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 $x$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$60−3=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 $x$x by $y%=x\left(100-y\right)%$y%=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
A bag of rice weighs $110$110kg. If the weight of the bag decreases by $40%$40% find the new weight of the bag.