fractions. fractions have numerators and denominators fractions represent the division of the...

FRACTIONS

Fractions have numerators and denominators

Fractions represent the division of the numerator by the denominator or it’s the same as 4 divided by 5

The numerator is the top number or tells us how many such pieces are being considered.

The denominator is the bottom number or tells us how many congruent (equal) pieces the whole is divided into.

numerator denominator

5/4

What is a fraction?

Fractions are one or more parts of a whole that is divided into equal parts. Fractions can represent numbers less than 1, equal to 1, or greater than 1. The whole can be broken up into regions, sets, or segments.

How does the denominator control a fraction?

If you share a cake evenly among two people, you will get

2

1

If you share a cake evenly among three people, you will get

3

1

If you share a cake evenly among four people, you will get

4

1

Conclusion: The larger the denominator the smaller the pieces, and if the numerator is kept fixed, the larger the denominator the smaller the fraction!!!

Equivalent fractions: are fractions that represent the same amount but they have different numerators and denominators. You can multiply or divide the numerator and denominator by the same number to get an equivalent fraction.

In the following picture we have ½ of a cake because the whole cake is divided into two equal parts and we have only one of those parts.

2

1

4

22

2

= X

Find the Equivalent Fraction• Multiply the numerator and the denominator

by the same number.

13

33

39

x =• or you can also divide the numerator and the denominator by the same number.

412 ÷ 4

4= 1

3

Equivalent Fractions

12

= 24

12

1414

• What number was multiplied by the numerator and the dominator to get the new equivalent fraction?

Make An Equivalent FractionFind the Missing Numerator!

Given the newdenominator, can you

find the missing numerator?

x 4

x 4

Make An Equivalent FractionFind the Missing Numerator!

Given the newdenominator, can you

find the missing numerator?

x 9

x 9

Given the newdenominator, can you

find the missing numerator?

Make An Equivalent FractionFind the Missing Numerator!

x 4

x 4

Make Equivalent FractionsFind the Missing Numerators!

55

54

42

63

44 12

45 28

Find a new Equivalent fraction by multiplying the numerator and dominator by the same number

• 1/3 = 2/7=

• 5/6= 5/10=

• 9/18= 12/24=

• 30/40 3/8 =

Putting Fractions in Simplest Form

A fraction is in its lowest terms is reduced or simplified if we cannot find a whole number that can divide into both its numerator and denominator. Reducing a fraction in lowest terms gives you its equivalent fraction with the lowest possible numerator and denominator.

Steps to Reducing Fractions or putting fractions into Simplest Forms: 1. Find the GCF of the numerator and the denominator.2. Divide the GCF into both the numerator and the denominator to

get the fraction in simplest form.

6= 1, 2, 3, 610= 1, 2, 5, 10 2 is the GCF so divide 2 into the numerator and the dominator to get the fraction in simplest forms.

10

6 = 3 5

Simplify Fractions

• Divide both numerator and denominator by the Greatest Common Factor

72

28 Factors are 1, 2, 4, 7, 14, 28

Factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 48, 72

Greatest Common Factor is 4

2872 ÷

÷ 44

==

718

So7228

=7

18

10= 1, 2, 5, 1060= 1, 2, 3, 4, 6,10, 30, 60 10 is the GCF and can be divided into both 10 and 60.

11= 1,1123= 1, 231 is the GCF and so this fraction is already in simplest form.

60

10

23

11

Fractions in Simplest Forms: Remember to first find the GCF, then divide.

40

35 35= 1, 5, 7, 3540= 1,2, 4,10, 20, 40 5 is the GCF and divides into both 35 and 40.

Simplification - Let’s Try It!

3

1

7

2

3

1

63

18=

5

2

114

78=

7

2

19

13

9

3=

84

24=

21

7=

15

6=

Simplify/Reduce the Fractions

• 8/32 =

• 7/56 =

• 24/36

• 32/48 =

Comparing Fractions with Like Denominators

710

510>

Susan walks a greater distance

That makes sensebecause 7 of

something is more than 5 of something

5 10

710

7 > 5 so

Comparing fractions with like denominators is a lot likeComparing fractions with like denominators is a lot likecomparing whole numberscomparing whole numbers

EXAMPLE: EXAMPLE: George walks mile to school. Susan walks mile. Who walks the greater distance? When fractions have the same denominator, compare the numerator.

14

34

The fractions 14

and34

have the same denominator.

Fractions with the same denominators are

Fractions with Like DenominatorsFractions with Like Denominators

like fractions.

Compare. Write <, >, or =.

46__ 5__

6

46

__ __65

<

From the model, < .46

__ __65

Compare. Write <, >, or =.

67__ 4__

7

67

__ __74

>

From the model, > .67

__ __74

Sometimes you can compare fractions just by looking at them

12

> 14

I’ll take12