Proportion Tables

A proportion table shows two quantities that stay in the same ratio. If one row or column is known, you can use that constant relationship to find the missing values.

1) Identify the proportional relationship

Look for pairs of numbers that belong together. If one value is multiplied by a number, the matching value must be multiplied by the same number.

2) Find the scaling factor

Compare a known pair in the table. For example, if one value goes from 3 to 12, the factor is ×4. Use that factor to fill in the missing entries in the same row or column.

3) Use multiplication or division carefully

• Multiply when you move from a smaller known value to a larger one.
• Divide when you need to go backward from a larger known value to a smaller one.

If the table is incomplete in more than one place, first find one reliable pair, then use it to build the rest.

4) Check your answer

Verify that every completed pair has the same ratio as the others. A quick test is to compare cross-products or to see whether each row/column is scaled by the same factor.

5) Give an exact, simplified answer

Do not round. Write fractions in simplest form if needed, and keep numbers exact.

Example strategy

Start with a known value, find the multiplier, complete the remaining cells, then check that all rows and columns are consistent.