Post on 24-Mar-2018
Math 7 IM Reference Sheets Unit 2
Unit 2: Rational Number Operations
Natural numbers (Números naturales)- Counting numbers (1, 2, 3…)
Whole numbers (Los números enteros)- Counting numbers, including 0.
Integers (enteros)- Positive (positivo) and negative (negativo) whole numbers
Rational Numbers (Numeros racionales)- Numbers that can be written as a fraction
Math 7 IM Reference Sheets Unit 2
Math 7 IM Reference Sheets Unit 2
Absolute Value vs Opposite numbers
Opposite numbers (homólogos) - Two numbers that are the same but have different signs (- or +)Examples: -2 and 2, -12345 and 12345
Absolute Value (Valor absoluto)- The distance a number is away from 0. (Distance is always positive).Examples: |−20|=20∧|20|=20
Math 7 IM Reference Sheets Unit 2
PropertiesAdditive Identity Property of 0 Adding zero to a number gives a sum identical to the given number.Example: a + 0 = a
Additive inverse Two numbers whose sum is 0 are additive inverses of one another.Example: 5 + (-5) = 0
Associative Property of Addition
The sum stays the same when the grouping of addends is changed. (a + b) + c = a + (b + c), where a, b, and c stand for any real numbers.(5 + 7) + 3 = 5 + (7 + 3) 12 + 3 = 5 + 10 15 = 15
Associative Property of Multiplication
(5 x 7) x 3 = 5 x (7 x 3) 35 x 3 = 5 x 21 105 = 105
The product stays the same when the grouping of factors is changed. (a x b) x c = a x (b x c), where a, b, and c stand for any real numbers.
Commutative Property of Addition
5 + 3 = 3 + 5 The sum stays the same when the order of the
Math 7 IM Reference Sheets Unit 2
addends is changed. a + b = b + a, where a and b are any real numbers.
Commutative Property of Multiplication
4 x 7 = 7 x 4 The product stays the same when the order of the factors is changed. a x b = b x a, where a and b are any real numbers.
Multiplicative Identity Property of 1
a x 1 = 1 x a = a The product of any number and 1 is equal to the original number.
Distributive Property Example: 5(6 + 8) = (5 × 6) + (5 × 8)
a × (b + c) = (a × b) + (a × c) and a × (b – c) = (a × b) – (a × c), where a, b, and c stand for any real numbers.
Math 7 IM Reference Sheets Unit 2
Distributive Property
Think about when you go to a fast food restaurant and buy a combo meal (ex. a burger, fries, and a drink). You and your friend get the same combo.
That means we have:
How many of each part of the combo will we be buying?
Distribute the 2 people We get 2 burgers, 2 fries, and 2 sodas
Math 7 IM Reference Sheets Unit 2
Another Example: The combo has 2 tacos and a soda. You are buying 3 of these combos. How many tacos will you have and how many sodas will you have?
Now let’s look at this:
Math 7 IM Reference Sheets Unit 2
You want to give each one of you r teachers 3 expo markers and a white board eraser for their classroom. You have 6 teachers. How many expo markers do you need? How many white board erasers do you need?
6(3Expo Markers+1white board eraser )
Examples:
2 (3apples+4 bananas )
4 ( x+2 )
variable A quantity that changes or can have different values. A symbol, usually a letter, that can stand for a variable quantity.
expression 5x + 3 A variable or combination of variables, numbers, and symbols that represents a mathematical relationship.
algebraic expression A group of numbers, symbols, and variables that express an operation or a series of operations.3x + 2
Math 7 IM Reference Sheets Unit 2
constant 5x + 4 A number with a value that is always the same.
coefficient 5x + 3 A numerical factor in a term of an algebraic expression.
common factor 12 (1, 2, 3, 4, 6, 12) 18 (1, 2, 3, 6, 9, 18) Common Factors of 12 and 18: 1, 2, 3, 6
Any common factor of two or more numbers.
common multiple 4, 8, 12, 16, 20, 24, 28, 32, 36… 6, 12, 18, 24, 30, 36, 42… Common Multiples of 4 and 6: 12, 24, 36…
Any common multiple of two or more numbers.
Rules for operations with Rational numbers
Adding and subtracting Integers- (sing to the tune of row, row, row your boat) Same sign keep and add, different signs subtract, keep the bigger number sign, then you’ll be exact!
Math 7 IM Reference Sheets Unit 2
Multiplying and Dividing Integers- Same signs= positive answerDifferent signs= negative answer
Order of Operations Rules describing what sequence to use in evaluating expressions. (1) Evaluate within grouping symbols. (2) Do powers or roots.
Math 7 IM Reference Sheets Unit 2
(3) Multiply or divide left to right. (4) Add or subtract left to right.
Math 7 IM Reference Sheets Unit 2
Math 7 IM Reference Sheets Unit 2
Math 7 IM Reference Sheets Unit 2