NZ Level 6 (NZC) Level 1 (NCEA) Percentage Change
Lesson When using percentages in the real world, we often deal with changes to amounts using percentages, whether they're increases or decreases. In both cases, we can go through some shortcuts to find our final amount.

## On the Rise

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

## Going Down

Decreases are very similar to increases.

For example we want to see what $60$60 after a decrease of $5%$5% is equal to.

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

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

#### Worked Examples

##### 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

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

#### NA6-1

Apply direct and inverse relationships with linear proportions

#### 91026

Apply numeric reasoning in solving problems