Essential Math 5 B - Unit 9, Lesson 6: Algebra: Numerical Expressions Unit Test
answers please
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@bot
Arrange the expressions below in order from least to greatest. Place the least at the top and greatest at the bottom.
I apologize, but you did not provide any expressions to order. Please provide the expressions you need to be arranged in order for me to assist you.
@bot
Arrange the expressions below in order from least to greatest. Place the least at the top and greatest at the bottom.
(
72
÷
8
)
−
2
×
3
+
1
72
÷
(
8
−
2
)
×
3
+
1
72
÷
(
8
−
2
)
×
(
3
+
1
)
72
÷
8
−
2
×
(
3
+
1
)
First, let's simplify each expression:
Expression 1: ((72 ÷ 8) − 2) × 3 + 1 = (9 - 2) × 3 + 1 = 21
Expression 2: 72 ÷ (8 − 2) × 3 + 1 = 72 ÷ 6 × 3 + 1 = 37
Expression 3: 72 ÷ (8 − 2) × (3 + 1) = 72 ÷ 6 × 4 = 48
Expression 4: 72 ÷ 8 − 2 × (3 + 1) = 9 - 2 × 4 = 1
Therefore, the expressions in order from least to greatest are:
Expression 4: 1
Expression 1: 21
Expression 3: 48
Expression 2: 37
So, the order is:
1 → 21 → 48 → 37
@bot
Drag the operation signs to make the equation true. An operation may be used once. more than once, or not at all
+−×÷
12
(
7
−
4
)
+
5
3 = 19
The correct arrangement of the operation signs is:
12 ÷ (7 - 4) + 5 × 3 = 19
Explanation:
(7 - 4) = 3
12 ÷ 3 = 4
5 × 3 = 15
4 + 15 = 19
So, the arrangement of the operation signs is:
÷ - + ×
Select all of the expressions that are equal to
8
×
35
.
A.
8
×
(
30
+
5
)
B.
5
+
3
×
35
C.
(
8
×
30
)
+
(
8
×
5
)
D.
(
8
+
30
)
×
(
8
+
5
)
E.
8
×
(
20
+
15
)
The expressions that are equal to 8 × 35 are:
A. 8 × (30 + 5) = 8 × 35 = 280
C. (8 × 30) + (8 × 5) = 240 + 40 = 280
E. 8 × (20 + 15) = 8 × 35 = 280
So, the correct options are A, C, and E.
Phillipa rode her bicycle every day over the weekend. Phillipa rode
[
(
13
.
5
+
8
.
5
)
÷
2
]
miles on Friday,
[
18
−
(
2
×
4
)
]
miles on Saturday and
[
20
−
(
5
−
3
)
]
miles on Sunday.
On which day did Phillipa ride her bicycle the most?
She rode her bicycle the most on
.
Phillipa rode her bicycle the following number of miles:
Friday = (13.5 + 8.5) ÷ 2 = 11 miles
Saturday = 18 − (2 × 4) = 10 miles
Sunday = 20 − (5 − 3) = 18 miles
Therefore, Phillipa rode her bicycle the most on Sunday with a distance of 18 miles.
@bot @bot @bot @bot @bot @bot
Part A
Write an expression for the number of songs they need for their show.
A.
(
11
−
4
)
+
3
×
11
−
4
−
5
B.
(
11
−
4
)
+
3
×
(
11
−
4
)
−
5
C.
(
11
−
4
)
+
3
−
4
×
11
−
5
D.
(
11
−
4
)
+
3
−
5
×
(
11
−
4
)
Part B
How many songs do they need for their show?
A.
39 songs
B.
31 songs
C.
25 songs
D.
23 songs
Part A: To write an expression for the number of songs they need for their show, we need to calculate the expression in one of the options.
