Download presentation

1
Ratio and Proportion

2
Computing Ratios If a and b are two quantities that are measured in the same units, then the ratio of a to be is a/b. The ratio of a to be can also be written as a:b. Because a ratio is a quotient, its denominator cannot be zero. Ratios are usually expressed in simplified form. For instance, the ratio of 6:8 is usually simplified to 3:4. (You divided by 2)

3
**Ex. 1: Simplifying Ratios**

Simplify the ratios: 12 cm b. 6 ft c. 9 in. 4 cm ft in.

4
**Ex. 1: Simplifying Ratios**

Simplify the ratios: 12 cm b. 6 ft 4 m in Solution: To simplify the ratios with unlike units, convert to like units so that the units divide out. Then simplify the fraction, if possible.

5
**Ex. 1: Simplifying Ratios**

Simplify the ratios: 12 cm 4 m 12 cm 12 cm 12 3 4 m ∙100cm

6
**Ex. 1: Simplifying Ratios**

Simplify the ratios: b. 6 ft 18 in 6 ft 6∙12 in 72 in 18 in in. 18 in. 1

7
Ex. 2: Using Ratios The perimeter of rectangle ABCD is 60 centimeters. The ratio of AB: BC is 3:2. Find the length and the width of the rectangle

8
Ex. 2: Using Ratios SOLUTION: Because the ratio of AB:BC is 3:2, you can represent the length of AB as 3x and the width of BC as 2x.

9
**Solution: Statement 2l + 2w = P 2(3x) + 2(2x) = 60 6x + 4x = 60**

Reason Formula for perimeter of a rectangle Substitute l, w and P Multiply Combine like terms Divide each side by 10 So, ABCD has a length of 18 centimeters and a width of 12 cm.

10
**Ex. 3: Using Extended Ratios**

The measures of the angles in ∆JKL are in the extended ratio 1:2:3. Find the measures of the angles. Begin by sketching a triangle. Then use the extended ratio of 1:2:3 to label the measures of the angles as x°, 2x°, and 3x°. 2x° 3x° x°

11
**Solution: Statement x°+ 2x°+ 3x° = 180° 6x = 180 x = 30 Reason**

Triangle Sum Theorem Combine like terms Divide each side by 6 So, the angle measures are 30°, 2(30°) = 60°, and 3(30°) = 90°.

12
Ex. 4: Using Ratios The ratios of the side lengths of ∆DEF to the corresponding side lengths of ∆ABC are 2:1. Find the unknown lengths.

13
**Ex. 4: Using Ratios SOLUTION:**

DE is twice AB and DE = 8, so AB = ½(8) = 4 Use the Pythagorean Theorem to determine what side BC is. DF is twice AC and AC = 3, so DF = 2(3) = 6 EF is twice BC and BC = 5, so EF = 2(5) or 10 4 in a2 + b2 = c2 = c2 = c2 25 = c2 5 = c

14
Using Proportions An equation that equates two ratios is called a proportion. For instance, if the ratio of a/b is equal to the ratio c/d; then the following proportion can be written: Means Extremes = The numbers a and d are the extremes of the proportions. The numbers b and c are the means of the proportion.

15
**Properties of proportions**

CROSS PRODUCT PROPERTY. The product of the extremes equals the product of the means. If = , then ad = bc

16
**Properties of proportions**

RECIPROCAL PROPERTY. If two ratios are equal, then their reciprocals are also equal. If = , then = b a To solve the proportion, you find the value of the variable.

17
**Ex. 5: Solving Proportions**

4 5 Write the original proportion. Reciprocal prop. Multiply each side by 4 Simplify. = x 7 4 x 7 4 = 4 5 28 x = 5

18
**Ex. 5: Solving Proportions**

3 2 = y + 2 y 3y = 2(y+2) 3y = 2y+4 y 4 =

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google