Number Sense
Expressions and Order of Operation Vocabulary
Power: A way of writing repeated multiplication
Numerical Expression: Consists of numbers and operations
Evaluate: To find the answer to a numerical expression, you must evaluate
Order of Operations: A set of rules used to evaluate the expression
1. Evaluate expressions inside grouping symbols
2. Evaluate powers
3. Multiply and divide from left to right
4. Add and subtract from left to right
Variable: A symbol, usually a letter, that represents one or more numbers
Algebraic Expression: Consists of numbers, variables, and operations.
In order to evaluate an algebraic expression, substitute a number for each variable, then find the resulting numerical expression
Numerical Expression: Consists of numbers and operations
Evaluate: To find the answer to a numerical expression, you must evaluate
Order of Operations: A set of rules used to evaluate the expression
1. Evaluate expressions inside grouping symbols
2. Evaluate powers
3. Multiply and divide from left to right
4. Add and subtract from left to right
Variable: A symbol, usually a letter, that represents one or more numbers
Algebraic Expression: Consists of numbers, variables, and operations.
In order to evaluate an algebraic expression, substitute a number for each variable, then find the resulting numerical expression
Adding/Subtracting
ADDING INTEGERS: If you are adding a positive and negative number together, the answer will be whichever has more.
Example: -45 + 10. There are 45 negatives and 10 positives. Therefore, the answer will be negative.
SUBTRACTING INTEGERS is adding the opposite. -2 - (-2) = -2 + 2 = 0
DISTANCE BETWEEN NUMBERS On a number line, the distance between two numbers x and y is given by |x - y|
The absolute value is used when evaluating the distance between 2 numbers. Example: What is the distance between -35 degrees celsius and 10 degrees celsius? |-35 - 10| = 45 degrees
Example: -45 + 10. There are 45 negatives and 10 positives. Therefore, the answer will be negative.
SUBTRACTING INTEGERS is adding the opposite. -2 - (-2) = -2 + 2 = 0
DISTANCE BETWEEN NUMBERS On a number line, the distance between two numbers x and y is given by |x - y|
The absolute value is used when evaluating the distance between 2 numbers. Example: What is the distance between -35 degrees celsius and 10 degrees celsius? |-35 - 10| = 45 degrees
Multiplying Integers
When multiplying:
Same signs = positive number Example: (8)(5) = 40 and (-8)(-5) = 40
Opposite signs = negative number Example: (-8)(5) = -40 and (8)(-5) = -40
Is it the same for dividing?
Same signs = positive number Example: (8)(5) = 40 and (-8)(-5) = 40
Opposite signs = negative number Example: (-8)(5) = -40 and (8)(-5) = -40
Is it the same for dividing?
Number Properties
Multiplication Property of Zero: any number multiplied by 0 will be 0.
- 0•a = 0 for all numbers a
- Ex. 0•5 = 0
- The product of a number and the multiplicative identity, 1, is the number.
- 1•a = 1
- Ex. 1•7 = 7
- The sum of a number and the additive identity, 0, is the number.
- 0 + a = a
- Ex. 0 + 45 = 45
- The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. Therefore, the commutative property of multiplication says that the order of the factors does not affect the product.
- Ex. (5)(6) = (6)(5)
- (a)(b) = (b)(a)
- The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. Therefore, the commutative property of addition says that the order of the numbers in a sum does not affect the sum.
- Ex. 7 + 8 = 8 + 7
- a + b = b + c
- The word "associative" comes from "associate" or "group";the Associative Property is the rule that refers to grouping. Therefore, the associative property of multiplication: (a•b)•c = a•(b•c)
- Ex. (7•8)•4 = 7•(8•4)
- The word "associative" comes from "associate" or "group";the Associative Property is the rule that refers to grouping. Therefore, the associative property of addition: (a + b) + c = a + (b+ c)
- Ex. 40 + (23 + 7) = (40 + 23) + 7
- a(b + c) = ab + bc
- 4(3 + 7) = (4)(3) + (4)(7) = 12 + 28 = 40
- 7(3x + 8) = 21x + 56
- Undistribute: 6x + 18 = ? --> Greatest Common Factor of 6 and 18 is 6, so we can take 6 out. 6x + 18 = 6(x + 3)