Ratio Table
In short: A ratio table is a table that lists pairs of numbers sharing the same ratio, where every column is made by multiplying or dividing another column by one number.
6th GradeRatios and Percents6.RP.A.3a
What is Ratio Table?
A ratio table organizes equivalent pairs side by side so you can scale a recipe, a price or a distance up or down. Each row or column holds one quantity, and each pair keeps the same comparison.
Precisely, if one column is \(a\) and \(b\), every other column has the form \(k \cdot a\) and \(k \cdot b\) for a nonzero number \(k\). Adding two columns also gives a valid column, because \(ka + ma = (k+m)a\).
How to spot it
- A problem gives one pair, such as 4 cups for 6 servings, and asks about many other amounts.
- Some cells of a table are blank and the rest follow a repeating pattern of multiplying.
- You must find a total cost, time or length for several quantities of the same item.
- A question asks you to extend, scale up or scale down a known pair step by step.
The method
- Write the known pair in the first column, with each quantity in its own row and a label on each row.
- Pick a convenient multiplier, such as 2, 5 or 10, and apply it to both rows in a new column.
- Add or subtract columns when that reaches a target value faster than one big multiplication.
- Read the answer from the column that matches the target, and check that the ratio table keeps the same comparison in every column.
Ratio Table: solved example
Problem
A trail mix recipe at a camp in Colorado uses 7 ounces of oats for every 4 ounces of almonds. How many ounces of almonds go with 49 ounces of oats?
Solution
Start the table with the column \(7\) oats and \(4\) almonds. To reach 49 ounces of oats multiply by \(49 \div 7 = 7\).
Multiply the almonds too: \(4 \times 7 = 28\). The batch needs 28 ounces of almonds.
Try it
Question 1
A table has the columns 5 and 12, then 15 and ?. Fill in the blank.
Show the answer
The multiplier is \(15 \div 5 = 3\), so the blank is \(12 \times 3 = 36\).
Question 2
A ferry carries 9 cars in 2 trips. Use a ratio table to find how many cars it carries in 5 trips at that pace.
Show the answer
Add the columns for 2 trips (9 cars) and 3 trips (13.5 cars): that gives 5 trips and 22.5 cars, or scale by 2.5 directly: \(9 \times 2.5 = 22.5\).
Ratio Table vs. Double Number Line
A table lists pairs in columns and is best for adding or multiplying columns together. A double number line stretches both quantities along two parallel lines so you can see how they grow at equal spacing. Both display the same equivalent pairs.
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Whole dictionary: A–Z · 6th Grade · Ratios and Percents