Chapter 1 Summary and Review 119Multiplication Properties of 0 and 1
The product of any whole number and 0 is 0.
The product of any whole number and 1 is
that whole number.
and
15 1 15 and 1(6) 60 9 0 3(0) 0
Commutative property of multiplication:The
order in which whole numbers are multiplied
does not change their product.
Associative property of multiplication: The
way in which whole numbers are grouped
does not change their product.
By the commutative property, the product is the same.By the associative property, the product is the same.(37) 10 3 (710)
5 9 9 5
To estimatea product, use front-end rounding
to approximate the factors. Then multiply.
To estimate the product for find
Round to the nearest tenRound to the nearest hundred74 873 70 (^900)
74 873, 70 900.
Application problems that involve repeated
additionare often more easily solved using
multiplication.
HEALTH CARE A doctor’s office is open 210 days a year. Each day
the doctor sees 25 patients. How many patients does the doctor see in
1 year?
This repeated additioncan be calculated by multiplication:25 210
The number of
patients seen
each yearWe can use multiplication to count objects
arranged in rectangular patterns of neatly
arranged rows and columns called rectangular
arrays.
Some key wordsand phrasesthat are often
used to indicate multiplication are:
double triple twice of times
CLASSROOMS A large lecture hall has 16 rows of desks and there
are 12 desks in each row. How many desks are in the lecture hall?
Therectangular arrayof desks indicates multiplication:16 12
The number of
desks in the
lecture hallThe area of a rectangleis the measure of the
amount of surface it encloses. Area is measured
in square units, such as square inches (written
in. ) or square centimeters (written cm ).
or
AlwLetters (or symbols) that are used to represent
numbers are called variables.
Area of a rectanglelengthwidth2 2Find the area of the rectangle shown below.
25 in.
4 in.Alw
Replace lwith 25 and wwith 4.
Multiply.
The area of the rectangle is 100 square inches, which can be written in
more compact form as 100 in.^2.