Ratio, Proportion & Unitary Method
Simplify any ratio with HCF working, divide an amount in a given ratio with a bar model drawn for you, test proportion, find a missing term and solve unitary-method word problems — every step in real numbers.
To divide an amount in a ratio, add the parts, then find one part. For ₹1,200 in 2 : 3 : 7, the parts total 12, so one part is 1200 ÷ 12 = ₹100 and the shares are ₹200, ₹300 and ₹700. The unitary method works the same way: if 5 pens cost ₹60, one pen costs ₹12, so 8 pens cost ₹96.
See it
Table
Step-by-step working
How it is done
Worksheet — 10 questions
Answer key
Make a worksheet
Ten printable questions on the topic chosen above, with a teacher’s answer key.
Ratio and proportion, made visible
Pick what you need, type the numbers from your question, and get the answer with a bar model and the full working — exactly as it should be written in the notebook.
Choose the job
Simplify, divide in a ratio, check proportion, find a missing term or use the unitary method.
Type the numbers
Whole numbers, decimals and fractions like 3/4 all work. Answers stay as exact fractions.
Look at the bars
The bar model shows the ratio as equal parts, so the share for each person is easy to see.
Practise it
Switch to Practice for marked questions, or print ten questions with an answer key.
What a ratio is
A ratio compares two quantities of the same kind by division. 36 : 48 means “36 for every 48”, and it has no unit.
Simplify by dividing both terms by their HCF: 36 : 48 = (36÷12) : (48÷12) = 3 : 4
Dividing in a ratio
Each share = Total × (its part ÷ sum of parts)
₹1,200 in 2 : 3 : 7 → sum of parts 12, one part = 1200 ÷ 12 = ₹100, so the shares are ₹200, ₹300 and ₹700.
Proportion
Four numbers a, b, c, d are in proportion when a × d = b × c — the product of the extremes equals the product of the means.
3 : 8 :: 15 : 40 → 3 × 40 = 120 and 8 × 15 = 120, so they are in proportion.
Unitary method
Direct variation (more gives more): 5 pens cost ₹60 → one pen costs 60 ÷ 5 = ₹12 → 8 pens cost 8 × 12 = ₹96.
Inverse variation (more gives less): 6 workers take 12 days → one worker takes 6 × 12 = 72 days → 8 workers take 72 ÷ 8 = 9 days.
Ratio, Proportion & Unitary Method — your questions
How do I divide an amount in a given ratio?
Add the parts of the ratio to get the total number of parts, divide the amount by that total to find one part, then multiply by each part. Sharing ₹1,200 in 2 : 3 : 7 gives 12 parts, so one part is ₹100 and the shares are ₹200, ₹300 and ₹700. The shares must add back to ₹1,200.
How do I simplify a ratio?
Divide every term by their HCF. For 36 : 48 the HCF is 12, so the ratio becomes 3 : 4. If the terms are decimals or fractions, first multiply through to make them whole numbers. A ratio in its simplest form has no common factor left except 1, which is the form expected in an answer.
When are four numbers in proportion?
Four numbers a, b, c and d are in proportion when a × d = b × c — the product of the extremes equals the product of the means. For 3 : 8 :: 15 : 40, both products come to 120, so they are in proportion. The same cross-multiplication finds a missing term: if 4 : 9 :: 12 : x, then 4x = 108, so x = 27.
What is the unitary method?
Find the value of one unit first, then multiply up to the quantity you want. If 5 pens cost ₹60, one pen costs 60 ÷ 5 = ₹12, so 8 pens cost 8 × 12 = ₹96. This is direct variation, where more gives more, and it is the method behind most cost, distance and quantity word problems in middle school.
What is the difference between direct and inverse variation?
In direct variation more gives more, so you divide to find one unit and then multiply. In inverse variation more gives less, so you multiply to find the one-unit value. If 6 workers take 12 days, one worker would take 6 × 12 = 72 days, so 8 workers take 72 ÷ 8 = 9 days — fewer days, not more.
What is the most common mistake with units in a ratio?
Forgetting that a ratio has no units, so both quantities must be in the same unit first. 50 paise : ₹2 is not 50 : 2 — convert ₹2 into 200 paise and the ratio is 50 : 200 = 1 : 4. The same applies to metres and centimetres, kilograms and grams, and hours and minutes.
How do I convert a ratio into a percentage?
Add the terms to get the total, then write each term over that total and multiply by 100. For 3 : 5 the total is 8, so the parts are 3/8 = 37.5% and 5/8 = 62.5%, which add to 100%. As a fraction, the ratio 3 : 5 means the first quantity is 3/5 of the second, not 3/8 of it.