Solving Proportional Equations

Friday, April 21, 2023

We are learning to…use proportional reasoning to solve problem situations.

When is using the Equivalent Ratios Method not a good idea?

Terri eats 13 grapes in 23 minutes. At this rate how many grapes will she eat in 37 minutes?

Solve this proportional reasoning problem using the Equivalent Ratios Method.

When might using the equivalent ratios method not be the best way to find the solution to a proportional relationship problem?

Solving Proportional Equations

Today we are going to use our equation solving skills to solve proportional relationships.

When solving equations:– To eliminate ADDITION we used:– To eliminate SUBTRACTION we used:– To eliminate MULTIPLCATION we used:– To eliminate DIVISION we will use:

The goal when solving any equation is to isolate the variable.

SUBTRACTIONADDITION

DIVISION

MULTIPLICAT`ION

How would you isolate the variable for the equation ?

43

x

(3) (3)

12x CHECK:

12

34

43

x

=1/3x1/3x

1/3x1/3x

1/3x1/3x

x

43

x

How would you isolate the variable without creating a drawing?

167

y

7

y16(7) (7)

112y

CHECK!

Are these equivalent fractions?

11216

7

10 6 7 Use the Distributive Property

70 42 10 7 6 7

How would you isolate the variable without creating a drawing?

6

4 8

x

4

x 6

8(4) (4)

3x

CHECK!

Are these equivalent fractions?

3 6

4 8

6 4 24Multiply by the Numerator:

Divide by the Denominator:

24 8

How would you isolate the variable without creating a drawing?

8

9 5

g

8

9 5

g(5) (5)

44

9g

5 8 40Multiply by the Numerator:

Divide by the Denominator:

40 9 ? How many times does 9 go into 40

without going over?

4 whole times (36), with 4 left over

So…

44

9