Notes for January 13 Proportions!!!. Word of the Day Inane stupid; dumb; pathetic.

Notes for January 13

Proportions!!!

SOLVING SIMPLE ONES

Word of the Day

Inanestupid; dumb;

pathetic

Today’s Objective

IWBAT solve algebraic proportions.

WARM-UP

Write 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.

1854

13

12848

A. =927

=9 • 227 • 2

=9 ÷ 927 ÷ 9

927

= Two ratios equivalent

to are and . 927

1854

13

Two ratios equivalent

to are and . 6424

12848

83

=64 • 224 • 2

6424

=

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

83

=64 ÷ 824 ÷ 8

6424

=

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

= 19

19

=3 ÷ 327 ÷ 3

327

=

19

=2 ÷ 218 ÷ 2

218

=

45=

12 ÷ 315 ÷ 3

1215

=

34=

27 ÷ 936 ÷ 9

2736

=

Since ,

the ratios are not

in proportion.

45

34

Simplify to tell whether the ratios form a proportion.

1449

B. and 1636

Since ,

the ratios are in

proportion.

15

= 15

15

=3 ÷ 315 ÷ 3

315

=

15

=9 ÷ 945 ÷ 9

945

=

27

=14 ÷ 749 ÷ 7

1449

=

49=

16 ÷ 436 ÷ 4

1636

=

Since ,

the ratios are not

in proportion.

27

49

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-multiply

2.) Set the products equal to each other

3.) Solve for x

4.) Box your answer


The most important thing to remember is to:


Solve for x in the following proportion:

124

2 x


Cross-multiply

124

2 x

2(12) = 24

4(x) = 4x


Set the products equal to each other

4x = 24What am I

called?


Solve for x 244 x

4

24

4

4x

6x


Solve for x in the following proportion:

6

155

x


Cross-multiply

6

155

x

5(-6) = -30

x(15) = 15x



15x = -30

What am I called?


Solve for x 3015 x

15

30

15

15 x

2x

Try some with your partner!

248

5 x

x

72

16

12

10025

2 x

36

91x

Try some on your own!

1

3x

6

3

x

1

2

x

2

12

3

2

4

5

x

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?

10

8

5

2x

DO THE SAME THING!!!


Cross-multiply

10

8

5

2x

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



20x = 40What am I

called?

Solve for x

4020 x

20

40

20

20x

2x



Solve the following proportion

x3

12

5

20


Cross-multiply

x3

12

5

20

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



60x = 60What am I

called?

Solve for x

6060 x

60

60

60

60x

1x


Try some with your partner!

24

3

8

5 x

x3

72

16

12

100

2

25

2 x

36

9

4

4x

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?

2

5

4

2

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-Multiply

2.) Set the products equal to each other

3.) Use the Distributive Property

4.) Solve for x

5.) Box your answer

Even more complex algebraic proportions

Cross-multiply

2

5

4

2

x

2(x – 2) = 2(x – 2)

-4(5) = -20


Set the products each to each other

2(x – 2) = -20


Use the Distributive Property and solve for x

20)2(2 x2042 x

420442 x162 x

2

16

2

2 x

8x

Even more complex algebraic proportions!

Solve the following proportion:

2

5

3

6

xx


Cross-multiply

2

5

3

6

xx

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


Set the products each to each other

-2(x + 6) = 3(x – 5)


Use the Distributive Property and solve for x

5)– 3(x 6) 2(x -

153122 xx

15331232 xxxx15125 x

121512125 x

x 3

535 x

On Your Own!

2

x 3

4

6

PRACTICE!

It’ll be a Party in

Ms. Ryan’s Room!

2

4

3

2x

2

3x

4

6

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 = 12/21

4. Solve for b: j

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

6

7

3

2 x

Notes for January 13 Proportions!!!. Word of the Day Inane stupid; dumb; pathetic.

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