Find Percentage of a Number and Again Go Back

Percentages

19 Finding the Percentage of a Given Number

It's Christmas, and the apprentices have a hazard to win the jar of candy on the left. The just requirement is that they estimate the number of candies in the jar.

Correct reply = 117

The winner is Bryce, a level 4 plumbing educatee. He credits his success in the processed counting game to the fact that his family endemic a candy shop when he was a kid, and information technology'south finally paid off.

Bryce decides to give some of the processed away. In fact, he decides to give 12% to his friend Patrick, 25% to his friend Matt, and 17% to his teacher.

The question becomes, how much practice each of these percentages represent out of the total number? And maybe in the end, we can notice out how much candy Bryce will go along for himself.

We'll offset with Patrick, who will get 12% of the candy. The showtime affair to practise is turn 12% into a fraction.

[latex]\Big\dfrac{12}{100}[/latex]

What this volition 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]

Take you noticed a pattern when information technology comes to decimals? Here is the relationship showing a few different means in which we can end up with 12%:

[latex]\LARGE12\%=\dfrac{12}{100}=0.12[/latex]

All three of these numbers represent the same corporeality. Learning to work between them is important in math, and it'south also important to begin to run into 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 past the number of candies in the jar.

[latex]\LARGE0.12\times117=14.04[/latex]

Now, slicing off 0.04 of a processed is hard to do, so nosotros'll use our rounding skills and circular down to 14 candies.

Now motility on to Bryce'south adjacent friend, Matt. Matt gets 25% of the candy.

Step 1: Plow the percentage into a fraction with a denominator of 100.

[latex]\Big\dfrac{25}{100}[/latex]

Step 2: Have the 25 and dissever it by the 100.

[latex]\LARGE25÷100=0.25[/latex]

Step iii: Take the 0.25 and multiply it past the number of candies in the jar.

[latex]\LARGE0.25\times117=29.25[/latex]

We would again circular downwardly to become our terminal respond of 29.

Nosotros won't worry nigh how many candies the instructor gets, simply what nosotros will calculate is how many candies Bryce keeps for himself. Nosotros want to calculate the percentage of candies Bryce ends up with, and so calculate how many candies that is.

Pace 1: Add upward the pct 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]\Big\text{Bryce gets }100\%-54\%=46\%[/latex]

Footstep 2: At this bespeak, nosotros've done a couple of examples in which we first took the pct and turned it into a fraction over 100. Then, nosotros took the percent and divided information technology by 100. What if we just skipped that step? What we end up doing for a percent is merely taking the decimal point and moving information technology over 2 places to the left (this represents dividing by 100). Try that.

[latex]\LARGE46\%=0.46[/latex]

Footstep 3: Accept the 0.46 and multiply it past the number of candies in the jar.

[latex]\LARGE0.46\times117=53.82[/latex]

This can be rounded upwardly to 54. Bryce still gets to consume a lot of processed, which will satisfy his sweet tooth, just he won't eat so much that he'll end up getting sick.

Practice Questions

Endeavor a couple of do questions. Check the video answer to see how you did.

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Source: https://opentextbc.ca/mathfortrades1/chapter/finding-the-percentage/

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