Pre-Algebra
Ratios and rates
Ratios
20 practice questions
0 video lessons
Theory + worked examples
Ratios
California Pre-Algebra • Standard 6.RP.1 • Ratios & Rates
Ratios is the opening topic of Ratios & Rates in the California Common Core State Standards. It is aligned to Standard 6.RP.1, which requires students to understand ratios and generate equivalent ratios.
A ratio compares two quantities and can be written three ways and simplified like a fraction.
Theory
A ratio compares two quantities and can be written \(3:2\), \(3\text{ to }2\), or \(\dfrac{3}{2}\).
Simplify ratios like fractions, by dividing by a common factor.
A ratio compares two amounts.
Ways to write a ratio.
Equivalent ratios:
\[a:b=ka:kb\]
Part-to-part and part-to-whole are different comparisons.
How to work with ratios
- Identify the two quantities compared.
- Write them in order as \(a:b\).
- Simplify by a common factor.
- Scale up or down for equivalents.
Example 1 — Write a ratio
There are \(8\) boys and \(12\) girls. Write the ratio of boys to girls.
Solution
Simplify \(8:12\).
| \(8:12\) | \(=\) | \(2:3\) |
Example 2 — Part to whole
In Example 1, what is the ratio of boys to all students?
Solution
Total is \(20\).
| \(8:20\) | \(=\) | \(2:5\) |
Example 3 — Equivalent
Write a ratio equivalent to \(3:4\) with first term \(9\).
Solution
Multiply both by \(3\).
| \(3:4\) | \(=\) | \(9:12\) |
Example 4 — Simplify
Simplify the ratio \(15:25\).
Solution
Divide both by \(5\).
| \(15:25\) | \(=\) | \(3:5\) |
Common pitfalls
Order matters: \(3:2\) is not \(2:3\).
Part-to-whole uses the total, not the other part.
Simplify to lowest terms.
Frequently asked questions
What is a ratio?
A comparison of two quantities.
How do I simplify a ratio?
Divide both terms by a common factor.
Does order matter?
Yes.
Simplify \(8:12\).
\(2:3\).
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