Math 1012 - Unit 4 (Ratios, Rates, Proportions, Measurement

Math 1012 - Ratios, Rates, Proportions, Measurement

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Ratios & Rates

• Ratios are used to compare amounts or quantities or describe a relationship between two amounts or quantities.

• Rates are a special type of ratio used to describe a relationship between different units of measure, such as speed, wages, or prices.

RATIOS

• Ratios compare quantities using division. This means that you can set up a ratio between two quantities as a division expression between those same two quantities.

• Example. If you have a platter containing 10 sugar cookies and 20 chocolate chip cookies, you can compare the cookies using a ratio.

• ratio of sugar cookies to chocolate chip cookies is: sugar cookies/chocolate chip cookies 10/20 = 1 to 2 or 1:2

RATES

• A rate is a ratio that compares two different quantities that have different units of measure.

• A rate is a comparison that provides information such as dollars per hour, feet per second, miles per hour, and dollars per Quart, for example.

• The word “per” usually indicates you are dealing with a rate. Rates can be written using words, using a colon, or as a fraction.

Multiple Choice

How many feet are in 2 1/2 miles?

• 5,280 feet

• 10, 560 feet

• 13,200 feet

Multiple Choice

A poll at Forrester University found that 4,000 out of 6,000 students are unmarried. Find the ratio of unmarried to married students. Express as a simplified ratio.

• 2 : 1

• 1 :2

• 2 : 3

Multiple Choice

Anyla rides her bike 18 blocks in 20 minutes. Express her rate as a simplified fraction.

• 18 blocks / 20 min

• 9 blocks / 10 min

• 1 block / 2 min

A unit rate compares a quantity to one unit of measure. You often see the speed at which an object is traveling in terms of its unit rate.

• Consider the example of a car that travels 300 miles in 5 hours. To find the unit rate, you find the number of miles traveled in one hour.

• 300 miles / 5 hours = 60 miles / hour

FINDING UNIT PRICE

• A unit price is a unit rate that expresses the price of something. The unit price always describes the price of one unit, so that you can easily compare prices.

Finding Unit Price

• A unit price is a unit rate that expresses the price of something. The unit price always describes the price of one unit, so that you can easily compare prices.

• The container on the left is cheaper, but you also get fewer blueberries. A better indicator of value is the price per single ounce of blueberries for each container.

Multiple Choice

A shopper is comparing two packages of rice at the grocery store. A 10-pound package costs $9.89 and a 2-pound package costs $1.90. Which package has the lower unit price to the nearest cent? What is its unit price?

• $0.99.

• $0.33

• $0.95

Proportions

Proportions

• A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. 

A proportion is usually written as two equivalent fractions.

• 12 inches / 1foot = 36 inches / 3 feet

Multiple Choice

Is the proportion 3/5 = 24/40 true or false?

• TRUE

• FALSE

If you know that the relationship between quantities is proportional, you can use

proportions to find missing quantities.

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Multiple Choice

Solve for the unknown quantity, x, 15/x = 6/10

• x = 25

• x = 150

• x = 30

VOLUMES & SOLIDS

Multiple Choice

Find the volume of a rectangular prism that is 8 inches long, 3 inches wide, and 10 inches tall (V = l •w • h).

• 24 inches³

• 21 inches³

• 240 inches³

Measurement & Length

Units of Length

• Length is the distance from one end of an object to the other end, or from one object to another.

• United States is based on the four customary units of

  length: inch, foot, yard, and mile.

Multiple Choice

A fence company is measuring a rectangular area in order to install a fence around its perimeter. If the length of the rectangular area is 130 yards and the width is 75 feet, what is the total length of the distance to be fenced?

• 130 feet

• 930 feet

• 690 feet

Measurement - Weight

Weight

• When you mention how heavy or light an object is, you are referring to its weight. In the U.S. customary system of measurement, weight is measured in ounces, pounds, and tons.

Multiple Choice

How many pounds is 72 ounces?

• 5 pounds

• 4 1/2 pounds

• 4 2/3 pounds

CAPACITY

The Metric System

What's the metric system?

• The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.

Multiple Choice

How many milliliters are in 1 liter?

• 10

• 100

• 1,000

• 10,000