Transcript Fraction Flowchart - Hench-maths

3
8
Fraction Flowchart
Decisions and Actions in evaluating
fraction problems
Graeme Henchel
http://hench-maths.wikispaces.com
Decision: What is the operation?
+,-
What is the operation?
x,÷
+, -
Decision: Are there Mixed Numbers?
For example
NO
3
2
5
is a mixed number
Mixed Numbers?
YES
+, - ACTION: Evaluate Whole numbers
Evaluate the whole number part and
keep aside till later
4+3=7
2
1
2
1
4 3  7

3
2
3
2
+, -
Decision: Are there common Denominators?
For example
3
7
NO
and
2
7
have the same (common) denominator
Common Denominators?
YES
+, -
Action: Find equivalent fractions
Find equivalent fractions with
common (the same) denominators
2 2 7 14
  
3 3 7 21
Multiply by a special form of 1
3 3 3 9
  
7 7 3 21
Multiply by a special form of 1
+, -
Action: Add or Subtract the numerators
Add (or subtract) the numerators
this is the number of parts 2+3=5
2
3
5


7
7
7
Keep the Common Denominator.
This is the name of the fraction
+, -
Decision: Is the numerator negative?
NO
Is numerator negative?
2 5 3
 
7 7
7
YES
This numerator is
negative
+, -
Action: Borrow a whole unit
Borrow 1 from the whole number part
Write it as an equivalent fraction
Add this to your negative fraction
2
3
n
3  2 1  2   2   2 
2
3
n
Remember to adjust your
whole number total
+, -
Action: Add any whole number part
3
3
3  3
5
5
+, -
That’s All Folks
x,÷
Decision: Are there Mixed Numbers?
For example
NO
3
2
5
is a mixed number
Mixed Numbers?
YES
x,÷ Action: Change to improper fractions
3 20 3 23
4 
 
5 5 5 5
OR
3
4
5
23

5
4X5=20
and 20+3=23
x,÷
Decision: Is this a X or a ÷ problem?
÷
X or ÷ ?
x
nd Fraction and
Action:
Invert
the
2
x,÷
replace division ÷ with multiply x
1 1

3 2
Invert the 2nd
fraction and
multiply
1 2
 
3 1
x,÷
Decision : Is cancelling Possible?
• Do numbers in the numerators and the
denominators have common factors
No
Common factors
in numerators
and denominators
Yes
x,÷
Action Simplify by cancelling
1
3 5

10 6
÷3
÷5
2
1
÷5
÷3
2
x,÷
ACTION: Multiply the numerators
AND the denominators
3 2 6
 
5 7 35
x,÷
Decision: Is the product improper
(top heavy)
No
Is the fraction
improper ?
(top heavy)
Yes
x,÷
Action: Change to a mixed
Number
17
2
3
5
5
4
4
1
x,÷
That’s All Folks
Credits