<< Chapter < Page Chapter >> Page >

Simplify:

18 ( −4 ) ÷ ( −2 ) 3

9

Got questions? Get instant answers now!

Simplify: −30 ÷ 2 + ( −3 ) ( −7 ) .

Solution

First we will multiply and divide from left to right. Then we will add.

−30 ÷ 2 + ( −3 ) ( −7 )
Divide. −15 + ( −3 ) ( −7 )
Multiply. −15 + 21
Add. 6
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Simplify:

−27 ÷ 3 + ( −5 ) ( −6 )

21

Got questions? Get instant answers now!

Simplify:

−32 ÷ 4 + ( −2 ) ( −7 )

6

Got questions? Get instant answers now!

Evaluate variable expressions with integers

Now we can evaluate expressions    that include multiplication and division with integers. Remember that to evaluate an expression, substitute the numbers in place of the variables, and then simplify.

Evaluate 2 x 2 3 x + 8 when x = −4 .

Solution

.
. .
Simplify exponents. .
Multiply. .
Subtract. .
Add. .

Keep in mind that when we substitute −4 for x , we use parentheses to show the multiplication. Without parentheses, it would look like 2 · −4 2 3 · −4 + 8 .

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Evaluate:

3 x 2 2 x + 6 when x = −3

39

Got questions? Get instant answers now!

Evaluate:

4 x 2 x 5 when x = −2

13

Got questions? Get instant answers now!

Evaluate 3 x + 4 y 6 when x = −1 and y = 2 .

Solution

.
Substitute x = −1 and y = 2 . .
Multiply. .
Simplify. .
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Evaluate:

7 x + 6 y 12 when x = −2 and y = 3

−8

Got questions? Get instant answers now!

Evaluate:

8 x 6 y + 13 when x = −3 and y = −5

19

Got questions? Get instant answers now!

Translate word phrases to algebraic expressions

Once again, all our prior work translating words to algebra transfers to phrases that include both multiplying and dividing integers. Remember that the key word for multiplication is product and for division is quotient .

Translate to an algebraic expression and simplify if possible: the product of −2 and 14 .

Solution

The word product tells us to multiply.

the product of −2 and 14
Translate. ( −2 ) ( 14 )
Simplify. −28
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Translate to an algebraic expression and simplify if possible:

the product of −5 and 12

−5 (12) = −60

Got questions? Get instant answers now!

Translate to an algebraic expression and simplify if possible:

the product of 8 and −13

8 (−13) = −104

Got questions? Get instant answers now!

Translate to an algebraic expression and simplify if possible: the quotient of −56 and −7 .

Solution

The word quotient tells us to divide.

the quotient of −56 and −7
Translate. −56 ÷ ( −7 )
Simplify. 8
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Translate to an algebraic expression and simplify if possible:

the quotient of −63 and −9

−63 ÷ −9 = 7

Got questions? Get instant answers now!

Translate to an algebraic expression and simplify if possible:

the quotient of −72 and −9

−72 ÷ −9 = 8

Got questions? Get instant answers now!

Key concepts

  • Multiplication and Division of Signed Numbers
    Same signs Product
    •Two positives
    •Two negatives
    Positive
    Positive
    Different signs Product
    •Positive • negative
    •Negative • positive
    Negative
    Negative
  • Multiplication by −1
    • Multiplying a number by −1 gives its opposite: −1 a = a
  • Division by −1
    • Dividing a number by −1 gives its opposite: a ÷ ( −1 ) = −a

Practice makes perfect

Multiply Integers

In the following exercises, multiply each pair of integers.

Divide Integers

In the following exercises, divide.

Simplify Expressions with Integers

In the following exercises, simplify each expression.

5 ( −6 ) + 7 ( −2 ) −3

−47

Got questions? Get instant answers now!

8 ( −4 ) + 5 ( −4 ) −6

Got questions? Get instant answers now!

