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Maths Exercices
Direct proportion

Two quantities are in direct proportion when they increase or decrease in the same ratio.

We want to paint our farm so we need to use the following paint mixture: four green pots and one pot white.


The ratio is 4 pots green to 1 pot white, or 4:1.

If we alse want to paint our neighbour's farm, which it is two times ours, we have to double the amount of paint and increase it in the same ratio.

We double the amount of green paint: 8 pots.
We double the amount of white paint: 2 pots.


The amount of green and white paint we need increase in direct proportion to each other.

Understanding direct proportions can help you to work out the value or amount of quantities either bigger or smaller than the one about which you have information.

How to solve proportions using the unitary method

If you know the cost of 4 light bulbs is £6.00, can you work out the cost of 3 light bulbs?

To solve this problem we need to know the cost of 1 light bulb.

If four light bulbs cost £6.00, then you divide £6.00 by 4 to find the price of 1 light bulb.
            (6 ÷ 4 = 1.5)

Now you know that they cost £1.50 each, to work out the cost of 3 light bulbs you multiply £1.50 by 3.

            (1.5 x 3 =4.5)

So, 3 light bulbs cost £10.00

How to solve proportions using the cross-multiply and divide method

direct proportion

The cost of 3 pens is 4.5 €. Work out the cost of 7 pens.

Two business associates invest money to set up a company. Initially John invests 690000 euros and Anthony 320000 euros. Two years later they share the profits in direct proportion to the amount of their initial investments. If Anthony receives 68000 euros, how much does John receive?
Solution =