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1.02 Percentage increase and decrease

Lesson

Increasing by a percentage

Exploration

Let's say we wanted to increase $40$40 by $2%$2% and find the end amount. That means we would have to first find $2%$2% of $40$40, which we can work out here:

$40\times2%=0.8$40×2%=0.8 

So the final amount would be $40+0.8=40.8$40+0.8=40.8.

A quicker way to do this would be to think completely in percentages. To find $40$40 after the $2%$2% increase, we are essentially finding $100%+2%=102%$100%+2%=102% of $40$40.

Let's see where this new approach takes us! If we use our existing know-how about percentages, $102%\times40=40.8$102%×40=40.8 as well!

So now we know that to find the increased amount by a percentage, multiply the amount by ($100%$100% $+$+ percentage).

Increase by percentage

Increase $x$x by $y%=x\left(100+y\right)%$y%=x(100+y)%

 

Decreasing by a percentage

Decreases are very similar to increases.

Exploration

For example, say we want to decrease $60$60 by $5%$5%. This would mean finding $5%$5% of $60$60 first, which is $60\times5%=3$60×5%=3, and then subtracting this amount. So the final amount is $60-3=57$603=57

The easier way to do this is to think of it as finding $100%-5%=95%$100%5%=95% of $60$60.

$95%\times60=57$95%×60=57

This is the same answer we got before! So for these kind of questions, to find the decreased amount by a percentage, multiply the amount by ($100%$100% $-$ percentage). 

Decrease by percentage

Decrease $x$x by $y%=x\left(100-y\right)%$y%=x(100y)%

 

Practice questions

QUESTION 1

We want to increase $1300$1300 by $40%$40% by following the steps outlined below.

  1. First find $40%$40% of $1300$1300.

  2. Add the percentage increase to the original amount to find the amount after the increase.

  3. Calculate $140%$140% of $1300$1300.

  4. Is increasing an amount by $40%$40% equivalent to finding $140%$140% of that amount?

    Yes

    A

    No

    B

QUESTION 2

We want to decrease $1500$1500 by $15%$15% by following the steps outlined below.

  1. First find $15%$15% of $1500$1500

  2. Subtract the percentage decrease from the original amount to find the amount after the decrease.

  3. Calculate $85%$85% of $1500$1500

  4. Is decreasing an amount by $15%$15% equivalent to finding $85%$85% of that amount?

    Yes

    A

    No

    B

QUESTION 3

A bag of rice weighs $110$110kg. If the weight of the bag decreases by $40%$40% find the new weight of the bag.

Outcomes

1.1.5

apply percentage increase or decrease in contexts, including determining the impact of inflation on costs and wages over time, calculating percentage mark-ups and discounts, calculating GST, calculating profit or loss in absolute and percentage terms, and calculating simple and compound interest

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