Download Topic 3-Multiplying Whole Numbers Study Guide Properties of

Topic 3-Multiplying Whole Numbers
Study Guide
Properties of Multiplication:
multiplication easier!
Four properties can be used to make
 Commutative Property of Multiplication: switch the order of the
factors and the product stays the same.
 Associative Property of Multiplication: regroup the factors and the
product stays the same.
 Identity Property of Multiplication: any number times 1 is that
number.
 Zero Property of Multiplication: any number times 0 is 0.
Mental Math Tricks : Use patterns of zeros to multiply numbers that end in
zeros!
Example: 90
Multiply 9
400
4 = 36
Then tack on the 3 zeros from the factors 90 400=36,000
Try these! 120
30
600 50
15 2,000
Estimating Products: You can use rounding or compatible numbers to
estimate!
 Rounding: round each number to a given place value to make the
calculation easy (using patterns of zeros from above.) Then multiply!
56
37
60
40 = 2,400
 Compatible numbers: change each number to compatible numbers
(numbers that are easy to compute with mentally).
259
43
250
40 = 10,000
 Is your estimate an overestimate or an underestimate? (Did you
round your numbers up or down?
Powers an d Exponents : You can express repeated multiplication of the
same number in a quick and easy way!
 Power: an expression made up of a base and an exponent that
indicates repeated multiplication.
 Base: the number being repeatedly multiplied by itself in a power
expression.
 Exponent: the small raised number in a power expression that tells
how many times the base is used as a factor.
Power
53
exponen
t
Base
53
exponential form
=
5∙5∙5
expanded form
=
125
standard form
Distributive Property : Multiplying a number by a sum or difference is the
same as multiplying by each number in the sum or difference and then
adding the products. (This can make mental multiplication easier!)
Example: 9
32 = 9 (30+2)
Multiply the 9 by the 30, then multiply the 9 by the 2, then add the
products!
9 30 + 9 2=
270 + 18=
288
Try these! Rewrite each expression using the Distributive Property:
6 (3+7)
15
(10 + 3)