Key takeaway: A ratio table is a table whose rows or columns list pairs of equivalent ratios, so every pair is found by multiplying or dividing both entries of another pair by the same number.
Grade 66.RP.A.3aRatios, Rates and Percents
Definition of Ratio Table
A ratio table organizes pairs of numbers that all show the same ratio. Each column (or row) holds one pair, and every pair is equivalent to the others.
Suppose a food truck sells 3 wraps for every 2 smoothies. A ratio table lists 3 and 2, then 6 and 4, then 9 and 6, and so on. To fill in a new column, multiply or divide both entries of an existing column by the same number, or add two columns together.
Notation
A ratio table has a label for each quantity and a column for each pair:
| Wraps | 3 | 6 | 9 | \(n\) |
|---|---|---|---|---|
| Smoothies | 2 | 4 | 6 | ? |
Each column is one equivalent ratio, such as \(3 : 2\) or \(9 : 6\).
Key facts
- Multiplying or dividing a whole column by one number creates another valid column.
- Two columns can be added to make a new column, because totals keep the same ratio.
- Plotting the columns as points on a graph puts them on a line through the origin.
- Pick convenient columns, such as the unit rate column, to reach the value you need faster.
Ratio Table example
A food truck sells 3 wraps for every 2 smoothies. On Saturday it sold 45 wraps. How many smoothies did it sell, if it kept the same ratio?
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Start with the column \(3\) wraps and \(2\) smoothies.
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Multiply the column by 5 to get \(15\) wraps and \(10\) smoothies.
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Multiply that column by 3 to get \(45\) wraps and \(30\) smoothies. (The two steps together multiplied by \(5 \times 3 = 15\).)
The truck sold 30 smoothies.
Common mistake
Watch out
Nora wants a new column in the 3-to-2 table. She adds 4 to both entries and writes \(7\) wraps and \(6\) smoothies.
Why it is wrong
Adding the same number to both entries changes the ratio: \(7 : 6\) is not \(3 : 2\). A new column must come from multiplying (or dividing) a whole column by one number, or from adding two whole columns. Times 2 gives \(6 : 4\); adding the columns \(3 : 2\) and \(6 : 4\) gives \(9 : 6\).
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Ratios, Rates and Percents