Chapter 2, Lesson 5: Solving Proportions

Ratio: a comparison of two quantities.
The ratio of a to b can be written as
§  a : b / §  / for
Proportion: a statement that two ratios are equal.

Examples

The ratio of the number of bones in a human’s ears to the number of bones in the skull is 3:11. There are 22 bones in the skull. How many bones are in the ears? / The ratio of red marbles to green marbles is 6:5. There are 18 red marbles. How many green marbles are there?
Rate: a ratio of two quantities with different units
Unit rate: a rate with the second quantity of 1 unit.

Examples

Ralf Laue of Germany flipped a pancake 416 times in 120 seconds to set the world record. Find the unit rate. Round your answer to the nearest hundredth.
Cory earns $52.50 in 7 hours. Find the unit rate. Round to the nearest hundredth if necessary. / A machine seals 138 envelopes in 23 minutes. Find the unit rate. Round to the nearest hundredth if necessary.

Cross Product Property

Words / Numbers / Algebra
In a proportion, cross products are equal.

Examples: Solve the proportions. Check your answers.

Percent: ratio that compares a number to 100.
You can use the proportion
to find unknown values.

Examples

Find 30% of 80. Use a proportion. / 230 is what percent of 200? Use an equation. / 20 is 0.4% of what number?
Use a proportion.
Find 20% of 60. / 48 is 15% of what number?
Scale: ratio between two sets of measurements.
A scale drawing or a scale model uses a scale to represent an object as smaller or larger than the actual object.

Examples

A contractor has a blueprint for a house drawn to the scale 1 in.:3 ft. A wall on the blueprint is 6.5 inches long. How long is the actual wall? / A contractor has a blueprint for a house drawn to the scale 1 in.:3 ft. A wall in the house is 12 feet long. How long is the wall on the blueprint?
The actual distance between North Chicago and Waukegan is 4 mi. What is the distance between these two locations on the map?
/ A scale model of a human heart is 16 ft long. The scale is 32:1 How many inches long is the actual heart that the model represents?

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