Section 3.4 Part 1: Multiplying and Dividing Integers and Variable Expressions with Integers

Evaluate 5a2−17a+8 when a=−2.

62 To evaluate 5a^2−17a+8 when a=−2, substitute −2 for a in the expression and simplify 5a^2−17a+8 5(−2)^2−17(−2)+8 20−(−34)+8 =62

Multiply: 10(−10).

-100

Simplify: 9−2[3−8(−2)].

-29 Following the order of operations, we should simplify inside the parentheses first, so we first find 3−8(−2). Since 8 and −2 have different signs, the product 8(−2)=−16 is negative, and we have 3−8(−2)=3−(−16) Subtracting a negative is like adding a positive, so 3−(−16)=3+16, which adds to 19. Substituting 3−8(−2)=19 into the original expression yields9−2[3−8(−2)]=9−2(19)Multiplying 2 by 19, this becomes 9−2(19)=9−38. Finally, subtracting 38 from 9 gives the negative value −29.

Divide: −28÷7.

-4

Divide: −63÷9.

-7

Divide: 64÷(−8).

-8

Simplify: (−3)(−3)−16÷(4−12).

11 Following the order of operations, we should simplify inside the parentheses first. Since 4−12=−8, we have (−3)(−3)−16÷(4−12)=(−3)(−3)−16÷(−8) Multiplication and division come before subtraction in the order of operations, so next we find the product (−3)(−3)=9, which is positive because the factors −3 and −3 have the same sign, and the quotient 16÷(−8)=−2, which is negative because 16 and −8 have different signs. So far we have (−3)(−3)−16÷(4−12)=9−(−2) Finally, subtracting a negative is like adding a positive, so 9−(−2)=9+2, which adds to 11.

Multiply: (−2)(−6).

12

Divide: −14÷(−7).

2

Multiply: (−3)(−8).

24

Simplify: 23−2(4−6).

27 Following the order of operations, we should simplify inside the parentheses first. Since 4−6=−2, we have 23−2(4−6)=23−2(−2) Next in the order of operations is multiplication, so we multiply 2 by −2. The signs are different, so the product 2(−2)=−4 is negative. We now have 23−2(4−6)=23−(−4) Subtracting a negative is like adding a positive, so 23−(−4)=23+4, which adds to 27.

Evaluate 8c2^−7c+2 when c=−2.

48 To evaluate 8c^2−7c+2 when c=−2, substitute −2 for c in the expression and simplify 8c^2−7c+2 8(−2)2−7(−2)+2 32−(−14)+2 =48

Multiply: (−10)(−5).

50

Evaluate 7a^2−14a+4 when a=−2.

60 To evaluate 7a^2−14a+4 when a=−2, substitute −2 for a in the expression and simplify 7a^2−14a+4 7(−2)^2−14(−2)+4 28−(−28)+4 =60

Evaluate 9y2−4y+8 when y=−8.

616 To evaluate 9y^2−4y+8 when y=−8, substitute −8 for y in the expression and simplify 9y^2−4y+8 9(−8)^2−4(−8)+8 576−(−32)+8 =616

Simplify: (−4)2−32÷(12−4).

Following the order of operations, we should simplify inside the parentheses first. Since 12−4=8, we have (−4)2−32÷(12−4)=(−4)2−32÷8 Multiplication and division come before subtraction in the order of operations, so next we find the product (−4)2=−8, which is negative because −4 and 2 have different signs, and the quotient 32÷8=4, which is positive because 32 and 8 are both positive. So far we have(−4)2−32÷(12−4)=−8−4Finally, subtracting 4 from −8 yields −8−4 =−12.