Stella Academy

elementary-math Module

Interactive Simulation Screen

SYS_OK

Lesson Directive // Proportions & RatiosREF_CORE

What is a Ratio?

a

b

=

c

d

Hover over a variable in the formula above, or see glossary below:

a

Part 1

units

b

Part 2

units

c

Scaled Part 1

units

d

Scaled Part 2

units

A ratio is a way to compare two or more quantities. If a recipe calls for 2 cups of flour for every 1 cup of sugar, the ratio of flour to sugar is 2 to 1 (written as 2:1 or 2/1).

INSIGHT: Ratios describe the relative sizes of two or more values.

What is a Proportion?

A proportion is simply an equation stating that two ratios are equal. If 2 cups of flour need 1 cup of sugar, then 4 cups of flour will need 2 cups of sugar.

INSIGHT: Proportions are scaled-up or scaled-down versions of the same ratio.

Solving for an Unknown

If you know three parts of a proportion, you can find the fourth using cross-multiplication. For a/b = c/d, it is always true that a×d = b×c.

INSIGHT: Cross-multiplication is a powerful tool to solve any proportion problem.

●Telemetry Control Console

CAL_SYS

Adjust Simulator Parameters

Syllabus Worked Example

Q: A car travels 150 miles on 5 gallons of gas. How many miles can it travel on 8 gallons?

1.Set up a proportion: \frac{\text{miles}}{\text{gallons}} = \frac{\text{miles}}{\text{gallons}}.

2.Plug in the known values: \frac{150}{5} = \frac{x}{8}.

3.Cross-multiply: 150 \times 8 = 5 \times x.

4.Solve the equation: 1200 = 5x, so x = \frac{1200}{5} = 240.

Result:x = 240 \text{ miles}