7.1 Ratio and Proportion

Objectives:

I will be able to…1. Discover and simplify ratios2. Discover and solve proportions3. Solve real life problems using ratios

& proportions

Intro• Who likes Coca-Cola?

• Ever wonder how much sugar you are really putting into your body each time you drink one?

VocabularyRatio: comparison of two quantities.

Ratio of a and b (3 ways to write it):

ba or a to b or a : b

Because a ratio is a quotient, the denominator cannot be zero

Using Ratios

Find the ratio of the length to width if AB = 36 cm and BC = 24 cm.

A B

D C*Always simplify

Using Ratios

The perimeter of an isosceles triangle shown is 56 inches. The ratio of LM : MN is 5 : 4. Find the lengths of the sides and the base of the triangle.

L

N M

20in:20in:16in

The perimeter of a triangle is 45in and the ratio of side is 1:3:5. Find the length of each side.

5, 15, 25 in

In a triangle, angles are in the ratio of 3:4:8. Find each angle.

36°, 48°, 96°

Using Ratios

Using Ratios in Real Life

• The ratio of male students to female students in the drama club at Campbell High School is 3:4. If there are a total of 42 students in the club, how many male and female students are there?

18 males and 24 females

Vocabulary

Proportion – two equal ratios made up of means and extremes

a

b

c

d

Extremes

Means

Are the following equations proportions?

a) 3 15 4 20

b) 4 12

6 16 c) 2 12

3 18

Simplify each ratio!

Vocabulary

Cross Product Property– the product of the extremes equals the product of the means.

a

b

c

d

Extremes

Means

ad = bc

Solving proportions.

a) 2

, solve for x7 21

x

b) 15 3 , solve for y

y 2 y

X = 6

y = ½

c) 3 2 , solve for z

4

z

z

z = -8

Using Proportions in Real Life

• A construction worker is placing rivets in a new bridge. He uses 42 rivets to build the first 2 feet of the bridge. If the bridge is to be 2200 feet in length, predict the number of rivets that will be needed for the entire bridge.

46, 200 rivets!

Exit Ticket• So, how many sugar

packets do you think are in a 20-oz. bottle of Coca-Cola?

• Based on the fact that there are 4 grams of sugar in 1 sugar packet, how many sugar packets are actually in a 20-oz. bottle of Coca-Cola?

Geometry

Homework:• p. 464 #12-14, 30, 40, 44, 46