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© Glencoe/McGraw-Hill 11 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionOrder of Operations
Evaluate (10 � 2) � 4 · 2.
(10 � 2) � 4 � 2 � 8 � 4 � 2 Subtract first since 10 � 2 is in parentheses.� 8 � 8 Multiply 4 and 2.� 0 Subtract 8 from 8.
Evaluate 8 � (1 � 5)2 � 4.
8 � (1 � 5)2 � 4 � 8 � 62 � 4 First, add 1 and 5 inside the parentheses.� 8 � 36 � 4 Find the value of 62.� 8 � 9 Divide 36 by 4.� 17 Add 8 and 9.
Evaluate each expression.
1. (1 � 7) � 3 2. 28 � 4 · 7 3. 5 � 4 � 3
4. (40 � 5) � 7 � 2 5. 35 � 7(2) 6. 3 � 103
7. 45 � 5 � 36 � 4 8. 42 � 6 � 2 � 9 9. 2 � 8 � 32 � 2
10. 5 � 22 � 32 � 8 11. 3 � 6 � (9 � 8)3 12. 3.5 � 102
Use the order of operations to evaluate numerical expressions.
1. Do all operations within grouping symbols first.
2. Evaluate all powers before other operations.
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.
© Glencoe/McGraw-Hill 16 Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionAlgebra: Variables and Expressions
Evaluate 6x � 7 if x � 8.
6x � 7 � 6(8) � 7 Replace x with 8.� 48 � 7 Use the order of operations.� 41 Subtract 7 from 48.
Evaluate 5m � 3n if m � 6 and n � 5.
5m � 3n � 5(6) � 3(5) Replace m with 6 and n with 5.� 30 � 15 Use the order of operations.� 15 Subtract 15 from 30.
Evaluate �a3b� if a � 7 and b � 6.
�a3b� � �
(7)3(6)� Replace a with 7 and b with 6.
� �432� The fraction bar is like a grouping symbol.
� 14 Divide.
Evaluate x3 � 4 if x � 3.
x3 � 4 � 33 � 4 Replace x with 3.� 27 � 4 Use the order of operations.� 31 Add 27 and 4.
Evaluate each expression if a � 4, b � 2, and c � 7.
1. 3ac 2. 5b3 3. abc
4. 5 � 6c 5. �a8b� 6. 2a � 3b
7. �b44� 8. c � a 9. 20 � bc
10. 2bc 11. ac � 3b 12. 6a2
13. 7c 14. 6a � b 15. ab � c
To evaluate an algebraic expression you replace each variable with its numerical value, then use theorder of operations to simplify.
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© Glencoe/McGraw-Hill 185 Mathematics: Applications and Concepts, Course 2
The table below shows phrases written as mathematical expressions.
The table below shows sentences written as an equation.
Write each phrase as an algebraic expression.
1. 7 less than m 2. the quotient of 3 and y
3. the total of 5 and c 4. the difference of 6 and r
5. n divided by 2 6. the product of k and 9
Write each sentence as an algebraic equation.
7. A number increased by 7 is 11.
8. The price decreased by $4 is $29.
9. Twice as many points as Bob would be 18 points.
10. After dividing the money 5 ways, each person got $67.
11. Three more than 8 times as many trees is 75 trees.
12. Seven less than a number is 15.
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionWriting Expressions and Equations
Phrases Expression Phrases Expression
9 more than a numberthe sum of 9 and a numbera number plus 9a number increased by 9the total of x and 9
x � 9
4 subtracted from a numbera number minus 44 less than a numbera number decreased by 4the difference of h and 4
h � 4
Phrases Expression Phrases Expression
6 multiplied by g6 times a numberthe product of g and 6
6ga number divided by 5the quotient of t and 5divide a number by 5
�5t�
Sentences Equation
Sixty less than three times the amount is $59.Three times the amount less 60 is equal to 59.59 is equal to 60 subtracted from three times a number.A number times three minus 60 equals 59.
3n � 60 � 59
MATH-7
Expressions
Exam not valid for Paper Pencil Test Sessions
[Exam ID:155T1Z
1 "Sixty less forty is some number." If n is that number, which best represents the statement?A 60 < 40 + nB 40 - 60 = nC 60 < 40 - nD 60 - 40 = n
2 A box contains 25 packages of notebook paper. The price of the box is $56.25. Each
of the packages of notebook paper costs the same amount. Which could be used to find p, the price of a package of notebook paper?
A = 56.25p 25
B p + 25 = 56.25C 25p = 56.25D p - 25 = 56.25
3 If a = 2.4, b = 3.6, and c = 3.7, what is the value of (a - 1.7 • b ) + a • c ?
A 5.16B -4.88C 4.75D 11.4
4 If a stands for the number, which best represents the sentence below?
"A number less than seventy-five is twenty-seven."
A a - 75 = 27B 75a = 27C 75 - a = 27D a ÷ 75 = 27
5 Write an equation for the given verbal sentence:
A number divided by six is one-half.
