Download MATH 60 Section 2.3 Multiplying and Dividing Signed Numbers

MATH 60 Section 2.3 Multiplying and Dividing Signed Numbers
I. Review: Multiplication means____________ ___________
4 (3) means:
4 (-3) means:
Multiplying a positive number by a negative number gives a
________________ number.
Because of the commutative property of multiplication:
4 x (-3) = (-3) x 4 =
So, multiplying a negative number by a positive number gives a
_______________number.
Now let’s look at patterns. Mathematics is the science of patterns. It is
designed and defined so that patterns are followed (as much as possible):
(-3) x 4 =
(-3) x 3 =
(-3) x 2 =
(-3) x 1 =
(-3) x 0 =
(-3) x (
)=
(-3) x (
)=
(-3) x (
)=
(-3) x (
) =
In order for the pattern to remain consistent, we find that multiplying a
negative number times a negative number gives a ______________
number.
M60 Sec. 2.3 p.2
II. Summary of Rules for Multiplication:
1. The product of two numbers with the same signs is _______________.
Ex. 1: (5) (11) =
Ex. 2: (-4) ( -7) =
Ex. 3: 7 ( 3) =
Ex. 4: -6 ( -4) =
2. The product of two numbers with the opposite signs is ____________.
Ex. 5: (-2) (3) =
Ex. 6: (+4) (-3) =
Ex. 7: 6 (-2) =
Ex. 8: -10 (5) =
3. The product of any number and zero is ____________.
Ex. 9:
3 (0) =
Ex. 10:
0 (4) =
Part B: Relating Multiplication and Division:
Division is the ________________ _________________ of multiplication.
Division can be done by multiplying by the _____________________.
So, the same rules of signs which apply to multiplication also apply to
division:
Ex. 1: 6
÷
Ex. 2: -4
÷-8=
Ex. 3:
2 =
M60 Sec. 2.3 p.3
Ex. 4:
=
Ex. 5:
=
Ex. 6: 36 ÷ - 9 =
Ex. 7: -35 ÷ 4 =
So Rules 1 and 2 can be further summarized: The product or quotient of
Any two numbers with the same sign will give a _____________ number.
And, the product or quotient of any two numbers with opposite signs will
give a _________ number.
4. The quotient of zero and any non-zero number is _______________.
That is, zero divided BY any number is ________________.
Ex. 8:
Ex. 9:
5. The quotient of any number and zero is ____________. That is,
division BY ZERO is ___________________.
Ex. 10:
Ex. 11:
6. Multiplying and dividing by (-1) changes the _______________
Of the number. It is the same as taking the ______________ of the
number.
Ex. 12:
- (-5) = -1 (-5) = (-5) ÷ (-1) =
M60 Sec. 2.3 p.4
Revisit order of operations:
Ex. 13: 12 ÷ (-6) (-3)
Ex. 14: -48 ÷ (-8) (-2) ÷ 4
Practice for the proficiency test: Compute without a calculator:
1. –5 – (-7)
6. –19 + 12
2. –11 – 23
7. –12 + 13
3. –2 – 9
8. 18 – 20
4. –15 – (-18)
9. –3 + (-8) – 14
5. 10 – (-6)
10. –20 – 5 + 7
11.
 23 1
12.
13.
27
3
14.
 4 
 8 
15.
16. 5  6  3
17.
18. 12  2  4  6  1 
19. Evaluate the expression - x + y for x = - 7 and y = - 3
20. Evaluate the expression (- 2)(x) – (5)(y) for x = 3 and y = - 4