Video: Percent of a Number

In this video, we will learn how to find the percentage of a number, including finding the part of the whole, and how to use this to solve word problems.

16:09

Video Transcript

In this video, we will learn how to find the percent of a number, including real-life problems in context.

We will begin by looking at some key facts about percentages. The word “percent” means out of 100. This means that 32 percent can be written as a fraction as 32 over or out of 100. The line in a fraction means divide, so 32 percent is the same as 32 divided by 100. Dividing by 100 moves all the digits two places to the right. So, 32 percent is the same as the decimal 0.32. We can, therefore, say that to convert a percentage into a decimal, we divide by 100. For example, 49 percent is equal to 0.49, and six percent is equal to 0.06. 240 percent is equal to 2.4. And in fact, any percentage greater than 100 will be equal to decimal greater than one. 14.7 percent is the same as the decimal 0.147.

We will now look at some percent of a number questions that we should be able to do mentally. We should recall that 50 percent is equal to the fraction one-half. This means that in order to find 50 percent of 42, we need to find a half of 42. One-half of 40 is equal to 20, and one-half of two is equal to one. Therefore, 50 percent of 42 is 21.

We should also recall that 25 percent is equal to one-quarter. This means that in order to find 25 percent of 80, we need to find one-quarter of 80. We can find one-quarter of any number by dividing by four or by halving and halving again. One-half of 80 is equal to 40, and a half of this is 20.

We should also recall that 75 percent is equal to three-quarters. We can, therefore, work out 75 percent of a number by finding 50 percent, 25 percent, and finding the sum of these values. Alternatively, we could find the 25-percent value and multiply this by three.

There are two other conversions we need to remember in order to solve percent of a number problems without a calculator. Firstly, 10 percent is equal to one-tenth. And secondly, one percent is equal to one hundredth. This means that in order to find 10 percent of a number, we divide by 10. And to find one percent, we divide by 100.

Let’s consider the question 10 percent of 56. This can be written as one-tenth of 56. As the word “of” in mathematics means multiply, we have one-tenth multiplied by 56. This could in turn be rewritten as 56 divided by 10. As this is equal to 5.6, we know that 10 percent of 56 is 5.6. We can calculate one percent of 245 in the same way. This is equal to one hundredth multiplied by 245 or 245 divided by 100. One percent of 245 is 2.45.

We can use this method for working out 10 percent and one percent to work out multiples of 10 and multiples of one. For example, 20 percent would be two times our 10 percent value, and seven percent would be seven times our one percent value. We will now use this knowledge to solve more complicated problems using calculator and non-calculator methods.

Fill in the missing value: 13 percent of 700 meters is blank centimeters.

There are two ways of approaching this problem. We could convert 700 meters into centimeters and then find 13 percent of this value. Alternatively, we could find 13 percent of 700 meters and then convert this into centimeters. We will use the second method in this case. The calculation 13 percent of 700 can be done with or without a calculator.

As the word ’percent’ means out of 100, we can write 13 percent as the fraction 13 over 100. The word ’of’ in mathematics means multiply, so we need to multiply thirteen one hundredths by 700. We could type this straight into the calculator. However, if we don’t have one, we could rewrite 700 as 700 over one. As 700 and 100 are both divisible by 100, we can cross simplify or cross cancel as shown. We then need to multiply the numerators and denominators separately.

13 multiplied by seven is equal to 91. This is because 10 multiplied by seven is 70 and three multiplied by seven is 21. Multiplying the denominators gives us one. And 91 divided by one is 91. This means that 13 percent of 700 is 91.

An alternative method would be to write the fraction thirteen one hundredths as a decimal. This is equal to 0.13. Multiplying this by 700 would also give us an answer of 91.

We could also work out 13 percent of any number by calculating 10 percent, three percent, and then adding our two answers. We can calculate 10 percent of any number by dividing the number by 10. Therefore, 10 percent of 700 is 70. We can work out one percent of any number by dividing by 100. Therefore, one percent of 700 is seven. Multiplying this by three gives us three percent of 700 is equal to 21. We can then add 70 and 21 to work out 13 percent of 700. This is equal to 91.

Using any one of these methods, we get the answer that 13 percent of 700 meters is 91 meters. There are 100 centimeters in one meter. So, to convert this answer into centimeters, we need to multiply by 100. 91 multiplied by 100 is 9100. Therefore, 13 percent of 700 meters is 9100 centimeters.

