Writing Ratios in Three Notations
Pre-algebra students in OpenStax Prealgebra 2E learn to express a ratio of two quantities in all three standard notations: word form (a to b), colon form (a:b), and fraction form (a/b). The ratio 20 to 36 can be written as 20:36 or 20/36, which simplifies to 5/9. Ratios compare same-unit quantities, and order matters: the ratio of 27 inches to 3 feet must first convert to common units (27 in to 36 in) before writing. Understanding all three notations is essential for proportional reasoning, unit rates, and algebraic problem solving.
Key Concepts
Property A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of $a$ to $b$ is written $a$ to $b$, $\frac{a}{b}$, or $a:b$.
Examples The ratio 20 to 36 can be written as $20\ \text{to}\ 36$, $20:36$, and $\frac{20}{36}$, which simplifies to $\frac{5}{9}$.
The ratio 45 to 18 can be written as $45\ \text{to}\ 18$, $45:18$, and $\frac{45}{18}$, which simplifies to $\frac{5}{2}$.
Common Questions
What are the three ways to write a ratio?
Word form (a to b), colon form (a:b), and fraction form (a/b). All three represent the same comparison.
How do you write the ratio 20 to 36 in all three forms?
20 to 36, or 20:36, or 20/36, which simplifies to 5/9.
Does the order of numbers in a ratio matter?
Yes. The ratio of a to b is different from b to a. Always match the order to the context described in the problem.
How do you compare quantities with different units in a ratio?
Convert both quantities to the same unit first, then write the ratio. For example, 27 inches to 3 feet becomes 27 inches to 36 inches.
What is the difference between a ratio and a fraction?
All ratios can be written as fractions, but fractions typically represent part-to-whole relationships while ratios compare any two quantities.