 # 2.05 Percentage increase and decrease

Lesson

### Percentage increases

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, and then add the answer to $40$40:

$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 increase $40$40 by $2%$2%, we are essentially finding $100%+2%=102%$100%+2%=102% of $40$40.

Using the calculator:

$102%\times40=40.8$102%×40=40.8

Therefore increasing by $2$2% is the same as finding $102$102% of a quantity.

Increase by percentage

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

### Percentage decreases

Decreases are very similar to increases, however we will be multiplying by a number less than $100$100%.

For example, if 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, so the final amount is $60-3=57$603=57.

or another way to do this is to think of it as finding

$100%-5%=95%$100%5%=95% of $60$60

Using the calculator:

$95%\times60=57$95%×60=57

Therefore decreasing by $5$5% is the same as finding $95$95% of a quantity.

Decrease by percentage

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

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

Yes

A

No

B

##### Question 3

By what decimal should a quantity be multiplied in order to increase it by $7.7%$7.7%?

##### Question 4

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

#### ACMEM013

apply percentage increases and decreases in situations; for example, mark-ups, discounts and GST