−8 ( −2 ) −3 ( −9 )

43

Got questions? Get instant answers now!

−7 ( −4 ) −5 ( −3 )

Got questions? Get instant answers now!

( 8 11 ) ( 9 12 )

9

Got questions? Get instant answers now!

( 6 11 ) ( 8 13 )

Got questions? Get instant answers now!

−10 ( −4 ) ÷ ( −8 )

−5

Got questions? Get instant answers now!

−8 ( −6 ) ÷ ( −4 )

Got questions? Get instant answers now!

65 ÷ ( −5 ) + ( −28 ) ÷ ( −7 )

−9

Got questions? Get instant answers now!

52 ÷ ( −4 ) + ( −32 ) ÷ ( −8 )

Got questions? Get instant answers now!

9 2 [ 3 8 ( −2 ) ]

−29

Got questions? Get instant answers now!

11 3 [ 7 4 ( −2 ) ]

Got questions? Get instant answers now!

( −3 ) 2 −24 ÷ ( 8 2 )

5

Got questions? Get instant answers now!

( −4 ) 2 32 ÷ ( 12 4 )

Got questions? Get instant answers now!

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

−2 x + 17 when

  1. x = 8
  2. x = −8

  1. 1
  2. 33

Got questions? Get instant answers now!

−5 y + 14 when

  1. y = 9
  2. y = −9

Got questions? Get instant answers now!

10 3 m when

  1. m = 5
  2. m = −5

  1. −5
  2. 25

Got questions? Get instant answers now!

18 4 n when

  1. n = 3
  2. n = −3

Got questions? Get instant answers now!

p 2 5 p + 5 when p = −1

8

Got questions? Get instant answers now!

q 2 2 q + 9 when q = −2

Got questions? Get instant answers now!

2 w 2 3 w + 7 when w = −2

21

Got questions? Get instant answers now!

3 u 2 4 u + 5 when u = −3

Got questions? Get instant answers now!

6 x 5 y + 15 when x = 3 and y = −1

38

Got questions? Get instant answers now!

3 p 2 q + 9 when p = 8 and q = −2

Got questions? Get instant answers now!

9 a 2 b 8 when a = −6 and b = −3

−56

Got questions? Get instant answers now!

7 m 4 n 2 when m = −4 and n = −9

Got questions? Get instant answers now!

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

The product of −3 and 15

−3·15 = −45

Got questions? Get instant answers now!

The product of −4 and 16

Got questions? Get instant answers now!

The quotient of −60 and −20

−60 ÷ (−20) = 3

Got questions? Get instant answers now!

The quotient of −40 and −20

Got questions? Get instant answers now!

The quotient of −6 and the sum of a and b

−6 a + b

Got questions? Get instant answers now!

The quotient of −7 and the sum of m and n

Got questions? Get instant answers now!

The product of −10 and the difference of p and q

−10 ( p q )

Got questions? Get instant answers now!

The product of −13 and the difference of c and d



Got questions? Get instant answers now!

Everyday math

Stock market Javier owns 300 shares of stock in one company. On Tuesday, the stock price dropped $12 per share. What was the total effect on Javier’s portfolio?

−$3,600

Got questions? Get instant answers now!

Weight loss In the first week of a diet program, eight women lost an average of 3 pounds each. What was the total weight change for the eight women?

Got questions? Get instant answers now!

Writing exercises

In your own words, state the rules for multiplying two integers.

Sample answer: Multiplying two integers with the same sign results in a positive product. Multiplying two integers with different signs results in a negative product.

Got questions? Get instant answers now!

In your own words, state the rules for dividing two integers.

Got questions? Get instant answers now!

Why is −2 4 ( −2 ) 4 ?

Sample answer: In one expression the base is positive and then we take the opposite, but in the other the base is negative.

Got questions? Get instant answers now!

Why is −4 2 ( −4 ) 2 ?

Got questions? Get instant answers now!

Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Prealgebra' conversation and receive update notifications?

Ask