## ProportionalRelationships

A proportion is an equation stating that two ratios are equal.

Proportions are used to solve a variety of problems in real-life situations. For example, proportions are used to
convert from one set of units to another, such as miles to kilometers, pounds to ounces, or dollars to yen.
Proportions are also used when making comparisons of dimensions, such as converting inches on a map to
miles in the real world.

One should understand the relationship between scale factors and their inverses as they relate to choices about
when to multiply and when to divide in converting measurements.

Conversion may also involve derived units which include those that measure speed, density, flow rates, population
density, etc.

Example: Simple Unit Conversion

There are 60 minutes in 1 hour. How many minutes are there in 24 hours? Example: Derived Unit Conversion

Convert 13.4m3 to km3 #### Try these questions

1. John is cruising down the lodge at a speed of 162 ft/s. How fast is he traveling in miles/hour?

1. 238 miles/hour

2. 162 miles/hour

3. 110 miles/hour

4. 63 miles/hour

2. Suppose the speed limit is 65 miles/hour, will John get a ticket?

1. Yes

2. No

3. May be

3. Problem 1 is a combination of simple and derived unit conversion. True or False?

Answer: False. It is only a derived unit conversion problem. The derived unit is speed.

#### ANSWERS TO PRACTICE TEST QUESTIONS

1. C.          110 miles/hour 2. A.          Yes, because John's speed is over the speed limit of 65 miles/hour

3. False. It is only a derived unit conversion problem. The derived unit is speed.

#### FINAL TEST QUESTIONS

1. A container of sugar is reported to have a mass of 73,700 cg. Express this quantity in kg.

1. 73.7 kg

2. 7.37 kg

3. 0.737 kg

4. 0.0737 kg

2. What is the conversion factor you used to solve problem 1? That is, converting cg to kg.

1. 1/1000

2. 1/10000

3. 1/100000

4. 1/1000000

3. Express the volume of one liter in cubic meters.

1. Volume = 0.001 m3

2. Volume = 0.01 m3

3. Volume = 0.1 m3

4. Volume = 1 m3

4. How many hours are there in 6.5 days?

1. 72

2. 144

3. 156

4. 168

5. A piece of copper weighs 17.62 lb. What is the weight in kg?

1. 7.99 kg

2. 17.62 kg

3. 38.84 kg

4. 0.01762 kg

6. If a bumblebee weighs 0.0022 kg, how many bees weigh 5.0 lb?

1. Approximately 1030909 bumblebees

2. Approximately 5010 bumblebees

3. Approximately 4990 bumblebees

4. Approximately 1031 bumblebees

1. C

2. C

3. A

4. C

5. A

6. D