# Fractions

Fun with Fractions

Jack Anderson

Bake a Cake with Fractions!

A Great Way to Review Basic Concepts

Expressing a Fraction as Part of a Whole

Classifying Fractions

Equivalent Fractions

Simplest Form of a Fraction

Fractions to Decimals

Let’s begin with a fun question to

*INTRODUCTION TO FRACTIONS *

*PicScience *

FRACTION

 A that names

of a whole

Or

of a group

GENERAL INFORMATION

 A fraction is always represented as a

with numerator and denominator

 Let’s Say

Or

 numerator (part chosen)

 denominator (total number of parts)

EXAMPLES OF SOME FRACTIONS

1

2

7

5

8

FRACTIONAL REPRESENTATION

 A circle is divided into 8 equal parts with 2 parts shaded in red. What fraction of the circle is shaded?

 Red parts – numerator – 2

 Total parts – denominator – 8

2

 So the fraction is represented as

8

WHAT FRACTION OF THE CIRCLE IS

 5 parts are shaded in red

 The circle is divided into 8 equal parts

 Parts – 5 (red) – numerator

 Whole – 8 –denominator

5

 So the fraction is represented as 8

 A rectangle divided into 5 equal parts with 2 of

the parts shaded in red. Write a fraction for the

 Parts – 2 (red) – numerator

 Whole – 5 –denominator

2

 So the fraction is represented as 5

CLASSIFYING FRACTIONS

 These fractions are similar because they all have

a denominator of 3.

1

2

3

3

3

3

1

2

 The fractions and are proper fractions.

3

3

3

 The fraction is an improper fraction.

3

CLASSIFYING FRACTIONS

EXAMPLES OF IMPROPER AND PROPER

FRACTIONS

*Fraction *

*Type *

*Words *

Proper

One-half

4

2

1

3

5

4 Improper

Four-thirds

1

2

Improper

Five-fifths

3

3

3

Proper

Two-thirds

3

CLASSIFYING FRACTIONS

The improper fractions above have a numerator that is equal to the denominator.

Each fraction above is equal to one whole, or one.

CLASSIFYING FRACTIONS

CLASSIFYING FRACTIONS

WRITE THE FRACTIONS AS A MIXED

NUMBER.

CLASSIFYING FRACTIONS

*Fraction *

*Words *

*Type *

Three-fourths

Proper

Five-halves

Improper

Two and one- fourth

Mixed number

One- third

Mixed number

Three and one- fifth

Mixed number

EQUIVALENT FRACTIONS

 These are equivalent fractions because they all

have the same value.

2

 The simplest form of all these fractions is .

3

EQUIVALENT FRACTIONS

EQUIVALENT FRACTIONS

Multiplying the numerator and the denominator of a fraction by the same nonzero whole number will change that fraction into an equivalent fraction but it will not change the value.

SIMPLEST FORM OF A FRACTION

 Simplest form – no common factors for numerator and denominator

 Factors – numbers that are multiplied to give a

product

BASIC CONCEPTS

 Any number multiplied or divided by doesn’t

change its value.

 Similarly dividing numerator and denominator by the same number won’t change the value of the fraction.

BASIC CONCEPTS

The value of the fraction

doesn’t change.

 Dividing the numerator and denominator by the same number is the same as dividing by 1.

FIND THE SIMPLEST FORM OF A FRACTION,

EXAMPLE 4

16

 First, find the common factors of the numerator

and denominator.

 Factors of 4: 1, 2, 4 (1 × 4 = 4; 2 × 2 = 4; 4 × 1 = 4)

 Factors of 16: 1, 2, 4, 8, 16 (1 × 16 = 16; 2 × 8 = 16; 4

× 4 = 16; 8 × 2 = 16; 16 × 1 = 16)

 Next, find the Greatest Common Factor.

 Greatest number that is a factor for both numerator and denominator.

 Here, it is 4.

S

4

IMPLEST FORM OF 16

 Divide the numerator and denominator by the

Greatest Common Factor.

 4 ÷ 4 = 1

 16 ÷ 4 = 4

4

1

 So, the simplest form of is .

16

4

FIND THE SIMPLEST FORM OF

 Common factors

 16 : 1, 2, 4, 8, 16

 84 : 1, 2, 4, 6, 7, 12, 14, 21, 42,84

 Once past the maximum value of the numerator there won’t be a common factor.

 Greatest Common Factor = 4

TOY CARS

 Alex has six toy cars. Three of the cars are blue.

How can you write a fraction for the blue cars in

simplest form?

 Fraction

 Common factors

 3 – 1, 3

 6 – 1, 2, 3, 6

6 FISH ARE GREEN AND 6 ARE BLUE, SO

OF THE FISH ARE BLUE.

1

6

 is the simplest form of

2

12

2

3

4

6

1

 , , and are other ways of representing 4

6

8

12

2

LET’S PLAY A GAME

This year, 100 people are playing the game. Of this number 30

people have never played before. How can you express this part of the group as a fraction and as a decimal?

 Write thirty-hundredths this way

 Ones Tenths Hundredths

30

 Of the 100 players, or 0.3 are new players.

100

30

 Simplest form of 100

 Factors of 30: 1, 2, 5, 6, 10, 15, 30

 Factors of 100: 1, 2, 4, 5, 10, 25, 50, 100

6 OF THE 100 DIDN’T FINISH THE GAME

 Fraction six-hundredths

 Ones Tenths Hundredths

of the last digit at the right.

FRACTIONS TO DECIMALS

 A decimal is another way of representing a

fraction.

 A decimal has no numerator or denominator.

 For example, the fraction can be expressed as a decimal,

 The period ( . ) represents the decimal point.

FRACTIONS TO DECIMALS

 Examples:

 0.9 nine-tenths

 0.3 three-tenths

 0.25 twenty five-hundredths

 Hint: Numbers after decimals are read as tenths

and hundredths.

BASIC CONCEPTS

 Note:

 Multiples of 10 in the numerator – increase the final value

 Multiples of 10 in the denominator – decrease the

final value

WRITE A DECIMAL AND FRACTION FOR THE

WHICH OF THE FOLLOWING IS

EQUIVALENT TO

2 ?

5

 Because the answer has a decimal in tenths, let’s

find an equivalent fraction with 10 in the

denominator.

2

2

 Multiply by .

5

2

WHICH OF THE FOLLOWING IS

EQUIVALENT TO 0.83?

 Ones Tenths Hundredths

 The last digit, 3, is in the hundredths place.

 So, the denominator is 100.

WHICH DECIMAL IS EQUIVALENT TO

1 ?

4

 Because the answer has a decimal in hundredths,

let’s find an equivalent fraction with 100 in the

denominator.

Now that you’ve reviewed fractions, let’s see how

well you understand the basic concepts.

If you don’t ace the quiz, you can come back to this lesson for a quick review.

Bake a Cake with Fractions!  