Ratio Calculator: Share, Simplify and Scale

Choosing the right mode

Four questions get set on this topic and they need four different pieces of arithmetic, so pick the mode that matches the wording in front of you before you type anything. A question that gives you an amount and asks you to divide it is a sharing question; one that gives you two measurements and asks for the simplest form is a simplifying question.

The sharing mode takes a total and two, three or four parts. The simplifying mode takes a value and a unit on each side, so 50 cm : 2 m can be entered exactly as it is written in the question rather than converted in your head first. The solving mode fills in the missing fourth value of a proportion, and the last mode rewrites any ratio as 1 : n for comparison.

Nothing is stored and nothing is sent anywhere. Change a figure and every line of working recalculates as you type.

• "Share PKR 6,000 in the ratio 3 : 4 : 5" — sharing mode
• "Write 45 minutes : 2 hours in its simplest form" — simplifying mode
• "3 : 8 = 12 : ?" or a recipe scaled up — solving mode
• "Which mix is stronger, 4 : 10 or 7 : 16?" — write both as 1 : n

The value of one part comes first

Sharing a total in a ratio is two steps, not one. Add the parts to find how many equal shares the total is being cut into, then divide the total by that sum to find what a single share is worth. Every share after that is a multiplication. The calculator prints that division on its own row — 60 ÷ 12 = 5 — because a pupil who writes it down almost never loses the question and a pupil who skips it usually does.

Simplifying works the other way round. Both sides are converted into the same unit, decimals are cleared by multiplying both sides by a power of ten, and then the highest common factor is divided out. The tool shows the converted pair, the factor it found and the division, so you can see why 50 cm : 2 m becomes 500 : 2000 and then 1 : 4.

Solving a : b = c : ? is shown twice over — once as a scale factor, where c ÷ a tells you what the whole ratio has been multiplied by, and once as the cross-multiplication that mark schemes accept. Both routes reach the same value, and different boards phrase the method differently, so it helps to recognise the one your teacher uses.

What it deliberately does not do

It does not read the question. Deciding whether 3 : 5 means three parts to five parts, or three parts out of five, is the comprehension the examiner is testing, and a tool that guessed would be doing the marked half of the work.

It does not round silently. Where a total will not divide exactly by the sum of the parts, it says so rather than quietly showing a decimal that looks like an answer. In a real exam question the numbers divide exactly, so a decimal share is nearly always a sign that a figure was copied down wrong.

It also will not convert between quantities that measure different things. Ask it for 3 kg : 4 litres and it refuses, because that ratio has no meaning, and a calculator that produced 3 : 4 anyway would be teaching a habit that fails later.

Where marks are actually lost

The single most expensive error in this topic is treating the second number of a ratio as a denominator. In 3 : 5 the first share is three eighths of the total, not three fifths, because the total is being cut into eight parts. The calculator states this in words underneath the shares for exactly the ratio you have entered.

The second is forgetting the units. 45 minutes : 2 hours is not 45 : 2; both sides have to be in the same unit before anything is cancelled, which is why the tool asks for a unit on each side rather than two bare numbers.

The third is answering the wrong question. Plenty of exam questions ask for the difference between two shares, or for how much more the largest share received, rather than for the shares themselves. The difference is shown alongside the shares so that step is not left as mental arithmetic at the end of a long calculation.