2. Index
• What is a fraction?
• Mixed Numbers method 1
• Mixed Numbers method 2
• Equivalent Fractions
• Special form of one Why
• Special form of one
• Finding equivalent fractions
• Simplifying Fractions
• Adding: Common denominators
• Adding: Different denominators
• Common denominators 1
• Common denominators 2
• ½+1/3 with diagram
• 1/3+1/4 with diagram
• ½ +2/5 with diagram
• 3/7+2/3 No diagram
• Adding Mixed Numbers
• Multiplying Fractions
• Multiplying Mixed Numbers 1
• Multiplying Mixed numbers 2
• Multiplying Mixed diagram
• Dividing Fractions
• Fraction Flowchart .ppt
• Fraction Flowchart .doc
(download)
• Decimal Fractions
• Fraction<->Decimal<-> %
• 100 Heart (Percentages)
3. What is a Fraction?
3
2
I’m the
NUMERATOR. I tell
you the number of
parts
I’m the
DENOMINATOR. I tell
you the name of part
A fraction is formed by dividing a whole into a
number of parts
4. Mixed numbers to improper fractions
=
3
1
2
Convert whole numbers to thirds
3
7
3
1
3
6
3
1
2 =+=
Mixed number
Improper fraction
5. Another Way to change Mixed
Numbers to improper fractions
5
2
3 Since 5/5=1 there are
5 fifths in each whole.
So 3 wholes will have
3x5=15 fifths.
Plus the 2 fifths
already there makes a
total of
15+2=17 fifths
5
17
=In short
5x3+2=17
6. Equivalent fractions
2
1
4
2
=
6
3
=
12
6
=
An equivalent fraction is one that
has the same value and position
on the number line but has a
different denominator
Equivalent fractions can be found by
multiplying by a special form of 1
........
5
5
4
4
3
3
2
2
1 etc=====
7. Multiplying By a Special Form of One
• Multiplying any number by 1 does not change
the value 4x1=4, 9x1=9 ……….
• Any number divided by itself =1.
Why does it work?
............
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1 ============
Multiplying a fraction by a special form of one
changes the numerator and the denominator but
DOES NOT CHANGE THE VALUE
9. Finding equivalent fractions
5
3
20
?Convert 5ths to 20ths
What do we multiply 5 by to get a product of
20?
That’s 4 so I must multiply by
4
4
5
3
20
12
4
4
5
3
=×
Special form of 1
10. Simplifying Fractions: Cancelling
• Simplifying means finding an equivalent
fraction with the LOWEST denominator by
making a special form of 1 equal to 1
18
12
6
6
3
2
×= 1
3
2
×=
3
2
=
18
12
618
612
÷
÷
=
3
2
=
Another way
of doing this
12. Adding Fractions with different
denominators
Problem:
You can’t add fractions with different denominators
without getting them ready first. They will be ready to
add when they have common denominators
Solution:
Turn fractions into equivalent fractions with a
common denominator that is find the Lowest
Common Multiple (LCM) of the two denominators
13. Finding the
Lowest Common Denominator
• The lowest common multiple of two numbers
is the lowest number in BOTH lists of multiples
3
1
2
1
+
Multiples of 2 are 2, 4, 6, 8, 10……
Multiples of 3 are 3, 6, 9, 12, ………
What is the lowest common
multiple?
14. Finding the
Lowest Common Denominator
• The lowest common multiple of two numbers
is the lowest number they will BOTH divide
into
3
1
2
1
+
2 divides into 2, 4, 6, 8…..
3 divides into 3, 6, 9….
What is the lowest number 2 and 3
both divide into?
15. +
The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths
6
5
6
2
6
3
2
2
3
1
3
3
2
1
=+=×+×
You can’t add fractions with
different denominators
Special form of 1
3
1
2
1
+
18. 3
2
7
3
+
What is the lowest number
BOTH 3 and 7 divide into?
Hmmmmm??????It is 21. So that is my
common denominator
21
?
21
?
+=
What special form
of 1 will change 7
to 21. Hmmmm?
It is 3/3
So I multiply
3/7 by 3/3
×
3
3
What special form
of 1 will change 3
to 21. Hmmmm?
It is 7/7
So I multiply
2/3 by 7/7
7
7
×
Now 3x3=9 and 2x7=14
Now I know the new
numerators
21
14
21
9
+=
Finally the fractions are READY to
add. I just have to add the
numerators 9+14=23
21
2
1
21
23
==
19. Adding Mixed Numbers
• Separate the fraction and the whole number sections,
add them separately and recombine at the end
2 ++++
+
2
1
3
1
5
6
5
7
=
=
= 7 6
5
2 +2
1
3
1
5
27. Division of fractions the short
version
2
1
3
1
÷
1
2
3
1
×=
Invert the 2nd
fraction and
multiply
3
2
=
28. Division with numbers only
the full story
3
2
1
3
2
2
2
3
2
1
2
2
1
1
2
3
1
2
1
3
1
2
1
3
1
===
×
×
==÷
29. An Alternative way
• Convert to equivalent fractions with a
common denominator and then you just
divide the numerators only
3
2
1
32
6
3
6
2
2
1
3
1
=
÷
=
÷
÷
=÷
36. +, - Decision: Are there Mixed Numbers?
For example is a mixed number
5
3
2
YESMixed Numbers?NO
37. ACTION: Evaluate Whole numbers
Evaluate the whole number part and
keep aside till later
2
1
3
2
7
2
1
3
3
2
4 ++=+
4+3=7
+, -
38. Decision: Are there common Denominators?
7
3For example and have the same (common) denominator
7
2
YESCommon Denominators?NO
+, -
39. Action: Find equivalent fractions
Find equivalent fractions with
common (the same) denominators
21
14
7
7
3
2
3
2
=×=
Multiply by a special form of 1
21
9
3
3
7
3
7
3
=×=
Multiply by a special form of 1
+, -
40. Action: Add or Subtract the numerators
7
5
7
3
7
2
=+
Add (or subtract) the numerators
this is the number of parts 2+3=5
Keep the Common Denominator.
This is the name of the fraction
+, -
41. Decision: Is the numerator negative?
YESIs numerator negative?NO
7
3
7
5
7
2 −
=−
This numerator is
negative
+, -
42. Action: Borrow a whole unit
Borrow 1 from the whole number part
Write it as an equivalent fraction
Add this to your negative fraction
n
n
+=+=+=+= 2
3
3
2
2
2
2123
Remember to adjust your
whole number total
+, -
48. Action: Invert the 2nd
Fraction and
replace division ÷ with multiply x
2
1
3
1
÷
1
2
3
1
×=
Invert the 2nd
fraction and multiply
x,÷
49. Decision : Is cancelling Possible?
• Do numbers in the numerators and the
denominators have common factors
Yes
Common factors
in numerators
and denominators
No
x,÷
60. 5
2
10
4
40%
0.4
Conversions
Write as a fraction with 100
as denominator then divide
numerator and denominator
by common factor of 20
5
2
20100
2040
%40 =
÷
÷
=
10
4
10100
1040
%40 =
÷
÷
=
Write as a fraction with
100 as denominator then
divide numerator and
denominator by common
factor of 10
Divide
numerator and
denominator by
a common
factor of 2
5
2
210
24
=
÷
÷
