Title: Fractions Explained
1Fractions Explained
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2Index
- 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
- ½1/3 with diagram
- 1/31/4 with diagram
- ½ 2/5 with diagram
- 3/72/3 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
- Fractionlt-gtDecimallt-gt
- 100 Heart (Percentages)
3What is a Fraction?
A fraction is formed by dividing a whole into a
number of parts
Im the NUMERATOR. I tell you the number of parts
Im the DENOMINATOR. I tell you the name of part
4Mixed numbers to improper fractions
Convert whole numbers to thirds
Mixed number
Improper fraction
5Another Way to change Mixed Numbers to improper
fractions
In short 5x3217
Since 5/51 there are 5 fifths in each whole. So
3 wholes will have 3x515 fifths. Plus the 2
fifths already there makes a total of 15217
fifths
6Equivalent fractions
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
7Multiplying By a Special Form of One
Why does it work?
- Multiplying any number by 1 does not change the
value 4x14, 9x19 . - Any number divided by itself 1.
Multiplying a fraction by a special form of one
changes the numerator and the denominator but
DOES NOT CHANGE THE VALUE
81
9Finding equivalent fractions
Convert 5ths to 20ths
Thats 4 so I must multiply by
What do we multiply 5 by to get a product of 20?
Special form of 1
10Simplifying Fractions Cancelling
- Simplifying means finding an equivalent fraction
with the LOWEST denominator by making a special
form of 1 equal to 1
1
Another way of doing this
11Adding Fractions with common denominators
12Adding Fractions with different denominators
Problem You cant 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
13Finding the Lowest Common Denominator
- The lowest common multiple of two numbers is the
lowest number in BOTH lists of multiples
Multiples of 2 are 2, 4, 6, 8, 10 Multiples of
3 are 3, 6, 9, 12, What is the lowest
common multiple?
14Finding the Lowest Common Denominator
- The lowest common multiple of two numbers is the
lowest number they will BOTH divide into
2 divides into 2, 4, 6, 8.. 3 divides into 3, 6,
9. What is the lowest number 2 and 3 both
divide into?
15You cant add fractions with different
denominators
The Lowest Common Multiple of 2 and 3 is 6 so
turn all fractions into sixths
Special form of 1
16Lowest common denominator is 10 so make all
fractions tenths
17Turn both fractions into twelfths
18Finally the fractions are READY to add. I just
have to add the numerators 91423
It is 3/3 So I multiply 3/7 by 3/3
It is 7/7 So I multiply 2/3 by 7/7
What is the lowest number BOTH 3 and 7 divide
into? Hmmmmm??????
What special form of 1 will change 7 to 21.
Hmmmm?
What special form of 1 will change 3 to 21.
Hmmmm?
It is 21. So that is my common denominator
Now 3x39 and 2x714 Now I know the new numerators
19Adding Mixed Numbers
- Separate the fraction and the whole number
sections, add them separately and recombine at
the end
20Multiplying Fractions
21Multiplying Fractions
22Multiplying Mixed Numbers 1
Change to Improper fractions before multiplying
23Multiplying Mixed numbers 2
24(No Transcript)
25Division of Fractions
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26The Traditional Way
- Turn the second fraction upside down and multiply
27Division of fractions the short version
Invert the 2nd fraction and multiply
28Division with numbers onlythe full story
29An Alternative way
- Convert to equivalent fractions with a common
denominator and then you just divide the
numerators only
30A visual representation
Form equivalent fractions with common denominators
31(No Transcript)
32(No Transcript)
33Fraction Flowchart
- Decisions and Actions in evaluating fraction
problems - Graeme Henchel
- http//hench-maths.wikispaces.com
34FLOWCHART and Skill set
The following should be used with the Fraction
Flow chart word doc. Download from
http//hench-maths.wikispaces.com
35Decision What is the operation?
What is the operation?
x,
, -
36Decision Are there Mixed Numbers?
, -
For example is a mixed number
YES
Mixed Numbers?
NO
37ACTION Evaluate Whole numbers
, -
Evaluate the whole number part and keep aside
till later
437
38Decision Are there common Denominators?
, -
For example and have
the same (common) denominator
YES
Common Denominators?
NO
39Action Find equivalent fractions
, -
Find equivalent fractions with common (the same)
denominators
Multiply by a special form of 1
Multiply by a special form of 1
40Action Add or Subtract the numerators
, -
Add (or subtract) the numerators this is the
number of parts 235
Keep the Common Denominator. This is the name of
the fraction
41Decision Is the numerator negative?
, -
YES
Is numerator negative?
NO
This numerator is negative
42Action Borrow a whole unit
, -
Borrow 1 from the whole number part Write it as
an equivalent fraction Add this to your negative
fraction
Remember to adjust your whole number total
43Action Add any whole number part
, -
44Thats All Folks
, -
45Decision Are there Mixed Numbers?
x,
For example is a mixed number
YES
Mixed Numbers?
NO
46Action Change to improper fractions
x,
OR
4X520 and 20323
47Decision Is this a X or a problem?
x,
x
X or ?
48Action Invert the 2nd Fraction and replace
division with multiply x
x,
Invert the 2nd fraction and multiply
49Decision Is cancelling Possible?
x,
- Do numbers in the numerators and the denominators
have common factors
Yes
Common factors in numerators and denominators
No
50Action Simplify by cancelling
x,
1
1
3
5
3
5
2
2
51ACTION Multiply the numerators AND the
denominators
x,
52Decision Is the product improper (top heavy)
x,
Yes
Is the fraction improper ? (top heavy)
No
53Action Change to a mixed Number
x,
54Thats All Folks
x,
55Representing Decimal Fractions
1
1
1
1
?
decimal point
?
56Representing Decimal Fractions
1
3
5
2
?
decimal point
?
57Converting Fractions to decimals and
- Graeme Henchel
- http//hench-maths.wikispaces.com
58(No Transcript)
59Conversions
Divide 2 by 5 Find ?25
Multiply by a special form of 1
Write as a decimal using place value
Write as a fraction with 10 as denominator
0.4
Multiply by a special form of 1
Multiply by special form of 1
40
60Conversions
Divide numerator and denominator by a common
factor of 2
Write as a fraction with 100 as denominator then
divide numerator and denominator by common factor
of 20
0.4
Write as a fraction with 100 as denominator then
divide numerator and denominator by common factor
of 10
40
61Conversions
0.4
Divide 40 by 100 ? Move decimal point 2 places
left
40
0
40
62Percentages100 hearts
- Graeme Henchel
- http//hench-maths.wikispaces.com
63Visual representations
Percent per hundred
64100100/100
6511/100
6655/1001/20
671010/1001/10
682020/1001/5
692525/1001/4
7033?33?/100?
715050/100½