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 $x$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$60−3=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 $x$x by $y$y$%$% $=$= $x\times\left(100-y\right)%$x×(100−y)%
Practice questions
Question 1
We want to increase $1300$1300 by $40%$40% by following the steps outlined below.
First find $40%$40% of $1300$1300.
Add the percentage increase to the original amount to find the amount after the increase.
Calculate $140%$140% of $1300$1300.
Is increasing an amount by $40%$40% equivalent to finding $140%$140% of that amount?
Yes
ANo
B
Question 2
We want to decrease $1500$1500 by $15%$15% by following the steps outlined below.
First find $15%$15% of $1500$1500
Subtract the percentage decrease from the original amount to find the amount after the decrease.
Calculate $85%$85% of $1500$1500
Is decreasing an amount by $15%$15% equivalent to finding $85%$85% of that amount?
Yes
ANo
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.