A. (11 − 4) + 3 × 11 − 4 − 5 = 7 + 33 - 4 - 5 = 31
B. (11 − 4) + 3 × (11 − 4) − 5 = 7 + 21 - 5 = 23
C. (11 − 4) + 3 − 4 × 11 − 5 = 7 - 33 - 5 = -31
D. (11 − 4) + 3 − 5 × (11 − 4) = 7 - 35 = -28
Therefore, the expression for the number of songs they need for their show is option B:
(11 − 4) + 3 × (11 − 4) − 5
Part B: To find out how many songs they need for their show, we need to evaluate the expression in option B:
(11 − 4) + 3 × (11 − 4) − 5 = 7 + 21 - 5 = 23
Therefore, they need 23 songs for their show. The answer is option D.
Use the order of operations to evaluate the expression.
4
×
(
3
4
−
1
2
)
+
3
×
6
A.
19
B.
20
1
2
C.
24
D.
33
To evaluate the expression using the order of operations, we need to follow the acronym "PEMDAS" which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
So, the expression becomes:
4 × (3/4 - 1/2) + 3 × 6
= 4 × (0.75 - 0.5) + 3 × 6
= 4 × 0.25 + 18
= 1 + 18
= 19
Therefore, the answer is A. 19.
Which expression represents the following calculation?
Find 7.4 times the difference between 87 and 24.
A.
7
.
4
×
87
−
24
B.
24
×
(
87
−
7
.
4
)
C.
24
×
87
−
7
.
4
D.
7
.
4
×
(
87
−
24
)
The calculation is to find 7.4 times the difference between 87 and 24.
The difference between 87 and 24 is 87 - 24 = 63.
So, we need to multiply this difference by 7.4.
The expression that represents this calculation is:
D. 7.4 × (87 - 24)
So, the answer is D. 7.4 × (87 - 24).
Use the order of operations to find the value of the expression.
2
+
3
×
16
−
2
×
21
−
3
A.
5
B.
14
C.
35
D.
44
To evaluate the expression using the order of operations, we need to follow the acronym "PEMDAS" which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
2 + 3 × 16 − 2 × 21 − 3
= 2 + 48 - 42 - 3
= 50 - 42 - 3
= 8 - 3
= 5
Therefore, the answer is A. 5.
Use the order of operations to find the value of the expression.
12
÷
2
×
3
−
(
7
−
5
)
A.
0
B.
6
C.
16
D.
19
To evaluate the expression using the order of operations, we need to follow the acronym "PEMDAS" which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
12 ÷ 2 × 3 - (7 - 5)
= 6 × 3 - 2
= 18 - 2
= 16
Therefore, the answer is C. 16.
Insert parentheses to make the statement true.
12
+
6
×
11
−
7
=
72
A.
12
+
(
6
×
11
)
−
7
=
72
B.
12
+
6
×
(
11
−
7
)
=
72
C.
(
12
+
6
)
×
11
−
7
=
72
D.
(
12
+
6
)
×
(
11
−
7
)
=
72
To insert parentheses to make the statement true, we need to follow the order of operations. Multiplication needs to be done before addition and subtraction.
A. 12 + (6 × 11) − 7 = 12 + 66 - 7 = 71 (not equal to 72)
B. 12 + 6 × (11 − 7) = 12 + 6 × 4 = 36 (not equal to 72)
C. (12 + 6) × 11 − 7 = 18 × 11 - 7 = 191 (not equal to 72)
D. (12 + 6) × (11 − 7) = 18 × 4 = 72 (equal to 72)
Therefore, the correct option is D. (12 + 6) × (11 − 7) = 72.
Determine which of the expressions could be used to represent the following calculation:
Divide the difference between 96 and 72 by 12.
Select all that apply.
A.
(
96
−
72
)
÷
12
B.
96
−
(
72
÷
12
)
C.
(
96
÷
12
)
−
72
D.
24
÷
12
E.
96
÷
6
The calculation is to divide the difference between 96 and 72 by 12.
The difference between 96 and 72 is 96 - 72 = 24.
So, we need to divide this difference by 12.
The expression that represents this calculation is:
A. (96 - 72) ÷ 12
Also, we can simplify option C:
(96 ÷ 12) − 72 = 8 - 72 = -64
Option D is just 2 which is not equal to the expression we need.
Option E is 96 ÷ 6 which is just 16 and not equal to the expression we need.
So, only options A and B are valid expressions for the given calculation.
Therefore, the correct options are A and B.