Fractions Re-cap2 Mathemati cs
Jan 19, 2016
Fractions Re-cap2
Mathematics
Which is bigger or ?38
512
To compare two fractions convert them to fractions with the same denominator.
First we need to find the lowest common multiple of 8 and 12.
The lowest common multiple of 8 and 12 is 24.
Now, write and as equivalent fractions over 24. 38
512
38
=24
×3
×3
9and
512
=24
×2
×2
10so,
38
512
<
Using equivalent fractions
Ordering fractions
Multiplying a fraction by a fraction
To multiply two fractions together, multiply the numerators together and multiply the denominators together:
38
What is × ?25
38
45
× =1240
3
10
=310
We could also cancel at
this step.
56
What is × ?12255
Start by writing the calculation with any mixed numbers as improper fractions.
To make the calculation easier, cancel any numerators with any denominators.
1225
356
× =
7
5
2
1
145
= 2 45
Multiplying a fraction by a fraction
Using cancellation to simplify calculations
712
What is 16 × ?
We can write 16 × as:712
161
×712
4
3=
283
=139
45
What is ÷ ?23
To divide by a fraction we flip the second fraction and multiply.
45
23
÷ can be written as54
23
×
Swap the numerator and the denominator and multiply.
54
23
× =1012
=56
Dividing a fraction by a fraction
This is the reciprocal of .45
67
What is ÷ ?353
Start by writing as an improper fraction. 353
185
353 =
185
÷67
=185
×76
3
1
=215
=154
Dividing a fraction by a fraction
Dividing fractions
When fractions have the same denominator it is quite easy to add them together and to subtract them.
For example,
3
5+
1
5=
3 + 1
5=
4
5
We can show this calculation in a diagram:
+ =
Adding and subtracting fractions
7
8–
3
8=
7 – 3
8=
4
8
Fractions should always be cancelled down to their lowest terms.
1
2 =1
2
We can show this calculation in a diagram:
– =
Adding and subtracting fractions
Fractions with different denominatorsFractions with different denominators are more difficult to add and subtract.
For example,
What is 56
–29
?
–
1518
–418
=
=15 – 4
18=
1118
Using a common denominator
1) Write any mixed numbers as improper fractions.
1 34
= 74
2) Find the lowest common multiple of 4, 9 and 12.
The multiples of 12 are: 12, 24, 36 . . .
36 is the lowest common denominator.
What is +19
?134
+512
3) Write each fraction over the lowest common denominator.
74
=36
×9
×9
63 19
=36
×4
×4
4 512
=36
×3
×3
15
4) Add the fractions together.
3663
+364
+3615
=36
63 + 4 + 15=
3682
= 2 3610
= 2 185
What is +19
?134
+512
Using a common denominator