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Lesson · Grade 8 · Mathematics

Finding the original amount before an increase

  • Grade 8
  • Mathematics
  • 2 min 3 s
  • British Columbia
  • BC8-MA-09

A salary is now $93 940, which is 122% of what it was. A bar model shows that this is the original 100% plus a 22% increase; writing 122% as the multiplier 1.22 and dividing gives the original salary, $93 940 ÷ 1.22 = $77 000, which is checked by 77 000 × 1.22 = 93 940. The video then shows the common mistake of taking 22% off the new salary ($73 273.20), shows on the bars why it takes off too much, and ends on the recap: original amount = new amount ÷ multiplier.

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In one sentence

The question this lesson answers

A salary is now $93,940. That is 122% of what it was before. What was it before?

The amount before a change is called the original amount. It is the whole, so it is 100%.

Transcript

What the lesson says

A salary is now $93,940. That is 122% of what it was before. What was it before?

The amount before a change is called the original amount. It is the whole, so it is 100%.

The new salary is the whole 100%, plus a 22% increase. A percent over 100 means more than the whole.

Write 122% as a decimal: 122 divided by 100 is 1.22.

1.22 is the multiplier: the number you multiply the original by to get the new amount.

So the original salary times 1.22 equals $93,940.

To undo multiplying by 1.22, divide by 1.22.

$93,940 divided by 1.22 is $77,000. That was the original salary.

Check: $77,000 times 1.22 is $93,940, the new salary. It works.

A common mistake is taking 22% off the new salary. That leaves 78%, and $93,940 times 0.78 is $73,273.20.

That is wrong. The increase was 22% of the original, but 22% of the new salary is a bigger piece, so too much comes off.

So to find the original amount, divide the new amount by the multiplier: $93,940 divided by 1.22 is $77,000.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Number: percents less than 1 and greater than 100 (decimal and fractional percents)BC8-MA-09

Previous: Percent increase: finding the new amountNext: Rates and Unit Rates: How Much for One

The outcomes and strands follow the British Columbia curriculum.

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