Fractions, Decimals, Fractions, Decimals, and Percentsand Percents

Fractions, Decimals, Fractions, Decimals, and Percentsand Percents

Parts of the wholeParts of the whole

Let’s watch this clip to see how some people can be confused on how fractions and percents can be used as examples.

Percent comes from the Latin per centum, or “per hundred”Consequently, a number such as 32% can be written as “32 per hundred” or the fraction

32/100. This fraction is equivalent to the decimal

0.32.Percent – is a ratio of a

number to 100.

The word “percent” meaning “per hundred” is used to show parts of a whole, the same as a fraction is used to represent part of a whole.

If you had a pizza that was cut into 100 pieces, 25% of the pizza would be 25 pieces!

Let’s begin with a simple concept. Consider the blue square below. Let’s think of this blue

square as One Whole Square. How let’s divide it into 100 pieces—every piece just the same size as every other piece. We can easily see that every one of the 100 pieces is shaded blue. So we say 100% of the square is shaded

blue. So 100% and 1 Whole are the same thing.

Since percent means “per hundred” it tells us how many for each hundred, 25% means 25 for each hundred, or 25 out of each hundred.

Here is our One Whole Square with a portion shaded green. What percent is shaded green.

In percent, every whole is divide into 100 pieces. Now count the pieces shaded green. There are 50 pieces out of 100 shaded green,

so 50% is green.

Once again our One Whole Square has a portion shaded, this time it’s blue. What percent is shaded blue. Remember, in

percents, every quantity is divided into 100 pieces. Now count the pieces shaded blue.

There are 86 pieces out of 100 shaded blue, so 86% of the pieces are shaded

blue.

Can you calculate what percent of our “One Whole” that is shaded red?

The Relationship The Relationship Between Fractions Between Fractions

Decimals and Decimals and PercentsPercents

The Relationship The Relationship Between Fractions Between Fractions

Decimals and Decimals and PercentsPercents

All represent part of a wholeAll represent part of a whole

How do we get from one form to another?

A percent is based on the number in terms of 100 or “per hundred”.

12%; 4%; 0.05%...

A fraction is based on the number into

which the whole is divided (the

denominator).The numerator (the top)

is the PART, the denominator (the

bottom) is the whole.½; ¼; ⅝…

A decimal is based on the number in terms of tenth, hundredths, thousandths, etc…0.5; 0.05; 0.005

Fraction to Decimal Divide the denominator into the numerator.

Place a decimal after the number inside the division “box” and

attach as many zeros as necessary to

complete the division. If the quotient does not

come out evenly, follow the rules for

“rounding off” numbers.

numerator

denominator

Decimal to percent

.50 = 50%

(0.50 x 100 = 50.0) Attach the % sign

Move the decimal point two (2) places

to the right (this multiplies the

number by 100)

Percent to decimal

50% = .5050 ÷ 100 = .50

Move the decimal point two (2) places to the left (this divides the

number by 100)

Percent to fraction

Place the number over 100 and reduce.

Fraction to percent

Multiply the number by 100, reduce and

attach a percent (%) sign.

Decimal to fraction

You will be using place value to do this! Count the decimal places of the decimal starting from the

decimal point. If there is one decimal point, place the number over 10 and reduce. If there are two decimal places, place the number over

100, and reduce. If there are three decimal places, place the number over 1000, and

reduce…Etc.(This is really just using your knowledge of place value to

name the denominator.)

1 decimal place = tenths,2 decimal places =

hundredths,3 decimal places =

thousandths

Remember that fractions,

decimals, and percents are

discussing parts of a whole, not how large the whole is.

Fractions, decimals, and percents are part of our world.

They show up constantly when you least expect them. Don’t let them catch you off guard. Learn

to master these numbers.

Percents to Remember

Problem Solving with Problem Solving with PercentsPercents

Problem Solving with Problem Solving with PercentsPercents

When solving a problem with a percent When solving a problem with a percent greater than 100%, the greater than 100%, the partpart will be greater will be greater

than the than the wholewhole..

There are three types of percent problems: 1) finding a percent of a number,

2) finding a number when a percent of it is known, and 3) finding the percent when the

part and whole are known

1) what is 60% of 30?

2) what number is 25% of 160?

3) 45 is what percent of 90?