Miscellaneous
Squares, Cubes & Square Roots... Oh My!
Order of Operations
Prime Factorization, GCF & LCM
Scientific Notation & Standard Form
100
What are rational numbers? Are integers rational numbers? Why? Give an example.
All rational numbers are numbers that can be written as fractions. Yes, integers are rational numbers. All integers can be written as fractions. For example, 4 can be re-formatted to look like a fractions, by placing a 1 as the denominator.
100
Write each power as a product of the same factor. Then find the value. -5 to the second power.
-(5 x 5) = - 25
100
Simplify: - 4[ 12 - ( 1+6)]
-20
100
Write the prime factorization of 84. Write the product using exponents.
= 2^2 x 3 x 7
100
Convert 6.063 x 10^3 to a standard number. A. 6,063 B. 60,630 C. 606,300 D. 6,063,000
A
200
True or False. If false, explain why. "Rational numbers are always natural numbers."
False. Fractions are rational numbers, but not natural numbers.
200
Andy said that -(4) squared is equal to -4 squared. Do you agree or disagree with Andy? Why or why not?
Agree. The negative is not included in the parentheses. Hence, both have a value of -16.
200
Simplify: - 2√25 + 18 ÷ 2
-1
200
Write the prime factorization of 51.
51 = 3 x 17
200
Which expression is equal to 25,340? A. 2.5340 × 10^3 B. 2.5 × 10^4 C. 2534 × 10^1 D. 2.534 × 10^4
D
300
Draw the tree diagram representing all of the number types we've seen thus far, on the board and explain it to the class in as much detail as possible.
Real --> Either irrational or rational Rational --> Integers --> Whole --> Natural
300
Evaluate: (-6) cubed + 6 cubed
0
300
1 ÷ (8+6)(-5 + 3)
- 1/28
300
Find the GCF of 15 and 63.
3
300
Write 0.000314 in scientific notation. A. 3.14 x 10^4 B. 3.14 x 10^-5 C. 3.14 x 10^-6 D. 3.14 x 10^-4
D
400
Estimate AND simplify the "square root of 32".
Estimate: Between 5 and 6. Approximately 5.6 Simplify: 4 x the square root of 2.
400
Simplify: √(1,000)2 = _____________
1,000
400
Simplify: 5 - (-4)^2(1-3)
37
400
Find the GCF and the LCM of 51 and 117.
GCF: 3 LCM: 1,989
400
Visible light travels in waves at a speed of 300,000 kilometers per second. What is the number expressed in scientific notation? A. 30 x 10^4 B. 3.0 x 10^5 C. 30 x 10^5 D. 3.0 x 10^6
B
500
Tell me at least three things that describe the following number.
"The opposite of the square root of 49"
500
Write each value using exponents: -4 x 5 x 5 x 5 x 2 x 2 x 4 x -4 = ___________
(-4) squared x 5 cubed x 2 squared x 4
500
Simplify: 2^3[3^2 – (21- 6)]
-48
500
Choose two numbers of your own. Using these two numbers walk us through how to find the LCM and GCF of those two numbers. What are the LCM and GCF in words? What's the only difference, when we are finding each one?
Example: 2 and 14 GCF: 2 LCM: 14 GCF: Greatest common factor: the largest number that can go into both of those numbers evenly LCM: Least common multiple: the smallest number that's a common product of both of those numbers.
500
A film company made a 10.5 million-dollar profit on its summer films. During that same time, a competitor made a 2.4 million-dollar profit. What is the dollar amount of the profit earned by these two companies, expressed in scientific notation? A. 1.29 x 10^5 dollars B. 12.9 x 10^6 dollars C. 1.29 x 10^7 dollars D. 1.29 x 10^12 dollars
C
M
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