Solving Numerical Expressions
Evaluate:
14 divide 2 + (5-4)
Answer: 8 --> Use Pemdas!
P: (5-4) = 1
D: 14 divided by 2 = 7
A: 7 + 1 = 8
Evaluate the expression 7.5 - h for h = 4.
Answer: 3.5
Substitute h for 4 ! 7.5 - 4 = 3.5
What is the prime factorization of 66?
Answer: 2 x 3 x 11
66 = 2 x 33 --> 33 = 3 x 11
* Only prime factors *
What does the word Evaluate mean?
Answer: To Solve! Looking for a numerical answer.
Large kites are sold in packages of 5.
Write an algebraic expression that can represent in total number of kites in p packages of large kites.
Answer: 5p or 5 x p
Multiply the variable and 5 together
Evaluate:
(6/2 + 7) - 5 times 2
Answer: 0 --> USE PEMDAS
P: (6/2 + 7) = 10
M: 5 x 2 = 10
S: 10 - 10 = 0
Evaluate the expression when b = 1/3
(b^3)
Answer: 1/3 x 1/3 x1/3 =1/27
1/27
What is the prime factorization of 140?
Answer: 2 x 2 x 5 x 7 or 2^2 x 5 x 7
140 = 2 x 70 --> 70= 7 x 10 10 = 2 x 5
What are the two coefficients in the expression:
1/3x - 5 + 4y
Answer: 1/3 and 4
--> are the numbers being multiplied by a variable
What is an equivalent algebraic expression for the following:
4(3c + 5)
Answer: 12c + 20
Distribute the 4 (multiply) to both terms
4 x 3c = 12c
4 x 5 = +20
Evaluate:
(6.5 + 3.2) - 7 divide 3.5
Answer: 7.7
P: 6.5 + 3.2 = 9.7
D: 7 divided by 3.5 = 2
S: 9.7 - 2 = 7.7
Evaluate the expression
When x = 18
x/4 + 12
Answer: 16.5
Substitute 18 for x --> 18/4 = 4.5 + 12 = 16.5
What is the Greatest Common Factor (GCF) between 20 and 48?
Answer GCF: 4
20 --> 2 x 2 x 5 48 --> 2 x 2 x 2 x 2 x 3
GCF: Look at the pairs, which numbers show up on both lists.
2 times 2 = 4
Are the following numbers prime or composite: (50 points for each correct answer)
13 9 35
15 27 17
Answer: Prime numbers only have 1 and itself as factors. Composite numbers have more than two factors
13: Prime 9: Composite 15: Composite
27: Composite 35: Composite 17: Prime
Joey wants to rent a car for a day. It will cost a daily fee of $100 dollars plus $0.75 per mile driven.
Part 1 (150 points): Let m = miles driven. Write an algebraic expression that shows the amount they he will pay to use the care.
Part 2: (150 points) Evaluate the expression for the amount Joe will pay if he drives 60 miles.
Answers: 100 + $0.75m
When m = 60 he will pay $145.
Evaluate the expression (Substitute)
100 + 0.75(60) --> 100 + 45 = $145
Evaluate:
(5^2 - 8/2) + 45 div 9 - 6
Answer: 20
P: 5^2 = 25 8/2 = 4 25 - 4 = 21
D: 45 divided by 9 = 5
A: 21 + 5 = 26
S: 26 - 6 = 20
Evaluate the expression
(2(x^2) +6) - 7
When x = 3
Answer: 17
Substitute x for 3 --> (2(3^2) + 6) - 7
9 x 2 = 18 + 6 = 24 - 7 = 17!
What is the Least Common Multiple (LCM) of the 8 and 14?
Answer: 56
8 --> 2 x 2 x 2 14 --> 2 x 7
LCM: Write all prime factors out and write an exponent to show how many times they show up in one list!
2^3 times 7^1 = 56
How many terms are in the following expressions: (200 points each)
4x^2 + 5x - 3
4 divide x - 7
Answer: Terms are separated by addition and subtraction signs
3 terms for
4x^2 + 5x - 3
2 terms for
4 divide x - 7
Combine like terms to create a equivalent expression:
6(3b + 10) - 5b - 18
Answer: 13b + 42
Distribute first: 6 x 3b = 18b 6 x 10 = 60
18b + 60 -5b - 18 --> Combine like terms -->
18b - 5b = 13b +60 -18 = +42 -->
13b + 42
Evaluate:
(6.75 - 4.25)^2 + (1/4 times 48) - 10
Answer: 8.25
P: 6.75 - 4.25 = 2.5 1/4 x 48 = 12
E: 2.5^2 =6.25
A: 6.25 + 12 = 18.25
S: 18.25 - 10 = 8.25
Evaluate the expression when y = 1 1/2
3/4 + 4y - (y divide 1/2)
Answer: 3 3/4
Step 1 Substitute --> 1 1/2 for every y.
3/4 + 4 (1 1/2) - (1 1/2 divided 1/2)
Step 2 Follow Pemdas --> 3/4 + 6 - 3 -->
6 3/4 - 3 = 3 3/4
Liam is having 24 adults and 16 children over for a party. Liam wants to have an equal amount of adults and children at each table.
250 Points: What is the greatest number of tables he could use?
250 Points: How many adults and children would be at each table?
Answer: 8 tables --> 3 adults and 2 children at each table
Part 1: Find GCF -->
24 = 2 x 2 x 2 x 3 16 = 2 x 2 x 2 x 2
GCF: Find Pairs --> 2 x 2 x 2 = 8
Part 2: Divided the people by the number of tables
24 adults divided by 8 = 3 adults at each table
16 children divided by 8 =2 children at each table
Are 6^2 and 2^6 the same value? To earn all the points you must prove mathematically and describe which math property exponents share or do not share.
Answer: NO!
6^2 = 6x6 = 36 2^6 = 2 x 2 x 2 x 2 x 2 x 2 = 64
36 = 64.
The do not share the commutative property like addition and multiplication do. You cannot switch the numbers around
Mr. Ciampi wants to rents a grill for his cook out. He will need it for 8 hours.
Company A charges a daily fee of 50 dollars plus 10 dollars per hour.
Company B charges 15 dollars per hour.
Part 1 (250 points): Write an algebraic expression that represents both company's rate.
Part 2: (250 points): Evaluate both expression to prove what would be a better deal for the rental.
Answer: Company B is a better deal!
Company A --> 50 + 10h
Company B --> 15h
Evaluate for h = 8 by substitution
Company A = 50 + 10(8) = 130
Company B = 15 (8) =120