 28/3
n = 9 1/3
Let’s check

(6/7)n = 8
well, we said that n = 9 1/3 so substitute back, but change to 28/3 first
(6/7)(28/3) ?=? 8
[read ?=? as ‘does that equal?’]

Now really do a side bar with the left side of the equation to see what
(6/7)(28/3) really equals. Simplify before you multiply
2(4) = 8 so
8 = 8



Try:
1. (1/7)a = 13

2. b/8 = 16


3. 3.6d = 0.9


4. (3/8)f = 129