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Mathematics · Ratio, proportion and percentages

What is a ratio?

Is the player who scores more baskets the more accurate one? Learn to compare two quantities by dividing, how to write a ratio, why order matters, and unit rates such as km/h, with examples from sport and shopping.

  • 15 min
  • 1 simulation
  • Mini quiz

Updated:

Preview

The question

A player is being picked for the school basketball team. In practice, Ali took 20 shots and scored 15. Burak took 12 shots and scored 10. Ali scored more baskets. But does that mean Ali is more accurate? Who should the coach pick?

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Number line

The goalkeeper's save rate

Drag the point or use the buttons to move in steps of 0.05. When you reach the right place, press Check.

Prediction

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Where do you think the goalkeeper's save rate falls on the number line?

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Frequently asked

5 questions

What is a ratio?

A ratio compares two quantities by dividing. The ratio of a to b is written a : b or a/b, and it answers "how many times b is a?" or "how much a is there for each b?"

Does the order in a ratio matter?

Yes. If the ratio of lemon juice to water is 1 : 4, you add 4 measures of water for every 1 measure of lemon juice. Read it as 4 : 1 and you get very sour lemonade.

What is the difference between comparing by subtraction and comparing by ratio?

Subtraction answers "how many more?", a ratio answers "how much per try?" 15 hits out of 20 shots is 15/20 = 0.75, while 10 hits out of 12 is about 0.83. The player with fewer hits is more accurate by ratio.

What is a unit rate?

A rate where the second quantity is 1 unit, such as km/h or the price per kilogram. A car that travels 150 km in 2 hours covers 150 ÷ 2 = 75 km per hour on average.

Does a ratio have a unit?

A ratio of two quantities in the same unit has no unit: 3 m to 6 m is 1 : 2. A ratio of quantities in different units carries a unit; km/h is distance divided by time.