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.
