Hello, and welcome to this video about computation with percentages!
Today we’ll learn how to solve different types of problems involving percentages and how this skill can help you in the real world.
Before we get started, let’s review a few things.
First, a ratio is a comparison of two or more numbers.
Some ratios are part-to-whole ratios, comparing a part of something to the whole group.
A percent is a part-to-whole ratio that’s expressed as a fraction of 100.
For example, the percentage 80% means 80 out of 100.
In this case, 80 is the part and 100 is the whole.
Solving problems with percentages involves translating a word problem into a mathematical equation.
There are three types of problems with percentages:
one, finding the part,
two, finding the whole
and three, finding the percent.
We’ll discuss these three problem types together and work on some examples to help you understand how to solve them.
Let’s start with the first problem type, finding the part.
The first problem type involves finding part of a given number that’s equal to a given percent.
Consider the following percentage problem:
What is 60% of 5?
To answer this question, we need to understand the information we are given in the problem.
Let’s look at each part of the word problem and translate it into an algebraic equation.
The first part of the sentence, “What is,” means “What number is equal to.”
Since we don’t know the number in question, we use the variable n to represent this portion of the equation.
The next portion of the question is “60%.”
Since 60% equals 0.60, write 0.60 in the equation after the equal sign.
The next part of the question is “of.”
When translating written equations into numerical equations, the word “of” indicates multiplication.
Therefore, write a multiplication sign after 0.60 in the equation.
The last portion of the question is 5.
Write 5 after the multiplication sign in the equation.
From here, solve the equation for n.
0.60 times 5 equals 3, so n equals 3.
Therefore, 60% of 5 is 3.
Now it’s your turn.
Consider the following percentage problem:
40% of 20 is what number?
Pause the video here, convert the written equation into an algebraic equation, and solve.
Now that you’ve tried this one on your own, let’s take a look at it together.
The algebraic equation that represents this question is: 0.40 times 20 equals n.
From here, solve the equation for n.
0.40 times 20 equals 8, so n equals 8.
Therefore, 40% of 20 is 8.
Great job!
The next percentage problem type is finding the whole.
In these problems, we are given the percent and its equivalent part.
We need to identify the whole.
Consider the following percentage problem:
3 is 60% of what number?
To answer this question, we need to understand the information we are given in the problem.
Let’s look at each part of the word problem and translate it into an algebraic equation.
The question starts with “3 is,” which means “3 is equal to.”
Start the equation with 3 and an equal sign.
The next part of the question is 60%.
Since 60% equals 0.60, write 0.60 in the equation after the equal sign.
The next word in the question is “of.”
When translating written equations to algebraic equations, the word “of” indicates multiplication.
Therefore, write a multiplication sign after 0.60 in the equation.
The next part of the question is “what number.”
Since we don’t know what number is being referred to, use the variable n to represent this number.
When multiplying a number by a variable, remember that no multiplication sign is needed.
We can write the equation with the coefficient 0.60 next to the variable n.
From here, solve the equation for n.
To solve for n, isolate the variable by doing inverse operations.
The opposite of multiplying by 0.60 is dividing by 0.60, so divide both sides of the equation by 0.60.
3 divided by 0.60 equals 5, so write 5 on the left side of the equation.
And 0.60 divided by 0.60 equals 1, so write 1n, or just n, on the right side of the equation.
Therefore, 3 is 60% of 5.
Now it’s your turn.
Consider the following percentage problem:
50 is 20% of what number?
Pause the video here, translate the written equation into an algebraic equation, and solve.
Now that you’ve tried this one on your own, let’s take a look at it together.
The algebraic equation that represents this question is: 50 equals 0.20n.
From here, solve the equation for n.
To solve for n, isolate the variable by doing inverse operations.
The opposite of multiplying by 0.20 is dividing by 0.20, so divide both sides of the equation by 0.20.
50 divided by 0.20 equals 250, so write 250 on the left side of the equation.
Then, if we divide the right side of the equation, we'll get 1, so we're left with 1n on the right side of the equation.
Since 1n is the same thing as n, 250 is equal to n.
So 50 is 20% of 250.
Nice work!
The last percentage problem type involves finding the percent.
In these scenarios, we are given the part and the whole and we need to find the percent.
Consider the following percentage problem:
What percent of 5 is 3?
To answer the question, we need to understand the information we are given in the problem.
Let’s look at each part of the word problem and translate it into an algebraic equation.
The question starts with “What percent”.
Since we don’t know the percent, we'll use the variable p to represent this number.
The next word in the question is “of.”
Remember, when translating written equations into algebraic equations, the word “of” indicates multiplication.
Therefore, write a multiplication sign after p in the equation.
The next part of the question is the number 5.
Write 5 in the equation after the multiplication sign.
The next part of the question is the word “is.”
When translating written equations into algebraic equations, the word “is” means “is equal to.”
Therefore, write an equal sign after 5 in the equation.
The next part of the equation is the number 3.
Write 3 in the equation after the equal sign.
When multiplying a number by a variable, remember that no multiplication sign is needed.
We can write the equation with the coefficient 5 next to the variable p, like this.
From here, solve the equation for p.
To solve for p, isolate the variable by doing inverse operations.
The opposite of multiplying by 5 is dividing by 5, so divide both sides of the equation by 5.
5 divided by 5 equals 1, so write 1p, or just p, on the left side of the equation.
3 divided by 5 equals 0.60, so p is equal to 0.60.
Now that we know p is equal to 0.60, we need to convert the decimal into a percentage to answer the original question.
0.60 is equal to 60 over 100, or 60%.
Therefore, 3 is 60% of 5.
Now it’s your turn.
Consider the following percentage problem:
11 is what percent of 20?
Pause the video here, convert the written equation into an algebraic equation, and solve.
Now that you’ve tried this one on your own, let’s take a look at it together.
The algebraic equation that represents this question is: 11 equals 20p.
From here, solve the equation for p.
To solve for p, isolate the variable by doing inverse operations.
Simply divide both sides of the equation by 20.
20 divided by 20 equals 1, so write p on the right side of the equation.
And 11 divided by 20 equals 0.55, so p is equal to 0.55.
Now that we know that p is equal to 0.55, we need to convert this decimal into a percentage to answer our original question.
0.55 is equal to 55 over 100, or 55%.
Therefore, 11 is 55% of 20.
Great work!
Computations with percentages are used all the time in the real world.
For instance, store discounts, interest rates, and test scores are often expressed as percentages.
Percentages are also used when calculating the tip on a bill at a restaurant.
I have one more problem for you to try.
This one is a little more challenging, but I know you can handle it!
Consider the following percentage problem:
Rachael is taking her friend out to dinner.
When she gets the check, the total is $56.75, not including the tip.
Rachael wants to leave a 20% tip.
How much money should Rachael leave for a tip?
Pause the video here, translate the written equation into an algebraic equation, and then solve.
Now that you’ve tried this one on your own, let’s take a look at it together.
To answer this question, we need to figure out what number is equal to 20% of $56.75.
The algebraic equation that represents this question is: n equals 0.20 times 56.75.
From here, solve the equation for n.
0.20 times 56.75 is equal to 11.35, so n equals 11.35.
Therefore, for a 20% tip, Rachael should leave $11.35.
Great job!
I hope this video about computation with percentages was helpful.
Thanks for watching, and happy studying!