Ratios & Proportional Relationships

Ratio Tables

Using a table of equivalent ratios to solve problems.

Intermediate20 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Prerequisites

Unit Rates

Scaling a Relationship All at Once

A recipe for 4 people uses 2 cups of rice. Before reading on, predict how much rice is needed for 10 people — and think about whether there's a faster way to find that than scaling one person at a time.

Definition — Ratio Table

A table listing pairs of quantities that are all equivalent to the same ratio, generated by multiplying (or dividing) both original quantities by the same set of numbers.

Since every row of a ratio table represents the same underlying relationship, any row can be scaled to reach any other row — not just by repeating single steps, but by finding one scale factor that jumps straight from a known row to the one you need.

Worked Example — Building a Ratio Table

Extend the ratio table for the rice recipe (4 people : 2 cups rice) to show 8 people and 12 people. Doubling 4 people gives 8 people, so double the rice too: 4 cups. To reach 12 people, multiply the original 4 people by 3, so multiply the rice by 3 as well: 6 cups.

Worked Example — Finding a Missing Value Using a Scale Factor

Using the same recipe (4 people : 2 cups rice), how much rice is needed for 10 people? Find the scale factor from 4 to 10: 10 ÷ 4 = 2.5. Apply that same scale factor to the rice: 2 × 2.5 = 5 cups of rice.

Tip

A ratio table doesn't have to be built up one small step at a time — dividing the target quantity by a known quantity gives a scale factor that jumps directly to the answer.

Common Mistakes

Adding a fixed amount to move down a ratio table instead of multiplying, such as adding 2 cups of rice for every additional 4 people rather than scaling proportionally.
Every row in a ratio table is connected by multiplication, not addition — find the scale factor between two people-counts and apply that same factor to the other quantity.
Applying a scale factor to only one of the two quantities in the ratio.
Whatever number one quantity is multiplied by to reach a new row, the other quantity must be multiplied by that same number.

Key Takeaways

A ratio table lists several equivalent ratios, all scaled from the same original relationship.
Any two rows in a ratio table are connected by a single scale factor, found by dividing one quantity by the other.
That scale factor applies to both quantities in the ratio, not just one.

Summary

Ratio tables make scaling a relationship to any size a matter of finding one multiplying factor. The final lesson in this unit applies that same scaling idea to one of the most common rates in everyday life — percent.

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