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Fractions. During this topic you will learn to: Understand the equivalence of fractions. Simplify a fraction. Change proper fractions to improper fractions. Change improper to proper fractions Add and Subtract fractions Multiply and Divide fractions. Which are the same as.

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Presentation Transcript
slide1

Fractions

During this topic you will learn to:

Understand the equivalence of fractions.

Simplify a fraction.

Change proper fractions to improper fractions.

Change improper to proper fractions

Add and Subtract fractions

Multiply and Divide fractions

slide2

Which are the same as

1

2

3

3

14

4

2

5

9

12

35

8

2

4

8

19

25

25

6

12

16

76

75

70

2

5

30

1

9

33

8

15

75

4

18

99

49

4

2

4

3

5

98

6

4

10

7

9

A Quarter

Two Fifths

A Half

A Third

slide3

Equivalent Fractions

Before we can look at adding fractions we need to get some practice in finding equivalent fractions.

So long as you multiply the top and the bottom of a fraction by the same number you will not change its size (because all you are doing is multiplying by 1!)

2

4

8

2

8

e.g.,

x

=

so

=

5

4

20

5

20

This is just 1 whole

slide4

Equivalent Fractions

Match up the fraction on the left with its equivalent on the right.

2

19

5

57

3

12

7

28

1

24

3

60

4

24

9

64

3

84

8

189

slide5

Improper Fractions

An improper fraction is one where the numerator (top number) is bigger than the denominator (bottom number).

This means that there must be more than one whole one.

3

e.g.

= 1

=

2

15

=

4

slide6

Improper Fractions

And Mixed Numbers

An improper fraction can also be written as a mixed number. This means a whole number and a fraction.

3

1

e.g.

= 1

=

= 1

2

2

15

3

=

= 3

4

4

slide7

Now Do

Time Up

Exercises 3, 4 & 5

You Have 10 min.

slide8

Simplifying Fractions

If you can find equivalent fractions then simplifying fractions should not be a problem.

Give me some equivalent fractions for:

12

18

slide9

Simplifying Fractions

Which one do you think is the simplest and why?

12

18

slide10

Simplifying Fractions

Simplifying a fraction just means finding an equivalent fraction with the smallest numbers possible

12

18

slide11

Now Do

Time Up

Exercises 1 & 2

You Have 7 min.

slide12

Improper Fractions

And Mixed Numbers

To convert an improper fraction into a mixed number:

How many times does the denominator go into the numerator ?

This is the whole number part.

The remainder is the numerator of the fraction part.

slide13

Improper Fractions

And Mixed Numbers

Example:

38

2

4

=

9

9

How many times does 9 go into 38?

What is the remainder?

slide14

Improper Fractions

And Mixed Numbers

To convert a mixed number into an improper fraction :

Multiply the whole number by the denominator then add the numerator

This is the numerator of the improper fraction

The denominator stays the same.

slide15

Improper Fractions

And Mixed Numbers

Example:

5

21

5

26

3

=

+

=

7

7

7

7

How many sevenths is 3 whole ones?

3 x 7 = 21

slide16

Now Do

Time Up

Exercise 8

You Have 7 min.

slide17

Adding Fractions

What do you think the answer to this is:

We can’t just add numerators and denominators or we end up saying 2 halves make a half

1

1

2

1

+

=

=

2

2

4

2

We know that 2 halves make a whole one:

1

1

2

+

=

=

1

2

2

2

All we add are the numerators, the denominator stays the same.

slide18

Now Do

Time Up

Exercise 9

You Have 5 min.

slide19

Adding Fractions

Before we can add fractions we have to make sure the denominators are the same This is where our equivalent fractions come in:

2

5

+

3

6

We have to turn the thirds into sixths

2

5

4

5

9

+

=

+

=

3

6

6

6

6

slide20

Now Do

Time Up

Exercise 10

You Have 10 min.

slide21

Multiplying Fractions

This is the easiest operation to do with fractions.

Just multiply the numerators to get the numerator of the answer,

And multiply the denominators to get the denominator of the answer.

2

3

6

e.g.

x

=

5

7

35

slide22

Dividing Fractions

You can treat division just like multiplication – there is just one step to do first.

Turn the fraction you are dividing by upside down.

Then change the division to a multiplication.

2

3

2

7

14

e.g.

=

x

=

5

7

5

3

15