Ratio

Elementary SchoolMiddle School

Definition

Written in the form "A : B" or "A to B." It may also be described as the quotient of "A and B" It compares the porportion of A and B relative to each other. For example, if there are 5 oranges and 10 apples. The ratio can be written as 5 : 10 or 1 : 2 (simplified). Like fractions, ratios are written in its simplist form.

Worked examples

\(5\) oranges to \(10\) apples \(\)→\( 5:10 = 1:2\)

Divide both parts by their GCF (5) to simplify the ratio to lowest terms.

\(12\) boys and \(18\) girls \(\)→\( 12:18 = 2:3\)

The ratio compares boys to girls; simplify by dividing both by 6.

\(3:4\) can be written as \(\frac{3}{4}\) or \(3\) to \(4\)

All three forms represent the same comparison between the two quantities.

Common mistakes

\(5:10\) is already simplified → \(5:10 = 1:2\) Like fractions, ratios must be reduced by dividing both parts by their greatest common factor.
\(2:3\) means \(2\) out of \(3\) total → \(2:3\) means \(2\) parts to \(3\) parts (\(5\) total) A ratio compares two separate quantities, not a part to the whole.
\(\frac{1}{2} = 1:2\) → \(\frac{1}{2} = 1:1\) in ratio form, or \(1:2\) means \(\frac{1}{3}\) of the total The fraction \(\frac{1}{2}\) is one part to one other part (1:1), not one to two parts.

Where you'll use it next

Ratios are foundational for proportions, similar figures, scale drawings, unit rates, and percent problems. You'll use them in geometry for side lengths, in algebra for slope and direct variation, and in real life for recipes, maps, and mixtures.

Found in 1 StudyPug lesson

Introduction to Ratios: Understanding Proportional Relationships

Grade 8 Math

Dive into the world of ratios and learn how to compare quantities effectively. Master ratio notation, simplification, and real-world applications to enhance your problem-solving skills in mathematics and everyday life.

8th Grade8th