Using Ratio Tables to Find the Whole
Ratio tables can be used to find the whole when a part and its percent are known. Scale the given percent down to a benchmark like 10% or 25% by dividing both values, then scale up to 100% to find the whole. For example, 30 is 60% of what number: divide both by 6 to get 5 at 10%, then multiply both by 10 to find 50 at 100%. The whole is 50. This strategy from Reveal Math, Course 1, Module 2 gives 6th grade students a visual and organized method for percent-of problems.
Key Concepts
Property A ratio table can be used to find the whole by creating a series of equivalent ratios. You can scale the given part and percent up or down by multiplying or dividing both quantities by the same number. The goal is to find the value (the whole) that corresponds to $100\%$.
Examples 30 is 60% of what number? We can scale down from 60% to 10% by dividing by 6, and then scale up to 100% by multiplying by 10. $$ \begin{array}{|c|c|c|c|} \hline \textbf{Part} & 30 & 5 & 50 \\ \hline \textbf{Percent} & 60\% & 10\% & 100\% \\ \hline \end{array} $$ So, 30 is 60% of 50. 45 is 75% of what number? We can scale down from 75% to 25% by dividing by 3, and then scale up to 100% by multiplying by 4. $$ \begin{array}{|c|c|c|c|} \hline \textbf{Part} & 45 & 15 & 60 \\ \hline \textbf{Percent} & 75\% & 25\% & 100\% \\ \hline \end{array} $$ So, 45 is 75% of 60.
Explanation A ratio table helps organize the relationship between the part and the percent. Start by writing the known part and percent in the table. Then, find a convenient "benchmark" percent (like 1%, 5%, 10%, or 25%) by dividing both the part and the percent by the same number. Finally, multiply your new part and percent by a number that scales the percent to 100% to find the whole.
Common Questions
How do I use a ratio table to find the whole in a percent problem?
Write the known part and percent in the table. Scale down to a benchmark like 10% or 25% by dividing. Then scale up to 100% by multiplying to find the whole.
30 is 60% of what number?
Divide both by 6: 30 becomes 5 at 10%. Multiply both by 10: 5 becomes 50 at 100%. The whole is 50.
45 is 75% of what number?
Divide both by 3: 45 becomes 15 at 25%. Multiply both by 4: 15 becomes 60 at 100%. The whole is 60.
Why do we scale to 100% when finding the whole?
The whole always corresponds to 100%. By scaling the given ratio until the percent reaches 100, the part automatically becomes the whole.
When is a ratio table better than a proportion equation for percent problems?
A ratio table is more visual and organized, making it easier for students who prefer step-by-step scaling. Both methods give the same answer.
When do 6th graders use ratio tables for percent problems?
Module 2 of Reveal Math, Course 1 covers this in the Fractions, Decimals, and Percents unit.