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Mathematics · Ratio, proportion and percentages

Direct proportion

How do the ingredients in a recipe change when more guests come? Discover why the ratio of directly proportional quantities stays constant, the unit rate, the relationship y = kx and map scales.

  • 20 min
  • 1 simulation
  • Mini quiz

Updated:

Preview

The question

Selin has a cake recipe for 4 people: 200 grams of flour, 2 eggs and 100 grams of sugar. But 6 people are coming to the birthday party. Should Selin add 2 to every ingredient and use 202 grams of flour? Or should she scale the ingredients up some other way? By the end of this lesson you'll be able to scale up the recipe without a mistake.

Try it yourself

No account needed: change the values and check your answer. Some simulations ask for a prediction before they start; it doesn't matter whether it's right or wrong.

Number line

The price of pens

Drag the point or use the buttons to move in steps of 5 TL. When you reach the right value, press Check.

Prediction

Predict first

How do you think the total price changes when the number of pens goes from 6 to 10?

It doesn’t matter whether you’re right; the simulation opens once you choose.

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The embedded page sets no cookies and does no tracking. A small link back to Kuazara sits underneath.

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Frequently asked

5 questions

Going from 4 people to 6, why don't we just add 2 to each ingredient?

Direct proportion is a multiplicative relationship, not an additive one. 6 people is 1.5 times 4 people, so the flour also becomes 1.5 times as much: 200 × 1.5 = 300 grams. Adding 2 people means adding food for 2 people: 2 × 50 = 100 grams, not 2 grams.

If one quantity grows while the other grows too, are they directly proportional?

Not always. A child's height increases as their age increases, but a 10-year-old is not twice as tall as a 5-year-old. For direct proportion the ratio y ÷ x has to stay constant.

What is the constant of proportionality good for?

The constant of proportionality is the amount for 1 unit. If 3 kg of apples cost 45 TL, the constant is 45 ÷ 3 = 15 TL/kg. Once you have it, you can find the price of any amount with y = 15 · x: for 5 kg, 15 · 5 = 75 TL.

Why does the graph of a direct proportion pass through the origin?

Because when x = 0, y = k · 0 = 0: if there are no people, you need no flour. So the graph is a straight line through the origin. If the line does not pass through that point, for example when there is a fixed entry fee, the relationship is not a direct proportion.

Should I use the scale-factor method or the unit rate?

Both give the same answer. If the factor is easy, such as 2 times when going from 4 people to 8, use it. If the factor is a fraction, finding the value for 1 first is often easier: 200 grams for 4 people means 50 grams for 1 person and 300 grams for 6 people.