Percentages
19 Finding the Percentage of a Given Number
It’s Christmas, and the apprentices have a chance to win the jar of candy on the left. The only requirement is that they guess the number of candies in the jar.
Correct answer = 117
The winner is Bryce, a level 4 plumbing student. He credits his success in the candy counting game to the fact that his family owned a candy store when he was a kid, and it’s finally paid off.
Bryce decides to give some of the candy away. In fact, he decides to give 12% to his friend Patrick, 25% to his friend Matt, and 17% to his instructor.
The question becomes, how much do each of these percentages represent out of the total number? And maybe in the end, we can find out how much candy Bryce will keep for himself.
We’ll start with Patrick, who will get 12% of the candy. The first thing to do is turn 12% into a fraction.
[latex]\LARGE\dfrac{12}{100}[/latex]
What this will eventually tell us is that, for every 100 candies there are in the jar, Patrick will get 12 of them. Now turn that fraction into a decimal by dividing 12 by 100.
[latex]\LARGE12÷100=0.12[/latex]
Have you noticed a pattern when it comes to decimals? Here is the relationship showing a few different ways in which we can end up with 12%:
[latex]\LARGE12\%=\dfrac{12}{100}=0.12[/latex]
All three of these numbers represent the same amount. Learning to work between them is important in math, and it’s also important to begin to see the relationships between numbers. Okay, back to Patrick.
The final step in this situation is to take the 0.12, which is really 12%, and multiply it by the number of candies in the jar.
[latex]\LARGE0.12\times117=14.04[/latex]
Now, slicing off 0.04 of a candy is hard to do, so we’ll use our rounding skills and round down to 14 candies.
Example
Now move on to Bryce’s next friend, Matt. Matt gets 25% of the candy.
Step 1: Turn the percentage into a fraction with a denominator of 100.
[latex]\LARGE\dfrac{25}{100}[/latex]
Step 2: Take the 25 and divide it by the 100.
[latex]\LARGE25÷100=0.25[/latex]
Step 3: Take the 0.25 and multiply it by the number of candies in the jar.
[latex]\LARGE0.25\times117=29.25[/latex]
We would again round down to get our final answer of 29.
Example
We won’t worry about how many candies the instructor gets, but what we will calculate is how many candies Bryce keeps for himself. We want to calculate the percentage of candies Bryce ends up with, and then calculate how many candies that is.
Step 1: Add up the percentage of the candies that the other three people have, and then subtract the sum from 100.
- Patrick gets 12%
- Matt gets 25%
- Instructor gets 17%
[latex]\LARGE12\%+25\%+17\%=54\%[/latex]
[latex]\LARGE\text{Bryce gets }100\%-54\%=46\%[/latex]
Step 2: At this point, we’ve done a couple of examples in which we first took the percentage and turned it into a fraction over 100. Then, we took the percentage and divided it by 100. What if we just skipped that step? What we end up doing for a percentage is just taking the decimal point and moving it over 2 places to the left (this represents dividing by 100). Try that.
[latex]\LARGE46\%=0.46[/latex]
Step 3: Take the 0.46 and multiply it by the number of candies in the jar.
[latex]\LARGE0.46\times117=53.82[/latex]
This can be rounded up to 54. Bryce still gets to eat a lot of candy, which will satisfy his sweet tooth, but he won’t eat so much that he’ll end up getting sick.
Practice Questions
Try a couple of practice questions. Check the video answer to see how you did.
Question 1
Find 37% of 229
Question 2
Find 78% of 1928