Download Multiply and Divide Rational Numbers, Writing Verbal Expressions

Multiply and Divide Rational
Numbers, Writing Verbal
Expressions Algebraically
Objective: To multiply and divide rational
numbers. To write verbal expressions for
algebraic expressions and to write algebraic
expressions for verbal expressions.
Sign Rules
• The product or quotient of two rational
numbers having the same sign is positive.
• The product or quotient of two rational
numbers having different signs is negative.
Example 1
• Find each product or quotient.
-5.4(0.05)
= -0.27
-6.84 ÷ (-2.4)
= 2.85
Multiplying Fractions
• To multiply fractions, multiply the numerators
and multiply the denominators.
• If the numerators and denominators have
common factors, you can simplify before you
multiply by canceling.
Example 2
• Find each product.
4 4
7 5
1 5
3
4 6
16

35
1 23

4 6
23

24
1
4
3 2
8 31
1

4
1
Example 3
• Find  7  21
5   
10
3


7

15

Dividing Fractions
• Two numbers whose product is 1 are called
multiplicative inverses or reciprocals.
• To divide one fraction by another fraction,
multiply the dividend by the reciprocal of the
divisor.
– First fraction times reciprocal of second fraction.
Example 4
• Name the reciprocal of each number.
4
9
7
2
8
5
9
4
23

8
8
23
5

1
1
5
Example 5
• Find each quotient.
3 1

5 4
3 4

5 1
12

5
3 2

10 9
3 9

10 2
27

20
7 1
2
8 3
7 7
 
8 3
1
7 3

8 71
3

8
2 4
 
3 5
1
2 5

3 42
5

6
Writing Verbal Expressions
• An algebraic expression consists of sums
and/or products of numbers and variables.
• In the algebraic expression 0.10d, the letter d
is called a variable.
• In algebra, variables are symbols used to
represent unspecified numbers or values.
• Any letter may be used as a variable.
Writing Verbal Expressions
z
• Examples: 0.10d, 2x + 4, 3 + , p • q, 4cd ÷ 3mn
6
1 term
2 terms
2 terms
1 term
1 term
• A term of an expression may be a number, a
variable, or a product or quotient of numbers
and variables.
• A variable term is a term that contains a
variable.
• A constant term is a term that only has a
number.
Writing Verbal Expressions
• In a multiplication expression, the quantities
being multiplied are factors, and the result is
the product.
• An expression like xn is called a power.
• The exponent indicates the number of times
the base is used as a factor.
base
xn
exponent
Example 6
• Write a verbal expression for each algebraic
expression.
8x2
Eight times x
squared.
y5 – 16y
Y to the fifth power
minus the product of 16
and y.
Check Your Progress
• Choose the correct answer for the following.
• Write a verbal expression for 7a4.
A.
B.
C.
D.
7 times a
7 times the product of 4 and a
7 times a to the fourth power
4 times a to the seventh power
Check Your Progress
• Choose the correct answer for the following.
• Write a verbal expression for x2 + 3.
A.
B.
C.
D.
The sum of 3 and x
The product of x squared and 3
The sum of x and 3 squared
The sum of x squared and 3
Write Algebraic Expressions
• In order to write algebraic expressions, you
will need to be able to translate words into
symbols.
Operation
Verbal Phrases
Addition
Sum, Plus, More than, Increased by, Added to
Subtraction
Difference, Minus, Less than, Decreased by, Subtracted from
Multiplication
Times, Product of, Multiplied by, Of
Division
Quotient of, Divided by
Example 7
• Write an algebraic expression for each verbal
expression.
5 less than a
number c.
c–5
9 plus the
product of 2
and d.
9 + 2d
Two fifths of
the area a.
2
2a
a or
5
5
Check Your Progress
• Choose the correct answer for the following.
• Write an algebraic expression for nine more
than a number h.
A.
B.
C.
D.
9–h
9h
9+h
h–9
Check Your Progress
• Choose the correct answer for the following.
• Write an algebraic expression for the
difference of 6 and 4 times a number x.
A.
B.
C.
D.
6 – 4x
(6 – 4) + x
6 + 4x
6x – 4
Check Your Progress
• Choose the correct answer for the following.
• Write an algebraic expression for one half the
size of the original perimeter p.
A.
B.
C.
D.
2p
½p
p2
p½
Real-World Problems
• Variables can represent quantities that are
known and quantities that are unknown.
• They are also used in formulas, expressions,
and equations.
Example 8
• Mr. Nehru bought two adult tickets and three
student tickets for the planetarium show.
Write an algebraic expression that represents
the cost of the tickets.
– Let a = adult tickets.
– Let s = student tickets.
2a + 3s
Check Your Progress
• Choose the correct answer for the following.
• Lorenzo bought a bag of peanuts that cost p
dollars and he gave the cashier a $20 bill.
Write an expression for the amount of change
that he will receive.
A.
B.
C.
D.
20 – p
p – 20
20 + p
20 ÷ p