Order of Operations
True or false: The product of eighty-six negative numbers is a negative number
False!
The product eighty-six negative numbers is a positive number because all the negative signs pair up, resulting in a positive answer.
What is the lowest common denominator of
5/6 + 7/24
Multiples of 6 are 6, 12, 18, 24, 30...
Multiples of 24 are 24, 48, 72...
The first number that is the same in both lists is 23, so the lowest common denominator is 24.
Name 3 natural numbers that are also a prime number
2, 3, 5, 7, 11
Why do we use scientific notation?
To express really big and small numbers
Represent 20:24 as a simplified fraction
20 /24 = 5/6
Solve -12 - (-15)
True
-12 - (-15)
= -12 + 15
= 3
What is the trick we learned to divide fractions?
3/4 ÷ 5/6
Keep (the first fraction the same).
Change (the operation from division to multiplication).
Flip (the second fraction... numerator becomes denominator and denominator becomes numerator).
True or false: The whole numbers are a subset of natural numbers
False!
Whole numbers contain 0 whereas natural numbers do not.
Consider 1.23 x 913
Explain why this is not in scientific notation.
Base is always in 10 in scientific notation
Solve for x using the multiplier method used in class:
4 : 11 = 10 : x
10 ÷ 4 = 2.5
x = 11 x 2.5 = 27.5
True or false: The product of (-1)27 x (-1)18 is positive.
False!
(-1)27 x (-1)18
= (-1)(1)
= -1 (negative!)
What would be the next line if we are cross reducing the following expression:
1/8 xx 4/7
Divide both 8 (denominator of first fraction) and 4 (numerator of second fraction) by 4. After cross reducing:
1/2 xx 1/7
A ________ set is a set that has elements that are countable
A finite set is a set that has elements that are countable
True or false: 10.23 x 10-6 is in scientific notation.
False!
There should only be one digit to the left of the decimal in the first number (i.e. the first number should be within the range of 1.0 to 9.999...).
Correction: 1.023 x 10-5
Solve for x using equation method:
10:30 = 5:x
x = 15
Solve -(7)2 - (-120) + 32
-(7)2 - (-120) + 32
= -49 - (-1) + 9
= -49 + 1 + 9
= -48 + 9
= -39
Solve
-1 2/3 ÷ 2 1/2
-5/3 ÷ 5/2 = -5/3 xx 2/5 = -1/3 xx 2/1 = -2/3
True or false:
sqrt8
is an irrational number.
True!
sqrt 8 = 2.82842712...
The decimal continues infinitely without a repeating pattern. Remember that crazy decimals are irrational!
Put 46,800,000,000,000 into scientific notation.
4.68 x 1013
Order the fractions from least to greatest:
3/4, 4/9, -2/3, 20/11, -3/5, 1 2/3
-2/3, -3/5, 4/9, 3/4, 1 2/3, 20/11
Solve (-7)2 + (-6) - (-12) x (-2) ÷ 23
(-7)2 + (-6) - (-12) x (-2) ÷ 23
= 49 - 6 - (24) ÷ 8
= 43 - 3
= 40
Simplify
2/7 + 1 1/2 ÷ 5/6
2/7 + 3/2 xx 6/5 = 2/7 + 3/1 xx 3/5 = 2/7 + 9/5 = 10/35 + 63/35 = 73/35 = 2 3/35
List all number sets that follow the density property.
1. the set of rational numbers is infinitely dense...
in between two specified rational numbers (i.e. fractions), there will always exist another rational number (fraction). This can go on forever, as you will always be able to “squeeze” another fraction in between two others.
2. the set of irrational numbers is infinitely dense
3. the set of all real numbers is infinitely dense
Express 4.589 x 10-8 as a standard number.
0.00000004589
The price for 3 litres of orange juice is $6.60. The price for 5 cartons of apple juice is $15.50. Find the difference in prices of orange and apple juice per litre of juice.
Price per litre of orange juice: $6.60 ÷ 3 = 2.2 = $2.20/L of orange juice
Price per litre of apple juice: $15.50 ÷ 5 = 3.1 = $3.10/L of apple juice
Difference in prices: $3.10 - $2.20 = 0.9 = $0.90