1
Fractions
1 3
2
3 4
1 5
Equivalent Fractions look different but hold the same value 1Â whole
1 2
1 2
1 5 1 6
1 10 1 12
1 4
1 4
1 4
1 8
1 3
1 3
1 3
1 5
1 5
1 6
1 6
1 8
1 8
1 8 1 1 1 1 10 10 10 10 1 1 1 1 1 12 12 12 12 12
1 4
1 5
1 5
1 1 1 6 6 6 1 1 1 1 8 8 8 8 1 1 1 1 1 10 10 10 10 10 1 1 1 1 1 1 12 12 12 12 12 12
1
1 3
2
Fractions
1 5
3 4
Equivalent Fractions look different but hold the same value
A
B
1 2
4 8
What is the fraction shaded red in each case?
1
2
1 3
Fractions
1 5
3 4
Equivalent Fractions look different but hold the same value
A What fraction of rectangle A is shaded?
2 3
B What fraction of rectangle B is shaded?
6 9
1
1 3
2
Fractions
1 5
3 4
Equivalent Fractions look different but hold the same value
A
3 6
B
2 8
Do rectangles A and B show equivalent fractions?
1
2
1 3
Fractions
1 5
3 4
Equivalent Fractions look different but hold the same value
How can I find an equivalent fraction to the one below?
1 3 1 3 1 3
x2
= x2
x3
= x3
x4
= x4
2 6
3 9
4 12
Whatever you do to the top you must do to the bottom and vice versa!
1
2
1 3
Fractions
1 5
3 4
Equivalent Fractions look different but hold the same value
Try these.
2 3 3 5
x4
= x4
x7
= x7
8 12
6 10
÷2
21
32 40
÷8
35
= ÷2
= ÷8
3 5 4 5
12
÷4
16
÷4
=
48
÷16
64
÷16
=
3 4 3 4
1
1 3
2
Fractions
1 5
3 4
Which fraction is bigger?
1 4
1 7
This seems obvious with a picture but how do we do it without a picture?
1
2
1 3
Fractions
1 5
3 4
Which fraction is bigger?
4 7
or
3 5
Numerator Denominator
The denominator tells us how many pieces the whole has been split into
If I can find a common denominator I can compare the fractions
3 4
is bigger than
2 4
Common Denominators
1
2
1 3
Fractions
1 5
3 4
Finding a common denominator
4 7
and
3 5
4 = 20 7 35
Easiest way is to multiply denominators
21 3 = 5 35
1
2
1 3
Fractions
1 5
3 4
Finding a common denominator
2 3
and
3 5
2 = 10 3 15
Easiest way is to multiply denominators
9 3 = 5 15
1
2
1 3
Fractions
1 5
3 4
Adding and Subtracting They must have a common denominator
1+ 3 = 4 7 7 7
4- 3 1 = 5 5 5
=
+ -
=
1
2
1 3
Fractions
1 5
3 4
Adding and Subtracting
+
What if they have different denominators
A common mistake is shown below
1+ 1 = 2 2 3 5
+
=
This doesn't make any sense!!
1
1 3
2
Fractions
1 5
3 4
Adding and Subtracting They must have a common denominator
1+ 1
2
3
+
=
= 6+ 6
Find common denominator by multiplying 2 by 3
= 3+ 2 6 6
Find equivalent fractions with denominator of 6
5 = 6
1
2
Fractions
1 3
1 5
3 4
Adding and Subtracting
= =
2+ 1 3 5 10 + 3
15
13
15
15
3- 2 4 3
= =
9- 8 12 12 1 12
1
2
1 3
Fractions
1 5
3 4
Adding and Subtracting
2+ 3 = 4+ 6 = 7 6 1 =1 6
1 2 3 6
Sometimes you end up with a bigger number on the top. We can write this another way.
=
1
2
Fractions
1 3
1 5
3 4
Adding and Subtracting
3
1 + 3
2
1 + 6 +
=
5
=
+
1
1 3
2
5 6 =
2 3 Its sometimes easier to visualise fractions with pictures
=
4
1
2
Fractions
1 3
1 5
Adding and Subtracting
3
4 + 5
2
3 5
+
3
3 5 -
-
=
5
7 5 =
=
2
1 5
=
= =
6
1
2 5
2 5
3 4
1
2
1 3
Fractions
1 5
Multiplying Fractions
1 1 What is 2 of 4 ?
3 4
1
2
1 3
Fractions
1 5
3 4
Multiplying Fractions
1 1 What is 2 of 4 ? 1 What is 2 x
1 4 ?
Is there a difference between these questions? From our work with areas of triangles
9m
Area =
1 2
x b x h
Area =
1 2
x 12 x 9
Area = 6 x 9
12m
Area = 54m2
Therefore 1 of 12 means 2
1 x 12 and vice versa 2
1
2
1 3
Fractions
1 5
3 4
Multiplying Fractions
We can see visually
1 1 1 2 of 4 = 8
or
One eighth
1 1 1 2 x 4 = 8 But can we do this without drawing a picture?
Rule
Multiply the numerators Multiply the denominators
1
2
1 3
Fractions
1 5
3 4
Multiplying Fractions
1 1 1 3 x 5 = 15 One Fifth
Solution 6 2 3 4 x 3 = 12 One Third
Solution
1
2
1 3
Fractions
3 4
1 5
Dividing Fractions
If we look firstly at
6รท 2
We interpret this as how many 2's are in 6 If we now look at
1 1 2 รท 4 =
2
1
2
1 3
Fractions
1 5
3 4
Dividing Fractions
Imagining the diagrams can become complex though
2 3 รท 8 5 =
?
We need a better way! Often mathematical rules are about spotting patterns
1 10 รท 2 = 20
2 10 x 1 = 20
1 9 รท 3 = 27
3 9 x 1 = 27
1 3 รท 4 = 12
4 3 x 1 = 12
Dividing is the same as multiplying by the inverse
1
2
1 3
Fractions
1 5
3 4
Dividing Fractions
Can we now solve this calculation without a diagram?
2 3 8 รท 5 =
2 3 8 รท 5 5 3 = 8 x 2 = 15 16
1 4 7 รท 3 3 4 = 7 x 1 = 12 = 1 75 7
? 5 3 รท 4 6 6 3 = 4 x 5 = 18 = 9 10 20
1
2
1 3
Fractions
1 5
3 4
Fractions of time
1 hour
=
60 mins
1 hour 4
=
15 mins
1 hour 2
=
30 mins
3 hour 4
=
45 mins
What fraction of an hour would 12 mins be?
1
2
1 3
Fractions
1 5
3 4
Fractions of time Changing minutes into a fraction of an hour
30mins =
12mins =
36mins =
30 60
÷ 10
=
÷ 10
12 60
÷6
36 60
÷6
=
÷6
=
÷6
3 6
÷3
=3 ÷
2 10
÷2
6 10
÷2
= ÷2
= ÷2
1 2 1 5
3 5
Always simplify as much as you are able to
1
2
1 3
Fractions
1 5
3 4
Fractions of time Changing fractions of an hour into minutes
1 hr = 60mins รท 5 = 12mins 5
1 hr = 60mins รท 3 = 20mins 3
5 hr = 60mins รท 12 x 5 = 25mins 12