Understanding fractions

NDHLOVU BCPowerPoint presentation: FractionsGrade 8

WORDS TO KNOW!

Fractions

Whole (One)

Unit Fractions

Equivalent Fractions

Numerator

Denominator

Common Denominator

Improper Fractions

Mixed Numbers

Learning Objective

Students will:

Understand how to add, subtract, divide and multiply fractions.

Understand how to find equivalent fractions by using multiplication and division rules.

Compare and order fractions by identifying common denominators and use the proper symbol. (<, >, and =)

MEANING OF A FRACTION

When an object is divided into equal parts, each part is called a fraction of the object.

This circle is divided into 4 equal parts. One of the 4 equal parts which is separated is written as ¼ and named as one-fourth.

Fraction has 2 numbers. Number above the line is called NUMERATOR and the number below the line is called DENOMINTOR.

Ex. In fraction 1/8 1 is numerator and 8 is denominator.

What fraction of the musical instruments have strings?

2

5

What fraction of the fish have stripes?

3

5

What fraction of the arrowshit the bulls eye?

1

3

What fraction of the pins areknocked down?

3

10

LIKE FRACTIONS & UNLIKE FRACTIONS

Fractions having same denominators are called like fractions.

Fractions having different denominators are called unlike fractions.

Improper Fractions and Mixed Numbers

An improper fraction can be converted to a mixed number and vice versa.

3

5An improper fraction is a fraction with the numerator larger than or equal to the denominator.

A mixed number is a whole number and a fraction together.

7

32

Any whole number can be transformed into an improper fraction.

,1

44

7

71

Improper Fractions and Mixed Numbers

3

21

3

5

Converting improper fractions into mixed numbers:- divide the numerator by the denominator - the quotient is the leading number,- the remainder as the new numerator.

7

17

7

372

7

32

Converting mixed

numbers into improper fractions.

,4

31

4

7More examples:

5

12

5

11

How does the denominator control a fraction?

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

2

1

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

3

1

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

4

1

How does the denominator control a fraction?

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

If you share a pizza evenly among eight people, you will get only

8

1

It’s not hard to see that the slice you get becomes smaller and smaller.

c.bc

a

b

a r wheneve i.e.

Addition and subtraction of Fractions

- addition means combining objects in two or more sets- the objects must be of the same type, i.e. we combine bundles with bundles and sticks with sticks.- in fractions, we can only combine pieces of the same size. In other words, the denominators must be the same.

5

1

5

1

5

2

1/7

1/7

1/7

1/7 1/7

1/7

1/7

1/7

1/7

1/7

1/7

1/7

7

2

7

6

7

4

1/8

1/8

1/8

1/8

1/8

1/8

1/8

8

3

8

1

2

1

8

4

Why were they so simple?

Because they all had the same denominator

They were all from the same families

What if they are of different families?

1/2

1/4

4

1

2

1

4

3 Because we

know that 1/2 = 2/4

1/8

1/8

1/8

1/4

1/8

1/8

1/8

1/8 1/8

8

5

4

1

8

3

Because we know that 1/4

= 2/8

But what about 1/4 + 1/3?

We can’t add, because they have different denominators – not in the same

family.

1/4

1/3

What family can we change them to?

What will be the new denominator?

1/4

1/3

4 and 3 both divide into 12

So we can change them into 12ths

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

12

3

4

1

12

4

3

1

12

7

3

1

4

1

What about 1/2 – 2/5?

What family can we change them to?

What will be the new denominator?

1/2

1/5

1/5

2 and 5 both divide into 10

So we can change them into 10ths

1/10

1/10

1/10

1/10

1/10 1/10

1/10

1/10

1/10

1/10 1/10

1/10

1/10

1/10

1/10 1/10

1/10

1/10

1/10

1/10

10

5

2

1

10

4

5

2

We can do this without the pictures:

10

1

10

4

10

55

2

2

1

Multiplication and Division

Easy one:

3

2

3

12

1/3

1/3

2/3

+ =

3

22

3

1And because of commutivity,

we can also say:

With two fractions:

half of ¾?

8

3

4

3

2

1

8

3

2

1

4

3or

Without the pictures:

10

3

2

1

5

3

21

4

7

2

3

2

2

1

12

6

4

3

3

2

And division?

Unfortunately, there is no easy way to show diagrams for division of fractions.

Nor is there any obvious way of trying to make sense of it.

The best thing is probably just to learn the rule!

To divide by a fraction

Do not change the first fraction

Change the division sign into a multiplication sign

Turn the second fraction upside down

Multiply the fractions

6

5

12

10

24

20

3

4

8

5

4

3

8

5

For example:

5

11

5

6

1

2

5

3

2

1

5

3

8

5

24

15

8

3

3

5

8

3

3

21

And finally, what to do about mixed numbers:

2

12

2

5

6

15

12

30

3

2

4

15

2

3

4

15

2

11

4

33

Finding Equivalent Fractions

For example

3/6 is equivalent to 10/20 because the relationship between the numerator and the denominator is the same in each case: 3 is ½ of 6, and 10 is ½ of 20.

Two fractions are EQUIVALENT if they are equal.This means that the relationship between the numerator and the denominator of one fraction is the same as the relationship between the numerator and denominator of the other fraction.

Another way you can look at it is if two fractions are equivalent, they will have a scale factor between them. The SCALE FACTOR is the number that you multiply or divide the numerator and denominator in one fraction by to get the numerator and denominator of the second fraction.

3 9

5 15=

x3

x3

By multiplying 3/5 by 3/3 (remember, that is the same as multiplying by 1 whole), I will arrive at the answer 9/15.

Remember that when you are doing this you must BE FAIR and perform the same operation to both the numerator and the denominator.

Don’t forget that when you multiply fractions, you multiply the numerators together and you multiply the denominators together.

A third way to determine if two fractions are equivalent is to CROSS MULTIPLY.

4 2

6 3=

=

x

=12

x

=

12

Multiply the numerator of one fraction by the denominator of the other.

Repeat this with the other numerator and denominator.

If the products are equal, then the fractions are equivalent.

Learn about and practice converting improper fractions and mixed numbers by clicking

the objects on this slide.

Click me to print a worksheet

Practice makes perfect

Click me for a visual demonstration

Click me to practice.

Click us to play fraction frenzy

Click me to play half baked fractions on fun

brain

Click me to watch the video

KEY POINTS

Remember, a fraction is an equal part of one whole

We can split shapes, objects and numbers into fractions

We write fractions as

A “View” to a Fraction

Where do you stand?

THANK YOU