Transcript Multiplying and Dividing Rational Numbers

MULTIPLYING RATIONAL NUMBERS
IF THE SIGNS ARE THE SAME,
MULTIPLY THEIR ABSOLUTE VALUES
AND THE ANSWER IS POSITIVE.
(+4)(+5) = 20
SIGNS ARE
THE SAME
(-4)(-5) = 20
(3)(6) = 18
(-10)(-4) = 40
THE ANSWER
IS POSITIVE
MULTIPLYING RATIONAL NUMBERS
IF THE SIGNS ARE THE DIFFERENT,
MULTIPLY THEIR ABSOLUTE VALUES
AND THE ANSWER IS NEGATIVE.
(+3)(-5) = -15
SIGNS ARE
DIFFERENT
(-3)(+5) = -15
(7)(-2) = -14
(-20)(3) = -60
THE ANSWER
IS NEGATIVE
MULTIPLYING RATIONAL NUMBERS
MULTIPLYING FRACTIONS
2 3
6
1
 

3 4 12
2
Multiply straight across
Reduce your answer
MULTIPLYING RATIONAL NUMBERS
MULTIPLYING FRACTIONS
7 6 42 21
 

4 11 44 22
Multiply straight across
Reduce your answer
MULTIPLYING RATIONAL NUMBERS
MULTIPLYING FRACTIONS
SECOND OPTION – REDUCE FIRST
3
7 6 21
 
42 11 22
Reduce - Cancel
Multiply straight across
MULTIPLYING RATIONAL NUMBERS
MULTIPLICATION PROPERTY OF -1
The product of any number and -1 is its
additive inverse (opposite).
5(-1) = -5
-5(-1) = 5
-30(-1) = 30
MULTIPLYING RATIONAL NUMBERS
Evaluate 3xy + 2y if x = 3 & y = -2
3xy + 2y = 3(3)(-2) + 2(-2)
= 9(-2) + 2(-2)
= -18 + (-4)
= -22
DIVIDING RATIONAL NUMBERS
SAME RULES AS FOR MULTIPLICATION!
IF THE SIGNS ARE THE SAME,
DIVIDE THEIR ABSOLUTE VALUES AND
THE ANSWER IS POSITIVE.
(+6)÷(+3) = 2
(-6)÷(-3) = 2
IF THE SIGNS ARE THE DIFFERENT,
DIVIDE THEIR ABSOLUTE VALUES AND
THE ANSWER IS NEGATIVE.
(+6)÷(-3) = -2
(-6)÷(+3) = -2
DIVIDING RATIONAL NUMBERS
DIVIDING FRACTIONS
2
2
6 3 6 10 4
    4
5 10 51 31 1
Invert and multiply (I.A.M.)
Reduce
Multiply straight across
DIVIDING RATIONAL NUMBERS
SIMPLIFYING ALGEBRAIC EXPRESSIONS
1
2
5 x  10 x  2

 x2
51
1
Reduce - Cancel
Can’t “cancel” unless able to do so in every term.
DIVIDING RATIONAL NUMBERS
SIMPLIFYING ALGEBRAIC EXPRESSIONS
2
3
8 y  12 2 y  3

82
2
Reduce - Cancel
Can’t “cancel” unless able to do so in every term.
DIVIDING RATIONAL NUMBERS
SIMPLIFYING ALGEBRAIC EXPRESSIONS
-1
-2
12m  6  2m  1

 12
2
2
Reduce - Cancel
Can’t “cancel” unless able to do so in every term.