Solving EquationsSolving Equations

Medina 1

With Decimal & Fractions

Steps to Solve Fractions Steps to Solve Fractions EquationsEquations

Medina 2

2. Undo addition or subtraction

You may not have to do all the steps to solve the equation

“You know you are done solving when there is a positive 1 in front of the variable.”

3. Undo multiplication or division

1. Multiply the WHOLE EQUATION by the least common denominator

Fractions – Finding the Least Fractions – Finding the Least Common DenominatorCommon Denominator

Medina 3

1 2 3 4 5 6 7 8 9 10 11 121 1 2 3 4 5 6 7 8 9 10 11 122 2 4 6 8 10 12 14 16 18 20 22 243 3 6 9 12 15 18 21 24 27 30 33 364 4 8 12 16 20 24 28 32 36 40 44 485 5 10 15 20 25 30 35 40 45 50 55 606 6 12 18 24 30 36 42 48 54 60 66 727 7 14 21 28 35 42 49 56 63 70 77 848 8 16 24 32 40 48 56 64 72 80 88 96

9 9 18 27 36 45 54 63 72 81 90 99108

10 10 20 30 40 50 60 70 80 90100

110

120

11 11 22 33 44 55 66 77 88 99110

121

132

12 12 24 36 48 60 72 84 96108

120

132

144

4 6and

2, 4 8and

LCM=1LCM=122

LCM=8 LCM=8

Solving Equations with Algorithm Solving Equations with Algorithm

Medina 4

To Solve:

34x 3

1

Original problem

Multiply the whole equation by 4

Check answer

3 14 4

x 4                  What is the common

denominator? 3 Add 3 to both sides

44x 4

4x1 1

Divide both sides by 4

4

Solving Equations with Algorithm Solving Equations with Algorithm

Medina 5

3 14 4

1

Check:

14

1

4

1x

3 14 4

x

441

Solving Equations with Algorithm Solving Equations with Algorithm

Medina 6

3

94

x -

3x

To Solve:

x 12-1

Original problem

Check answer

4                  36-

3 3

Multiply the whole equation by 4

Divide both sides by 3What is the

common denominat

or?4

Solving Equations with Algorithm Solving Equations with Algorithm

Medina 7

12-

Check:

9- 9-

12x -

3

94

x -

3

94

-1

3

1

Steps to Solve Decimal Steps to Solve Decimal EquationsEquations

Medina 8

Multiplying the whole equation by a power of 10 that would make decimals into integersPowers of

10

Then solve the new equation using the 2 steps.

1 2 310 ,10 , 10

100,1000, 10000

Solving Equations with Algorithm Solving Equations with Algorithm

Medina 9

5.6 3.6y

56

To Solve:

x 2-1

Original problem

Check answer

10                  36

10 10

Multiply the whole equation by 10

Divide both sides by 10

What power of 10 would make both decimals whole numbers?

10

10y 56 56

10y 20-Subtract 56 to both sides

Solving Equations with Algorithm Solving Equations with Algorithm

Medina 10

Check:

3.63.6 2x -

5.6 3.6y

5.6 3.62-