Ratio

Ratio and proportion

Share quantities; connect direct and inverse proportion.

Predict, test and explain

Step 1 of 3

Predict

Share 60 in the ratio 2:3. What is the first share?

60\div(2+3)=12

Scroll the diagram sideways to see every label.

A=24

B=36

Each equal part has the same value. The two shares add to the original total. Rounded labels may be approximate.

Shares
Quantity	Value
One part	$=12$
First share	$=24$
Second share	$=36$

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Predict

Try it in the simulation. Change one thing at a time.

Explain

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Hints, self-check and connections

Try a self-check

Fixed values, separate from the diagram controls.

y is directly proportional to x. When x = 3, y = 18. Find y when x = 5.

$y\propto x$

Hint

Find the constant y divided by x first.

Reveal answer

y = 30. The constant multiplier is 18 ÷ 3 = 6.

$y=6x,\qquad y=6\times5=30$

Build an explanation

Hint 1

For ratio sharing, add the ratio parts. Divide the total by that sum to find the value of one part.

Hint 2

In direct proportion, y = kx: y/x stays constant for non-zero x. Multiplying x by a factor multiplies y by the same factor.

Hint 3

In inverse proportion, y = k/x: xy stays constant and x cannot be zero. For positive quantities, doubling x halves y.

Worked example

This example uses fixed values, separate from the diagram controls.

Share £30 in the ratio 3:2. What are the shares if the total doubles and the ratio stays the same?

There are 3 + 2 = 5 equal parts. One part is £30 ÷ 5 = £6.
The shares are 3 × £6 = £18 and 2 × £6 = £12.
With a total of £60, one part is £12, so the shares become £36 and £24.
Each share doubled because each is directly proportional to the total when the ratio is fixed.

Answer: £18 and £12; with a £60 total, £36 and £24.

Connect this idea

Watch out: A straight-line graph shows direct proportion only when it passes through the origin. Inverse proportion uses a constant product, not a constant difference.