Proportion tables
Complete direct proportion tables with a whole or decimal constant and, in Grade 8, inverse proportion tables where the product stays the same.
Start over?
Teaching Guide: Ratio and Proportion from Grade 6 to Grade 8
Proportion is one of the maths tools used most outside school: comparing prices, scaling a recipe, working out a journey time or sharing money fairly. This free ratio and proportion worksheet generator builds A4 worksheets on proportion tables, direct and inverse proportion, compound proportion and sharing in a ratio, with real-life word problems, realistic numbers and exact answers, plus a step-by-step answer key.
Student worksheet 
Answer key Is it proportional?
Compare quotients and products to decide whether two quantities are in direct or inverse proportion, with traps such as quantities that grow together without being proportional.
Direct and inverse proportion
From the unitary method to the rule of three, with contexts such as prices, recipes, fuel use, workers and days or speed and time. The “Direct or inverse?” type mixes them.
Sharing in a ratio
Sharing an amount in direct proportion between two or three people and, in Grade 8, in inverse proportion using the reciprocals and the LCM. See also the fraction operations worksheets.
Compound proportion
Problems with three quantities where pupils decide whether each relation is direct or inverse before setting up a single proportion.
Step-by-step answer key
The data laid out, the kind of proportion and why, the unitary method or the rule of three, and the full answer. For more problems, try the maths word problems.
Frequently Asked Questions about Ratio and Proportion
How can I tell direct from inverse proportion?
Two quantities are in direct proportion when multiplying one by a number multiplies the other by the same number: all the quotients are equal (more kilograms, more money). They are in inverse proportion when multiplying one divides the other by the same number: all the products are equal (more workers, fewer days). If neither happens, they are not proportional.
How do you solve a direct proportion problem?
With the unitary method, find the value of one unit first: if 3 kg cost €6, 1 kg costs 6 ÷ 3 = €2, so 7 kg cost 2 × 7 = €14. With the rule of three, line the data up in two rows and work out x = (6 × 7) ÷ 3 = 14.
And an inverse proportion problem?
Multiply along the row and divide: if 6 workers take 10 days, 4 workers take x = (6 × 10) ÷ 4 = 15 days. The product 6 × 10 = 60 is the total amount of work, which does not change.
Which grades are the worksheets for?
Level 1 suits Grade 6 (the unitary method and whole constants), level 2 Grade 7 (the rule of three and decimal constants) and level 3 Grade 8 (decimals, inverse proportion, sharing in inverse proportion and compound proportion).
Are the answers exact?
Yes. The data are always chosen so that the answer is exact, with at most two decimal places for prices and measures, and with realistic numbers for each context.
Is any student data sent to a server?
No. Every worksheet is created in your browser and no student data is stored. Templates are kept in your browser’s memory.
More worksheet generators you may like
Map and Plan Scale
Ratio scale and scale bar worksheets: real and map distances, finding the scale, and village maps and floor plans printed at true size to measure with a ruler.
Percentage
Percentage of an amount, one amount as a percentage of another, increases and decreases with the multiplier, successive and reverse percentages, percentages, fractions and decimals and word problems, with a step-by-step answer key.
Statistical Charts
Pictograms, bar charts, line graphs and pie charts to read and to draw, and frequency tables with mode, mean and median, with new data every time and an answer key.