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FractionsFractions
• SimplifyingSimplifying
• EquivalencesEquivalences
Equivalent Fractions of one Equivalent Fractions of one halfhalf
16
8
40
20
8
4
14
7
10
5
2
1
The bottom number is twice the top number
The top number is half the bottom number
InIn a fraction the top number is a fraction the top number is the numerator. The bottom the numerator. The bottom number is the denominator.number is the denominator.
22
1112
8
Which of these fractions are equivalent to a half. Look at the relationship between the numerator and the denominator.
11x2=22 so yes
8x2=16 so no
30
1515x2= 30 so yes
It is relatively easy to see if a fraction equals a half or not.
Which of these are equivalent Which of these are equivalent to a third?to a third?
30
109
36
25
2No
Yes
Yes
Yes 217
129
300
100Yes
No
Yes
Is the bottom number three times the top number?
Simplifying fractions –Simplifying fractions – a general method a general method
You have to find a common divisor –You have to find a common divisor –
a number which will go into both the a number which will go into both the top number and the bottom number top number and the bottom number and leave and leave no remainderno remainder
Find a number that will go into Find a number that will go into the numerator and the numerator and denominator and leave no denominator and leave no remainderremainder
100
25
20
5
100
25
What number will go into 25 and 100 and leave no remainder?
5 is a possibility
What number will go into 5 and 20 and leave no remainder?
We can’t go any further
5 is a possibility again
4
1
20
5
100
25
42
28
21
14
42
28
Find a number that will go into Find a number that will go into the numerator and the numerator and denominator and leave no denominator and leave no remainderremainder
What number will go into 28 and 42 and leave no remainder?
They are both even numbers so two will work
What number will go into 14 and 21 and leave no remainder?
We can’t go any further
7 will
3
2
21
14
42
28
Simplifying fractions- You need Simplifying fractions- You need to know your times tables to know your times tables
Even numbers end in 0, 2, 4, 6, 8 –Even numbers end in 0, 2, 4, 6, 8 –
Two will always go into and even number.Two will always go into and even number.
Here are some even numbersHere are some even numbers
3274
9618
110
To see if 3 goes into a number – see if To see if 3 goes into a number – see if three goes into the sum of the digits three goes into the sum of the digits – example - 39 (3+9=12=3x4)– example - 39 (3+9=12=3x4)
Here are some numbers that are Here are some numbers that are divisible by threedivisible by three
Simplifying fractions- You need Simplifying fractions- You need to know your times tables to know your times tables
51 5+1=6=3x2
108 1+0+8=9=3x3
63 6+3=9=3x3
48
4+8=12=3x4
Five will go into any number that ends in Five will go into any number that ends in zero or fivezero or five
Ten will go into any number that ends in Ten will go into any number that ends in zerozero
Twenty five will go into any number that Twenty five will go into any number that ends in 00, 25, 50, 75ends in 00, 25, 50, 75
Simplifying fractions- You need Simplifying fractions- You need to know your times tables to know your times tables
Try to simplify these Try to simplify these fractionsfractions
63
18
77
44
300
125
60
35
35
6040
82
7
2
21
6
12
7
12
5
7
4
12
51
7
12
20
12
20
41
