warm up. chapter 4 solving & applying proportions

Warm UpSimplify each product.

1)

Chapter 4Solving & Applying

Proportions

Section 4 – 1 Ratio &

ProportionObjectives:

To find ratios & proportions

To solve proportions

Ratio:A comparison of two numbers by division

The ratio of a to b is:

a : b or , where b ≠ 0Examples:

Ratio of Girls to Boys is : 10 : 9

The Ratio of the number of Miles Run in 20 Minutes is :

Rate:When a and b represent quantities measured in different units

Unit Rate:A rate with a denominator of 1.

Example:

Example 1 Using Unit Rates

The table at the right gives prices for different sizes of Gatorade. A) Find the unit rate for the 12-oz size.

Price Volume

$1.00 12 oz

$1.75 20 oz

$2.50 32 oz

B) Find the unit rates for the other two sizes. Price Volu

me

$1.00 12 oz

$1.75 20 oz

$2.50 32 oz

D) Why are unit rates important?

C) Which of the three sizes has the lowest cost per ounce?

Unit Analysis:The process of selecting conversion factors to produce the appropriate factors.

Example: You need to convert 3 hours to minutes.

Conversion factor:

To change hours to minutes, multiply by the conversion factor:

= 180 Minutes

O Example: You need to convert 9 feet to yards.

Conversion factor:

To change feet to yards, multiply by the conversion factor:

= 3 yards

O Example: You need to convert 300 feet to miles.

Conversion factor:

To change feet to miles, multiply by the conversion factor:

≈ .06 miles

Important Conversions:

12 inches = 1 feet3 feet = 1 yard5,280 feet = 1 mile

60 seconds = 1 minute60 minutes = 1 hour24 hours = 1 day365 days = 1 year

16 ounces = 1 pound

100 cm= 1 meter

Example 2 Converting Rates

A) A cheetah ran 300 feet in 2.92 seconds. What was the cheetah’s speed in miles per hour?

Homework

Textbook Page 185 – 186; #1 – 13, 38 – 42 Even

B) A sloth travels 0.15 miles per hour. Convert this speed to feet per minute.

C) 1 qt/min = ____ gal/week

Section 4 – 1 Continued

Objectives:To solve proportions

Proportion:

An equation that states that two ratios are equal

Example:

Cross Products:

In the proportion, : ad and bc are the cross products

𝑎𝑏

=𝑐𝑑

Cross Products of a Proportion:

If , then ad = bc

Example: , so 2(12) = 3(8)

Example 4 Using Cross Products

A) Use cross products to solve the proportion

B) Use cross products to solve the proportion

C) Use cross products to solve the proportion

D) Use cross products to solve the proportion

Example 5 Solving Multi-Step Proportions

A) Solve the proportion

B) Solve

C) Solve

𝑥+214

=𝑥10

D) Solve

E) Solve

3+𝑥7

=48

You can use proportions to solve world problems!

To write a correct proportion, form rates on each side that compare units in the

same way,

Example:

Example 6 Real-World P.S.

A) In 2001, Lance Armstrong won the Tour de France, completing the 3454 – km course in about 86.3 hours. Traveling at his average speed, how long would it take him to ride 185 km? Round your answer to the nearest tenth.

B) Suppose you walk 2 miles in 35 minutes. How far would you walk in 60 minutes, if you were to continue at the same rate?

C) Suppose you walk 5 miles in 45 minutes. How far would you walk in 1 hour, if you were to continue at the same rate?

Homework

Page 185 – 186; #14 – 28 Even & 32 - 37