4 1 ratios proportions
Download
Skip this Video
Download Presentation
4-1 Ratios & Proportions

Loading in 2 Seconds...

play fullscreen
1 / 25

4-1 Ratios & Proportions - PowerPoint PPT Presentation


  • 129 Views
  • Uploaded on

4-1 Ratios & Proportions. Notes. A ratio is a comparison of two quantities. . Ratios can be written in several ways . 7 to 5, 7:5, and name the same ratio. 15 ÷ 3 9 ÷ 3. bikes skateboards. Example 1: Writing Ratios in Simplest Form.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' 4-1 Ratios & Proportions' - kyrie


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide2

Notes

A ratio is a comparison of two quantities.

Ratios can be written in several ways.

7 to 5, 7:5, and name the same ratio.

slide3

15 ÷ 3

9 ÷ 3

bikes

skateboards

Example 1: Writing Ratios in Simplest Form

Write the ratio 15 bikes to 9 skateboards in simplest form.

15

9

Write the ratio as a fraction.

=

5

3

Simplify.

=

=

5

3

The ratio of bikes to skateboards is , 5:3, or 5 to 3.

slide4

shirts

jeans

24 ÷ 3

9 ÷ 3

Check It Out! Example 2

Write the ratio 24 shirts to 9 jeans in simplest form.

Write the ratio as a fraction.

24

9

=

8

3

Simplify.

=

=

8

3

The ratio of shirts to jeans is , 8:3, or 8 to 3.

practice
Practice
  • 15 cows to 25 sheep
  • 24 cars to 18 trucks
  • 30 Knives to 27 spoons
slide6

When simplifying ratios based on measurements, write the quantities with the same units, if possible.

slide7

3 yards

12 feet

9 ÷ 3

12 ÷ 3

=

=

=

3

4

3

4

The ratio is , 3:4, or 3 to 4.

Example 3: Writing Ratios Based on Measurement

Write the ratio 3 yards to 12 feet in simplest form.

First convert yards to feet.

3 yards = 3 ● 3 feet

There are 3 feet in each yard.

Multiply.

= 9 feet

Now write the ratio.

9 feet

12 feet

Simplify.

slide8

36 inches

4 feet

36 ÷ 12

48 ÷ 12

=

=

=

3

4

3

4

The ratio is , 3:4, or 3 to 4.

Check It Out! Example 3

Write the ratio 36 inches to 4 feet in simplest form.

First convert feet to inches.

4 feet = 4 ● 12 inches

There are 12 inches in each foot.

= 48 inches

Multiply.

Now write the ratio.

36 inches

48 inches

Simplify.

practice1
Practice
  • 4 feet to 24 inches
  • 3 yards to 12 feet
  • 2 yards to 20 inches
slide10

Notes

Ratios that make the same comparison are equivalent ratios.

To check whether two ratios are equivalent, you can write both in simplest form.

slide11

1

9

1

9

12

15

3

27

27

36

2

18

Since ,

the ratios are equivalent.

B.

A.

=

and

and

2

18

3

27

2 ÷ 2

18 ÷ 2

3 ÷ 3

27 ÷ 3

=

=

=

=

4

5

3

4

Since ,

the ratios are not equivalent.

12

15

27

36

12 ÷ 3

15 ÷ 3

27 ÷ 9

36 ÷ 9

=

=

=

=

Example 4: Determining Whether Two Ratios Are Equivalent

Simplify to tell whether the ratios are equivalent.

1

9

1

9

4

5

3

4

slide13

8

30

30

7

1

2

12

45

Possible answer: ,

Possible answer: ,

4

15

7

21

3.

4.

1

3

14

42

Lesson Quiz: Part I

Write each ratio in simplest form.

1. 22 tigers to 44 lions

2. 5 feet to 14 inches

Find a ratio that is equivalent to each given ratio.

slide14

36

24

16

10

5.

6.

8

64

16

128

and ; yes, both equal

28 18

32 20

8

5

3

2

14

9

8

5

1 8

=

; yes

; no

Lesson Quiz: Part II

Simplify to tell whether the ratios are equivalent.

and

and

7. Kate poured 8 oz of juice from a 64 oz bottle. Brian poured 16 oz of juice from a 128 oz bottle. Are the ratios of poured juice to starting amount of juice equivalent?

vocabulary
Vocabulary
  • A proportion is an equation stating that two ratios are equal.

To prove that two ratios form a proportion, you must prove that they are equivalent. To do this, you must demonstrate that the relationship between numerators is the same as the relationship between denominators.

examples do the ratios form a proportion
Examples: Do the ratios form a proportion?

x 3

Yes, these two ratios DO form a proportion, because the same relationship exists in both the numerators and denominators.

7

21

,

10

30

x 3

÷ 4

8

2

No, these ratios do NOT form a proportion, because the ratios are not equal.

,

9

3

÷ 3

example
Example

÷ 5

3

7

=

8

40

÷ 5

cross products
Cross Products
  • When you have a proportion (two equal ratios), then you have equivalent cross products.
  • Find the cross product by multiplying the denominator of each ratio by the numerator of the other ratio.
example do the ratios form a proportion check using cross products
Example: Do the ratios form a proportion? Check using cross products.

4

3

,

12

9

These two ratios DO form a proportion because their cross products are the same.

12 x 3 = 36

9 x 4 = 36

example 2
Example 2

5

2

,

8

3

No, these two ratios DO NOT form a proportion, because their cross products are different.

8 x 2 = 16

3 x 5 = 15

solving a proportion using cross products
Solving a Proportion Using Cross Products
  • Use the cross products to create an equation.
  • Solve the equation for the variable using the inverse operation.
example 1 solve the proportion
Example 1: Solve the Proportion

Start with the variable.

20

k

=

17

68

Simplify.

Now we have an equation. To get the k by itself, divide both sides by 68.

68k

17(20)

=

68k

=

340

68

68

k

5

=

example 2 solve the proportion
Example 2: Solve the Proportion

Start with the variable.

Simplify.

Now we have an equation. Solve for x.

2x(30)

5(3)

=

60x

=

15

60

60

x

¼

=

example 3 solve the proportion
Example 3: Solve the Proportion

=

Start with the variable.

Simplify.

Now we have an equation. Solve for x.

(2x +1)3

5(4)

=

6x + 3

=

20

x

=

example 4 solve the proportion
Example 4: Solve the Proportion

=

Cross Multiply.

Simplify.

Now we have an equation with variables on both sides. Solve for x.

3x

4(x+2)

=

3x

=

4x + 8

x

-8

=

ad