Equivalent Ratios
In short: Equivalent ratios are pairs of comparisons with identical value, built by scaling each term with one shared nonzero factor, so that 3 : 4, 6 : 8 and 12 : 16 all match.
6th GradeRatios and Percents6.RP.A.3a
What is Equivalent Ratios?
Two comparisons are equivalent ratios when they describe the same relationship at different sizes. A smoothie blending 3 cups of mango with 4 cups of yogurt keeps its taste in a triple batch.
Precisely, \(a : b\) and \(c : d\) are equivalent when a single nonzero number \(k\) satisfies \(c = k \cdot a\) and \(d = k \cdot b\). Their fractions \(\frac{a}{b}\) and \(\frac{c}{d}\) have the same value.
How to spot it
- A recipe must be doubled, tripled or cut in half while keeping the same taste or color.
- A table lists pairs of numbers where both columns grow by the same factor.
- You are asked whether two comparisons, such as 6 : 15 and 10 : 25, match.
- A problem gives one pair and asks for a missing number in a larger or smaller pair.
The method
- Choose the multiplier or divisor that links the known numbers, for instance \(3 \to 12\) uses \(\times 4\).
- Apply the same operation to the other number: \(4 \times 4 = 16\).
- Write the new pair, \(12 : 16\), and keep the order of the quantities.
- To test two pairs, check that the same factor works for both numbers, or compare simplified forms.
Equivalent Ratios: solved example
Problem
A paint mixer at a hardware store uses 5 drops of blue for every 9 drops of white. How many drops of blue go with 63 drops of white to get the same shade?
Solution
Compare the white amounts: \(9 \to 63\) means multiplying by \(63 \div 9 = 7\).
Multiply the blue by the same factor: \(5 \times 7 = 35\). The pair \(35 : 63\) matches \(5 : 9\), so the mixer needs 35 drops of blue.
Try it
Question 1
Are 6 : 15 and 10 : 25 a match?
Show the answer
Yes. Divide the first by 3 to get \(2 : 5\), and divide the second by 5 to get \(2 : 5\).
Question 2
Find the missing number: \(8 : 14 = \_\_ : 77\).
Show the answer
\(14 \times 5.5 = 77\), so \(8 \times 5.5 = 44\). The missing number is 44.
Equivalent Ratios vs. Proportion
Equivalent ratios are two comparisons with the same value, like 3 : 4 and 12 : 16. A proportion is the statement that links them with an equals sign, \(\frac{3}{4} = \frac{12}{16}\), often used to solve for an unknown number.
Keep going
Lessons
Worksheets and quizzes
- Ratio Tables and Graphs of Ratios – Worksheet
- Ratio Tables and Graphs of Ratios – Quiz
- Ratios and Ratio Language – Worksheet
- Ratios and Ratio Language – Quiz
Related words
Whole dictionary: A–Z · 6th Grade · Ratios and Percents