· web viewtwo numbers that are the same but have different signs (- or +)

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


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


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


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.


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


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:


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


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!


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.


(3) Multiply or divide left to right. (4) Add or subtract left to right.

· web viewtwo numbers that are the same but have different signs (- or +)

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