Exponents
In the expression 53, identify the base and the exponent.
Base: 5
Exponent: 3
What is the prime factorization of the number 36?
23 x 32
Write an algebraic expression for the phrase: "seven less than a number "n"
The phrase "less than" means the operation must happen after the number is introduced.
n - 7
When solving a math problem using the Order of Operations, which operation should you always perform first?
You should always perform the operations inside Parentheses (or any Grouping symbol like brackets or braces) first.
Evaluate the expression x + 15 when x = 7.
22
Write the exponential expression 45 in expanded form.
4 x 4 x 4 x 4 x 4
What is the Greatest Common Factor (GCF) of 24 and 40?
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Common Factors: 1, 2, 4, 8
Answer: 8
Write a numerical expression for the phrase: "the quotient of thirty-two and eight, plus five."
The "quotient" means division. The phrase implies the division happens first, then the addition.
(32/8) + 5
Evaluate the expression: 15 - 3 X 4
Multiplication first: 3 times 4 = 12
Subtraction last: 15 - 12 = 3
Answer: 3
Find the value of the expression 4y - 6 when y = 5.
***DAILY DOUBLE***
14
Evaluate (find the value of) the expression 26
64
What is the Least Common Multiple (LCM) of 9 and 12?
Multiples of 9: 9, 18, 27, 36, 45, 54...
Multiples of 12: 12, 24, 36, 48, 60...
Answer: 36
A pizza costs C dollars. A delivery fee of $4 is added to the cost, and then the total is divided equally among three friends. Write an expression that represents how much each friend pays.
First, add the fee to the cost: C + 4
Then, divide the total by 3
(C + 4)/3
Evaluate the expression: 20 / (10 - 6) + 3
Parentheses first: 10 - 6 = 4. The expression becomes 20 / 4 + 3.
Division next: 20 / 4 = 5. The expression becomes 5 + 3.
Addition last: 5 + 3 = 8
Answer: 8
Evaluate the expression 9w when w = 0.
Write the following repeated multiplication using exponents:y * y * y * y
y4
A baker has 30 chocolate chip cookies and 42 oatmeal cookies. She wants to create identical boxes of cookies, with no cookies left over. What is the greatest number of identical boxes she can make?
(Think GCF)
GCF of 30 and 42:
30 = 2 times 3 times 5
42 = 2 times 3 times 7
Common Prime Factors: 2 times 3 = 6
Answer: 6 identical boxes
Which expression correctly represents the phrase "four times the sum of a number X and ten"?
A) 4x + 10
B) 4 + x + 10
C) 4(x + 10)
D) x + 4(10)
A) 4x + 10
Evaluate the expression: 1 + 42 / 2
Exponents first: 42 = 4 times 4 = 16
Division next: 16 / 2 = 8
Addition last: 1 + 8 = 9
Answer: 9
Find the value of the expression m2 - 8 when m = 4
8
Evaluate 8 cubed.
8 x 8 x 8
= 512
Two bus routes start at the same station at 8:00 AM. Route A leaves every 15 minutes, and Route B leaves every 20 minutes. At what time will both buses leave the station at the same time again?
(Think LCM)
This is an LCM problem (Least Common Multiple).
Multiples of 15: 15, 30, 45, 60...
Multiples of 20: 20, 40, 60...
The LCM is 60, meaning the buses will leave together again in 60 minutes.
Answer: 60 minutes after 8:00 AM is 9:00 AM
Turn the following into an expression:
Twelve minus the product of five and Y
12 - 5Y
Evaluate the expression: 18 - 2 * 5 + 7
Multiplication first: 2 * 5 = 10. The expression becomes 18 - 10 + 7.
Subtraction and Addition are done from left to right.
Subtraction: 18 - 10 = 8. The expression becomes 8 + 7.
Addition: 8 + 7 = 15
Answer: 15
Evaluate the expression a + 2b when a = 10 and b = 3
16