Ratio
A ratio is a comparison of two quantities expressed as a fraction, with a colon (3:4), or in words (3 to 4). Ratios describe relationships between parts, and should always be reduced to simplest form — but unlike mixed numbers, ratios are not written as improper fractions converted to mixed numbers. For example, if a class has 12 boys and 18 girls, the ratio of boys to girls is 12:18, which simplifies to 2:3. This 7th grade math concept is foundational for proportional reasoning and is covered in Saxon Math, Course 2.
Key Concepts
Property A ratio is a way to describe a relationship between two numbers. A ratio like 3 to 4 can be written as $3:4$ or as a fraction, $\frac{3}{4}$. Ratios are usually reduced to their simplest form but are not expressed as mixed numbers.
Examples In a class of 28 students with 12 boys, there are 16 girls. The boy girl ratio is $\frac{12}{16}$, which simplifies to $\frac{3}{4}$. If the ratio of red marbles to green marbles is 4 to 5, the 'total' part of the ratio is $4+5=9$. The fraction of red marbles is $\frac{4}{9}$. A team won 4 out of every 7 games played, so they must have lost 3. The team's win loss ratio is 4 to 3, or $\frac{4}{3}$.
Explanation Ratios are fantastic for comparing quantities, like the number of wins to losses for your favorite team. They can be written as fractions or with a colon. The trick is to remember the 'secret' third number: the total! If a win loss ratio is 4 to 3, the total number of games considered in that set is 7. This helps solve many problems.
Common Questions
What is a ratio in math?
A ratio is a comparison of two quantities. For example, if there are 3 cats and 4 dogs, the ratio of cats to dogs is 3:4, or 3/4, or ‘3 to 4.’
How do you write a ratio?
A ratio can be written three ways: with a colon (3:4), as a fraction (3/4), or in words (3 to 4). All three mean the same thing.
How do you simplify a ratio?
Divide both numbers in the ratio by their greatest common factor (GCF). For 12:18, the GCF is 6, so 12:18 simplifies to 2:3.
What is the difference between a ratio and a fraction?
A fraction represents a part of a whole (numerator/denominator). A ratio compares two separate quantities that may or may not be part/whole. However, ratios can be written as fractions and simplified the same way.
Why can’t ratios be written as mixed numbers?
Ratios are simplified but left as fractions, not converted to mixed numbers, because the ratio compares two things — converting to a mixed number would misrepresent that comparison.
When do students learn about ratios?
Ratios are introduced in 6th grade and extended throughout 7th grade math, where they form the basis for proportional reasoning, rates, and unit rates.
Which textbook covers ratios?
Saxon Math, Course 2 covers ratios and their applications in 7th grade math.