We will now look at another question, this time using a calculator method.

What is 72.3 percent of 376 rounded to the nearest hundredth?

In order to calculate any percentage of a number on a calculator, we firstly need to convert the percentage into either a fraction or a decimal. As the word ’percent’ means out of 100, we can convert from any percentage to a decimal by dividing by 100. When dividing by 100, all of our digits move two places to the right. This means that 72.3 divided by 100 is 0.723. The word ’of’ in mathematics means multiply, so we need to multiply 0.723 by 376.

Typing this into the calculator gives us 271.848. We were asked to round our answer to the nearest hundredth. This means to two decimal places. Therefore, the deciding number is the eight in the thousandths column. If the deciding number is greater than or equal to five, we round up. 271.848 to the nearest hundredth is 271.85. This means that 72.3 percent of 376 rounded to the nearest hundredth is 271.85.

We will now look at a question where the percentage is greater than 100.

What is 130 percent of 70?

As 130 percent is greater than 100, our number will actually increase. The answer must be greater than 70. Finding 130 percent of a number is the same as a 30-percent increase. We can do this using a couple of methods. One way would be to find 30 percent of 70 and then add the answer onto 70. In order to calculate 10 percent of any number, we divide by 10. Therefore, 10 percent of 70 is equal to seven. Multiplying this by three gives us that 30 percent of 70 is equal to 21.

An alternative method would be to turn 30 percent into a decimal, in this case 0.3, and then multiply by 70. This would also give us an answer of 21. We can, therefore, calculate 130 percent of 70 by adding 21 to 70. This is equal to 91.

A different method here would be to convert 130 percent into a decimal. We know that in order to convert from percentages to decimals, we divide by 100. Therefore, 130 percent is the same as 1.3. This means that we need to multiply 1.3 by 70. This is the same as 1.3 multiplied by 10 multiplied by seven. 1.3 multiplied by 10 is equal to 13. And we are left with 13 multiplied by seven. Once again, this gives us an answer of 91. 130 percent of 70 is 91.

Our last couple of questions involve slightly harder percentages in context.

Fill in the missing value: Six and three-quarter percent of 400 kilograms is blank kilograms.

Let’s begin by considering the percentage in this question, six and three-quarter percent. The fraction three-quarters written as a decimal is 0.75. This means that six and three-quarter percent is the same as 6.75 percent. We need to calculate 6.75 percent of 400 kilograms. To convert from a percentage to a decimal, we need to divide by 100. 6.75 divided by 100 is 0.0675 as all of our digits move two places to the right. We can, therefore, calculate 6.75 percent of 400 by multiplying 0.0675 by 400.

We could do this by multiplying by 100 and then multiplying by four. This gives us an answer of 27. Six and three-quarter percent of 400 kilograms is 27 kilograms. Therefore, the missing value in the statement is 27.

Fill in the missing value: 60.4 percent of a kilogram is blank grams.

We recall that 1000 grams is equal to one kilogram. This means that we need to calculate 60.4 percent of 1000 grams. To convert from a percentage to a decimal, we divide by 100. 60.4 divided by 100 is 0.604. This means that in order to calculate 60.4 percent of 1000 grams, we need to multiply 0.604 by 1000. Multiplying by 1000 moves all of our digits three places to the left. So, this is equal to 604. The missing value in the statement is 604 as 60.4 percent of a kilogram is 604 grams.

We will now summarize some of the key points from this video. The word ’percent’ means out of 100. This means that we can convert from percentages to decimals by dividing by 100. 34 percent is the same as the fraction 34 over 100 and the decimal 0.34.

We can work out the percent of any number using calculator and non-calculator methods. On a calculator, we simply multiply the fraction or decimal by the number. Some key conversions that help us with non-calculator methods are that 50 percent is equal to one-half, 25 percent is equal to one-quarter, and 75 percent is equal to three-quarters.

We also recall that 10 percent is equal to one-tenth and one percent is equal to one hundredth. This means that we can calculate 10 percent of any number by dividing by 10 and one percent of any number by dividing by 100. These allow us to calculate slightly more complicated percentages by looking at multiples of 10 and multiples of one.

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