Rational Numbers
Fractions, Decimals, Exponents
Fractions, Decimals, Exponents
What is the first step you have to take to add or subtract fractions like 2/5 + 3/4?
Find the common denominator by finding the Least Common Multiple or LCM.
In this case
5: 5, 10, 15, 20, 25, 30, 35, 40
4: 4, 8, 12, 16, 20, 24, 28, 32, 36
And then find the equivalent fraction for each before adding.
The opposite of -8
Positive 8
Which is an example of the commutative property?
a. 3a + 5b = 8ab c. 3a + 5b = 5b + 3a
b. 3a + 5b = 8 + a + b d. (3a + 5b)= 3a+5b
Commutative property states you can change the order when adding or multiplying numbers or terms with variable.
C
Combine like terms:
12v + 8m + 9v
21v + 8m
Would this algebraic equation be true or false if g = -8?
6g + 18 = -40
False
6g + 18 = -40
6(-8) + 18 = -40
-48 + 18 = -40
-30 = -40
How do you divide decimal numbers like
100.5 / 0.05
Move the decimal point to the end of the divisor and the same number of hops in the dividend
0.05 changes to 005
100.5 changes to 10050
Which is greater?
-9 or -6
Using a number line, remember the number on the right is always greater than the number on the left.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
-9 < -6
Which of these shows the Identity Property for Multiplication?
a. 4 x 1 - 4 c. 4 x 0 = 0
b. 4 x 0 = 4 d. 4 + 0 = 4
Identity means you get the same answer you started with, so for multiplication you must multiply by 1.
The Identity Property for Addition means you add zero.
Combine Like Terms:
(3b - 6k) + (-5b + 8k)
(3b - 6k) + (-5b + 8k)
(3b + -5b) + (-6k + 8k)
-2b + 2k
How would you use inverse operations to find the value of the variable:
r + 18 = 42
Inverse of addition is subtraction from both sides
r + 18 = 42
-18 = -18
r = 24
How would you find the value of
(2/5)3
Multiply
2/5 x 2/5 x 2/5
What is the absolute value of -7 or | -7 |?
Since -7 is 7 hops from zero, the absolute value of -7 is 7.
Which is an example of the associative property?
a. (8a + 5b + 2m) = (2m + 5b + 8a)
b. (8a + 5b) + 2m = (5b + 8a) + 2m
c. (8a + 5b) + 2m = 5b + (8a + 2m)
The Associative property for addition or multiplication means you can change the location of the parentheses but the numbers or terms stay in the same order.
What is the value of this expression if m = -5
-4m + 7m
-4m + 7m
-4(-5) + 7(-5)
20 + -35
-15
How would you use inverse operations to find the value of the variable:
10n = 120
Since 10n means 10 x n, the inverse would be dividing both sides by 10
10n = 120
10/10n = 120/10
n = 12
How do you change a decimal to a percentage?
Example: 3.58
Multiply the decimal by 100
3.58 x 100 = 358%
-8 + 5 + -10 - 8
-8 + 5 + -10 - 8
-3 + -10 - 8
-13 - 8 (Use Additive Inverse Property "Keep, -13 + -8 Change, Opposite Sign) -21
How would this expression be written if you used the Distributive Property to simplify it?
5 ( 8s + 4h)
You would need to distribute the 5 to each term in the parentheses by multiplying it.
5 ( 8s + 4h)
40s + 16 h
How would you write an inequality for this condition:
You can have no more than 60 minutes playing video games today.
use v for video games.
v ≥ 60 or 60 ≤ v
How would you use inverse operations to find the value of the variable in:
p/5 = 12
Since the problem shows p is divided by 5, the inverse would be multiplication
p/5 = 12
5p/5 = 12 x 5
p = 60
How do you change a fraction to a percentage?
Example: 3/4
Step 1: Divide the numerator by the denominator to get a decimal
Step 2: Multiply answer times 100
Step 3: Add the % sign
How do you prove that opposites are equal using absolute value?
|-6| and |6|
|-6| and |6|
6 = 6
How would you use the distributive property to simplify this expression?
- 5 (6h - 2b)
First: use the Additive Inverse Property to change
6h - 2b by using "Keep, Change, Opposite Sign"
-5 (6h + -2b) Then multiply each term by -5
-30h + 10b
When putting the solution for an inequality on a number line, would the circle be colored in or left open for this inequality:
b > 98
An open circle (not colored in) indicates the variable is not equal to the value given.
A closed circle (colored in) indicates the variable can also be equal to the value given
This would be not colored in as it is just less than 98.
Would the value, 9 make this equation a true statement or a false statement?
8c + 16 = 12c - 20
9 would make this a true statement
Proof: 8(9) + 16 = 12(9) - 20
72 + 16 = 108 - 20
88 = 88