Download 0.05 100 0.5 100 = 5 50 =

solve two-step equations with rational
numbers (decimals).
Goal: I will be able to
Tool Bag
Formulas, equations,
Vocabulary, etc.
Review
Here’s How…Notes & Examples
Division with Decimals
Option 1:
0.05

0.5
0.05  100 



0.5  100 
5

50
51

5 10
1

10
Option 2:
0.05

0.5
5 0.01

5 0.1
0.01

0.1
0.1 0.1

0.1
1

10
Method 1: Traditional + Decomposition
Example #1 0.5x  0.2  0.25
Goal: Get x by itself.
0.5x  0.2  0.2  0.05 How can I decompose 0.25?
0.5x  0.05
0.5 x 0.05

0.5
0.5
x  0.1
The inverse of multiplication is
division
Divide both sides by 0.5
Use division method reviewed.
Method 2: Clear Decimals
To clear decimals, multiply by
0.5x  0.2  0.25 the power of ten (10, 100, …)
0.5x(100)  0.2(100)  0.25(100)
50 x  20  25
What sum should we decompose
25 into?
50 x  20  20  5
50 x  5
Simplify
50 x
5

50
50
Divide both sides by 50.
1
x
10
Method 3: Change to Fractions
0.5x  0.2  0.25
What is 0.5 as a fraction?
5
2
25
x

10
10 100
5  10 
2  10  25
x

 
 
10  10  10  10  100
50
20
25
x

100
100 100
50
20 25
100
x

100
 
   100
100
100 100
What is 0.2 as a fraction?
What is 0.25 as a fraction?
Re-write with fractions.
Use our fraction skills, get a
common denominator.
What is the common
denominator?
Multiply by forms of 1.
Simplify.
Multiply everything by 100.
50 x  20  25
Simplify.
50 x  20  20  5 Decompose the 25.
50 x  5
Simplify.
50 x
5

50
50
1
x
10
Divide both sides by 50.
You Try
1) 0.28x  0.7  0.56
With your partner, solve
using 2 of the 3 ways.