Notes for January 13

Proportions!!!

SOLVING SIMPLE ONES

Word of the Day

Inanestupid; dumb;

pathetic

Today’s ObjectiveIWBAT solve

algebraic proportions.

WARM-UPWrite each fraction in lowest terms (simplify).

1416

1.

972

3.

2464

2.

45120

4.

78

38

18

38

A ratio is a comparison of two quantities by division.

Ratios that make the same comparison are equivalent ratios.

In one rectangle, the ratio of shaded squares to unshaded squares is 7:5. In the other rectangle, the ratio is 28:20.

Both rectangles have equivalent shaded areas.

7:5 28:20

Example 1: Finding Equivalent Ratios

Find two ratios that are equivalent to each given ratio.

B.

185413

12848

A. =927 =9 • 2

27 • 2=9 ÷ 9

27 ÷ 9927 = Two ratios equivalent

to are and . 927

1854

13

Two ratios equivalent to are and . 64

2412848

83

=64 • 224 • 2

6424=

Multiply or divide the numerator and denominator by the same nonzero number.

83=64 ÷ 8

24 ÷ 86424=

Ratios that are equivalent are said to be proportional, or in proportion. Equivalent ratios are identical when they are written in simplest form.

Simplify to tell whether the ratios form a proportion.

1215

B. and 2736

327

A. and 218 Since ,

the ratios are in proportion.

19= 1

919=3 ÷ 3

27 ÷ 3327 =

19=2 ÷ 2

18 ÷ 2218 =

45=12 ÷ 3

15 ÷ 31215=

34=27 ÷ 9

36 ÷ 92736=

Since ,the ratios are not in proportion.

45 3

4

Simplify to tell whether the ratios form a proportion.

1449

B. and 1636

Since ,the ratios are in proportion.

15= 1

515=3 ÷ 3

15 ÷ 3315 =

15=9 ÷ 9

45 ÷ 9945 =

27=14 ÷ 7

49 ÷ 71449=

49=16 ÷ 4

36 ÷ 41636=

Since ,the ratios are not in proportion.

27 4

9

315

A. and 945

We can also use cross products to figure out whether two ratios are in proportion.

Tell whether the ratios are proportional.

410

615

Since the cross products are equal, the ratios are proportional.

60

=?

60 = 60

Find cross products.604

10615

Algebraic Proportions

Algebraic proportions are the same as regular proportions.

The cross-products must equal each other!

KEYPOINT

Solving Algebraic Proportions

To solve algebraic proportions, follow these steps:

1.) Cross-multiply2.) Set the products equal to

each other3.) Solve for x4.) Box your answer

Solving Algebraic Proportions

The most important thing to remember is to:

Solving Algebraic Proportions

Solve for x in the following proportion:

1242 x

Solving Algebraic Proportions

Cross-multiply

1242 x

2(12) = 24

4(x) = 4x

Solving Algebraic Proportions

Set the products equal to each other

4x = 24What am I

called?

Solving Algebraic Proportions

Solve for x 244 x

424

44

x

6x

Solving Algebraic Proportions

Solve for x in the following proportion:

6155

x

Solving Algebraic Proportions

Cross-multiply

6155

x

5(-6) = -30

x(15) = 15x

Solving Algebraic Proportions

Set the products equal to each other

15x = -30What am I

called?

Solving Algebraic Proportions

Solve for x 3015 x

1530

1515

x

2x

Try some with your partner!

2485 x

x72

1612

100252 x

3691

x

Try some on your own!

13

x6

3x

12

x2

12 3

24

5x

Notes for January 14th

Proportions!!!

SOLVING COMPLEX

ONES

Let’s not make it too

hard to begin with. Let’s start

by just throwing a coefficient in front of

the x.

More Complex Algebraic Proportions

What happens when you see one of these?

108

52

x

DO THE SAME THING!!!

More Complex Algebraic Proportions

Cross-multiply

108

52

x

2x(10) = 20x8(5) = 40

More Complex Algebraic Proportions

Set the products equal to each other

20x = 40What am I

called?

Solve for x 4020 x

2040

2020

x

2x

More Complex Algebraic Proportions

More Complex Algebraic Proportions

Solve the following proportion

x312

520

More Complex Algebraic Proportions

Cross-multiply

x312

520

20(3x) = 60x12(5) = 60

More Complex Algebraic Proportions

Set the products equal to each other

60x = 60What am I

called?

Solve for x 6060 x

6060

6060

x

1x

More Complex Algebraic Proportions

Try some with your partner!

243

85 x

x372

1612

1002

252 x

369

44

x

As a kicker, I have much expertise in

this manner …

LET’S KICK IT UP!!!

Even more complex algebraic proportions!

What happens when you see a proportion?

25

42

x

KEYPOINT!!! When solving proportions like

that, you must remember that each numerator and denominator are together – like a couple. You cannot separate them.So in order to do this, you must use the

Distributive Property.

Steps for Solving Complex

Proportions1.) Cross-Multiply2.) Set the products equal to

each other3.) Use the Distributive

Property4.) Solve for x5.) Box your answer

Even more complex algebraic proportions

Cross-multiply

25

42

x

2(x – 2) = 2(x – 2)

-4(5) = -20

Even more complex algebraic proportions

Set the products each to each other

2(x – 2) = -20

Even more complex algebraic proportions

Use the Distributive Property and solve for x

20)2(2 x2042 x

420442 x162 x

216

22

x

8x

Even more complex algebraic proportions!

Solve the following proportion:

25

36

xx

Even more complex algebraic proportions

Cross-multiply

25

36

xx

-2(x + 6) = -2(x + 6)3(x - 5) = 3(x – 5)

Even more complex algebraic proportions

Set the products each to each other

-2(x + 6) = 3(x – 5)

Even more complex algebraic proportions

Use the Distributive Property and solve for x

5)– 3(x 6) 2(x -

153122 xx15331232 xxxx

15125 x121512125 x

x 35

35 x

On Your Own!

2x 3

46

PRACTICE!It’ll be a Party in

Ms. Ryan’s Room!

24

32x

23x

46

Exit Ticket1. Are these two

ratios in proportion?j

A. YesB. NoC. Not sure

2. Solve for k: j

A. k = 40B. k = 4C. k = 5D. k = 8

3. Solve for x (simplify your answer): j

A. x = 12B. x = 4/7C. x = -21D. x = 12/214. Solve for b:

j

A. b = 1.5B. b = 8.5C. b = -1.5D. B = -8.5

67

32

x