A ratio describes a multiplicative comparison between two quantities, with the order of the quantities determining its meaning; in context, each term must be identified with its units and interpreted as “for every” corresponding units of the other quantity. The understanding includes distinguishing part-to-part from part-to-whole comparisons, interpreting ratios represented in words, tables, diagrams, or and notation, and recognizing equivalent ratios as the same relationship rather than a difference comparison, supporting later proportional reasoning.
A ratio compares quantities by saying how much of one quantity there is for a given amount of another. The order matters.
In a class, 8 students choose soccer and 4 students choose basketball.
1. Identify the quantities and their units.
2. Write the ratio in the requested order.
The ratio of soccer students to basketball students is
This means for every 8 soccer students, there are 4 basketball students.
3. Simplify the ratio if possible.
Both numbers can be divided by :
So the relationship can also be described as 2 soccer students for every 1 basketball student. The ratios and describe the same relationship.
4. Notice the difference between part-to-part and part-to-whole.
This means 2 out of every 3 students are soccer students.
Always check the order and label what each number represents. For example, would mean basketball to soccer, not soccer to basketball.
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