Chapter 7 Section 1Ratios and Proportions

Objectives Students will be able to write and

solve ratios Students will be able to write and

solve proportions

Ratio Comparison of two quantities by

division Written as:

• a/b• a : b• a to b

Always write in simplest form (reduced form)

Make sure units of measure are the same

Example A bonsai tree 18 in wide and stands 2

ft tall. What is the ratio of the width compared to the height?

First covert measurements to either inches or feet

Then write the ratio in simplest form 18 : 24 3 : 4

Example A pigmy rattlesnake has average

length of 18 inches, while a Western diamondback rattlesnake averages 5ft. 6in. What is the ratio of the length of a pigmy to a Western diamondback rattlesnake?

18 : 66 3 : 11

Dividing Quantities into Ratios The measures of two supplementary angles are in

the ratio 1:4. What are the measures of the angles?

Write the ratio in words: angle 1 angle 2

Then write using variables: x 4x

Set up an equation: x + 4x = 180 Solve the equation: x = 36 Substitute x back into the ratio

Angle 1 = 1(36) = 36 Angle 2 = 4(36) = 144

Dividing Quantities into Ratios The measures of two complementary angles are in

the ratio 1:3. What are the measures of the angles?

Write the ratio in words: angle 1 angle 2

Then write using variables: x 3x

Set up an equation: x + 3x = 90 Solve the equation: x = 22.5 Substitute x back into the ratio

Angle 1 = 1(22.5) = 22.5 Angle 2 = 3(22.5) = 67.5

Extended Ratio Compares 3 or more numbers Written as

• a : b : c

Example The lengths of the sides of a triangle are

in the extended ratio 4 : 7 : 9. The perimeter is 60 cm. What are the lengths of the sides?

Write an equation: 4x + 7x + 9x = 60 Solve for x: x = 3 So the lengths of the sides are:

• 4(3) = 12• 7(3) = 21• 9(3) = 27

Proportions When two ratios are equal Use cross products to solve

proportions

Properties of Proportions

Solving 9 = a

2 14 15 = 3

m+1 m

Writing Equivalent Proportions x/6 = y/7 What ratio completes the

equivalent proportion?• x/y = ?• 6/x = ?• (y + 7)/7 = ?

Homework Pg. 436 #9 – 32, 40 – 43