Problem-Solving with Proportions

What are conversion factors?

• Ratios that help you convert one unit of measurement to another.

• Numbers used to solve math problems.

• Symbols used in algebraic equations.

• Methods to measure distances accurately.

Answer explanation

Conversion factors are ratios that allow you to convert between different units of measurement. They show you how the units are related to each other. For example, if you want to convert feet to inches, the conversion factor is 1 foot = 12 inches.

An airport runway is 2 kilometers long. Convert this length to meters. Hint: 1 kilometer = 1000 meters

• 200 meters

• 20 meters

• 2000 meters

• 0.2 meters

Answer explanation

To convert kilometers to meters, use the conversion factor that 1 kilometer is equal to 1000 meters. Set up a proportion using the given value and the conversion factor:

Let 'x' represent the length of the runway in meters.

Proportion: 1 kilometer / 1000 meters = 2 kilometers / x meters

Cross-multiplying and dividing, you get: x meters = (1000 meters × 2 kilometers) ÷ 1 kilometer = 2000 ÷ 1 = 2000

Therefore, 2 kilometers is equal to 2000 meters.

Tags

CCSS.2.MD.A.2

A 6-foot tall ladder casts a shadow that is 10 feet long. If a tree casts a shadow that is 25 feet long, how tall is the tree?

• 12 feet

• 15 feet

• 18 feet

• 20 feet

Answer explanation

To solve this problem, set up a proportion using the ratios of the ladder's height to its shadow length and the tree's height to its shadow length.

Let 'x' represent the height of the tree.

Proportion: 6 feet / 10 feet = x feet / 25 feet

Cross-multiplying and dividing, you get: x feet = (6 feet × 25 feet) ÷ 10 feet = 150 ÷ 10 = 15 

Therefore, the tree is 15 feet tall.

Tags

CCSS.7.RP.A.3

A recipe calls for 3/4 cup of sugar. Convert this volume to tablespoons. Hint: 1 cup = 16 tablespoons

• 6 tablespoons

• 9 tablespoons

• 18 tablespoons

• 12 tablespoons

Answer explanation

To convert cups to tablespoons, use the conversion factor that 1 cup is equal to 16 tablespoons. Set up a proportion using the given value and the conversion factor:

Let 'x' represent the volume in tablespoons.

Proportion: 1 cup / 16 tablespoons = (3/4) cup / x tablespoons

Cross-multiplying and dividing, you get: x tablespoons = (16 tablespoons × (3/4) cup) ÷ 1 cup = 12 ÷ 1 = 12

Therefore, 3/4 cup of sugar is equal to 12 tablespoons.

Tags

CCSS.6.RP.A.3D

A train travels 150 miles in 3 hours. If another train travels 450 miles, how long does it take?

• 6 hours

• 7.5 hours

• 9 hours

• 10 hours

Answer explanation

Set up a proportion using the ratios of the distance and time taken by the first train and the second train.

Let 'x' represent the time taken by the second train.

Proportion: 150 miles / 3 hours = 450 miles / x hours

Cross-multiplying and dividing, you get: x hours = (450 miles × 3 hours) ÷ 150 miles = 1350 ÷ 150 = 9

Therefore, it takes the second train 9 hours to travel 450 miles.

Tags

CCSS.6.RP.A.3B