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Lesson · Grade 8 · Mathematics

Rates and Unit Rates: How Much for One

  • Grade 8
  • Mathematics
  • 2 min 4 s
  • British Columbia
  • BC8-MA-10

A car that travels 270 km in 3 hours is shown on a double number line, and dividing both rows by 3 gives the unit rate of 90 km/h, checked by counting up 90, 180, 270. The video then shows the common mistake of dividing 3 by 270, works a second example (48 L in 6 minutes is 8 L/min) and ends on a recap: divide both quantities by the same number so the second one is 1.

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In one sentence

The question this lesson answers

A car travels 270 kilometres in 3 hours. How far does it go in 1 hour?

This is a rate: it compares two quantities with different units, kilometres and hours.

Transcript

What the lesson says

A car travels 270 kilometres in 3 hours. How far does it go in 1 hour?

This is a rate: it compares two quantities with different units, kilometres and hours.

A unit rate is the amount for 1 unit of the second quantity. Here, that is the distance in 1 hour.

A double number line has two rows that line up matching amounts: kilometres on top, hours below.

Both rows start at 0, and 270 kilometres lines up with 3 hours.

We want 1 hour, so divide both rows by 3. 3 hours divided by 3 is 1 hour.

270 kilometres divided by 3 is 90 kilometres. So the car goes 90 kilometres in 1 hour.

Check by counting up one hour at a time: 90, 180, 270. Yes, 3 times 90 is 270.

So the unit rate is 90 kilometres per hour, where per means for each.

A common mistake is dividing the wrong way round: 3 divided by 270.

That gives about 0.011, which is hours for each kilometre, not kilometres in each hour.

We want kilometres per hour, so divide the kilometres by the hours.

Now a tap fills 48 litres in 6 minutes. How much does it fill in 1 minute?

We want 1 minute, so divide both rows by 6. 48 litres divided by 6 is 8 litres.

So the unit rate is 8 litres per minute. Check: 6 times 8 is 48.

A unit rate is how much for one. To find it, divide both quantities by the same number so that the second one is 1.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Number: numerical proportional reasoning (rates, ratio, proportions, and percent)BC8-MA-10

Previous: Finding the original amount before an increaseNext: Solving a proportion with equivalent ratios

The outcomes and strands follow the British Columbia curriculum.

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