Download Rules for Integers (Signed Numbers) Rules for Fractions and 4 and

Rules for Integers (Signed Numbers)
1.
1. Terminology
Adding Rules:
Positive + Positive = Positive
5+4=9
Negative + Negative = Negative
(-7) + (-2) = -9
Negative + Positive =
Add and keep
the same sign
Subtract & use the sign
Positive + Negative =
2.
Rules for Fractions
of the larger number
(- 7) + 4 = -3
6 + (-9) = - 3
(- 3) + 7 = 4
5 + (-3) = 2
Subtracting Rules: *(Change to Addition and follow adding rules)
a.
b.
(-5) - (-3) = (-5) + 3 = -2
d.
3 - 5 = 3 + (-5) = -2
3
4
and
4
3
Multiplying Rules:
a.
Find all factors common to both
numerator and denominator
b.
“Divide out” the common factors
c.
3. Multiplying Fractions
a.
Multiply numerator times numerator
and denominator times denominator
b.
Can also cancel common factors
Reduce to lowest terms if possible
Positive x Positive = Positive:
3x2=6
Negative x Negative = Positive:
(-2) x (-8) = 16
b.
Flip second fraction only (reciprocal)
Negative x Positive = Negative:
(-3) x 4 = -12
c.
Multiply fractions
Positive x Negative = Negative:
3 x (-4) = -12
d.
Reduce to lowest terms if possible
Change ÷ to •
5. Adding and Subtracting Fractions
a.
Rewrite fractions as equivalent
Fractions with a common denominator
12 ÷ 3 = 4
Negative ÷ Negative = Positive:
(-12) ÷ (-3) = 4
Negative ÷ Positive = Negative:
(-12) ÷ 3 = -4
Positive ÷ Negative = Negative:
12 ÷ (-3) = -4
4
5
)
12 4  3 4


15 5  3 5
Only considered in lowest terms when the numerator and
a.
Positive ÷ Positive = Positive:

denominator have no common factors left other than 1.
c.
Dividing Rules:
12
15
from both numerator and denominator.
4. Dividing Fractions
4.
and 4
Equivalent fractions: represent the same quantity. (ex:
before multiplying
3.
1
4
2. Reducing fractions to lowest terms
Positive – Positive = Positive + Negative = Subtract & use the sign of the
larger number:
denominator
Reciprocals: two fractions whose product is 1 (top and bottom are
switched.) Ex:
Negative - Negative = Negative + Positive = Subtract & use the sign of the
larger number (Change double negatives to a positive)
Denominator: bottom number of a fraction
numerator
(how many equal pieces the whole is divided into)
c.
Positive - Negative = Positive + Positive = Positive
5 - (-3) = 5 + 3 = 8
2
9
(how many pieces are being considered)
Negative - Positive = Negative + Negative = Negative
(- 5) - 3 = -5 + (-3) = -8
Numerator: top number of a fraction
b.
Add (subtract) numerators,
keep common denominator
c.
Reduce to lowest terms if possible
3 1
3 2 1
6 1
5
      
4 8
4 2 8
8 8
8
4 5 4  5 20 2
 


5 6 5  6 30 3
or
2 1
4 5 4 5 2
 

5 6 5  6 3
1 3
3 6 3 10 30 5
   

8 10 8 6 48 8
1 3

6 4
1 2 3 3
   
6 2 4 3
2 9
 
12 12
11

12