A = x 6
1 2
B = 6 x
1 2
C = x 6
1 5
D 6x = 1 2
6 Which expression represents the phrase "one-third of a number"?
A d - 1 3
B d 3
C 3dD d - 3
7
What is the value of - 1 + if x = 3, y = 7, and z = 2?2x 2 - 11x 2
y z
A 11B -3C 12D -5
8 A taxi charges $5 per ride plus $0.25 for each mile driven. Debbie paid $7.50 for her
ride. Which of the following could be used to find the number of miles she rode in the taxi?A 5x = 0.25(7.50)B 0.25x = 7.50C 5x + 0.25 = 7.50D 0.25x + 5 = 7.50
9 Which best represents the number sentence shown?
t - 9 = 5
A Nine subtract a number is five.B Nine less a number is five.C Nine less than a number is five.D A number less than nine is five.
10 Which algebraic equation best represents the verbal sentence below?
“Three increased by two times a number equals thirty-two”
A 3 = 2s - 32B 3 + 2s = 32C 3 – 2s = 32D 5s = 32
11 Which algebraic expression best represents the verbal expression shown?
“Eleven times the sum of a number and five”
A 11 + 5xB 11 + x 2 + 5C 11 + 5 + xD 11(x + 5)
12
What is the value of if a = -4, b = 3?a + 4b a + b
A -24B -8C 8D 0
13 What is the value of xy - 2y when x = -3 and y = 6?
A -30B -120C 6D 30
14
What is the value of when x = -4 and y = 3?x + y xy
A -1 12
B -7 12
C 7 12
D 1 12
15 Which expression has a value of 9.2 when r = 2.4 and s = 6?
A
B
C
D
16 Which best represents the number sentence shown?
14 + x = -42
A Negative forty-two minus a number is fourteen.B Fourteen minus a number is forty two.C Fourteen plus forty-two is a negative number.D Fourteen plus a number equals negative forty-two.
17 What is the value of |y | + 4 - y • x if x = 7 and y = -2?
A 16B 20C -8D -12
18 Which expression has a value of -27 when w = 5 and s = 6?
A
B
C
D
19 Directions: Type your answer in the box.
What is the value of the expression 3q - 6 when q = -2?
20 If x = 2, y = 6, and z = 4, which expression is equivalent to 4?
A - x - y z
z x
B - x + y z
z x
C + x + y z
z x
D + x - y z
z x
21 If a stands for the number, which best represents the sentence below?
"The product of six and a number less five is ten."
A 5 - = 106 a
B 6a - 5 = 10
C 10 = - 56 a
D 5 - 6a = 10
22
If b = 5, what is the value of 7 + - 1?5b 4
A 14B 12.25C 13D 6.25
23
What is the value of where x = -1, y = -3, and z = 0?x² – y z
A -2B 4C -4D Undefined
24
What is the value of + 2w - 7 if w = -3?13w 13
A -17B -10C -16D -4
25
If y = -5, what is the value of - 6 + 3y ?2y + 2 4
A 11B 13C -23D -24
26 Look at the expression.
+ 6
Which replacement values for x , y , and z will give the expression a value of 8?
x (4 + z ) y
A x = 1, y = 5, and z = 2B x = 2, y = 5, and z = 1C x = 2, y = 1, and z = 5D x = 5, y = 2, and z = 1
27 What value can be substituted into the following expression to create a whole
number?
-6 + xA -2B 7C 0D 5
28 What is the value of m (h + p ) - p ÷ h + m if h = -1, m = 3, and
p = 4?A 16B 8C 0D 2
29 Look at the expression.
(2 a + c ) - 4c • b
Which replacement values for a , b , and c will give the expression a value of 34?A a = 6 , b = 3 , and c = 2B a = -6 , b = 3 , and c = -2C a = 6 , b = 3 , and c = -2D a = 6 , b = -3 , and c = -2
30 Look at the expression.
If x = -8, and z = 6, then what must the value of y be for the expression to be equivalent to 1?
x + 4 2y + z
A -1B -5C -2D 0
31 Which best represents the number sentence shown?
x - 6 = 4
A A number less six is 4.B Six subtract a number is four.C The product of a number and six is four.D A number less than six is four.
32 Which expression does NOT have a value of 18 when l = 3, w = 4, and h = 2 ?
A 2l + 2w + 2hB 2( l + w ) + 2hC 2l + 2( w + h )D 2( l + 2w ) + 2h
33 Which expression represents the phrase “three less than a number“?
A x - 3B 3 - xC 3 < xD 3x
34 Which phrase best represents the following?
“ A number less 4”
A 4 – nB n < 4C n – 4D n > 4
35 A box contains 50 packages of pencils. The price of the box is $10.25. Each package
of pencils cost the same amount. Which could be used to find p , the price of a package of pencils.A p - 50 = 10.25B p + 50 = 10.25
C = 10.25p 50
D 50p = 10.25
36 Which phrase does NOT represent the following?
7 + 2n
A Seven more than twice a number.B A number plus seven times two.C The product of two and a number plus seven.D The sum of seven and two times a number.
37 Which number sentence best represents the verbal expression shown?
“Four minus six times a number equals twelve”
A 6n – 4 = 12B 4 – 6n = 12C 12 – 4 = 6nD 6 – 4n = 12
38 Which best represents the number sentence shown?
• 4 = 12a 6
A Twelve is the result of a number times six plus four.B The product of six and a number multiplied by four is twelve.C A number divided by six less four plus twelve.D The quotient of a number and six times four is twelve.
39 Which of the following is an expression?
A 4 + a + 5cB 13a = 2C 4 = a + 6D 12
40 Which of the following is an equation?
A 6xB 6x + 3C 6x + 3 - 4D 6x + 3 = 4
