Mathematics - Fundamentals - Unit 1: Integers

Today's high temperature is 72°F. If yesterday's high temperature was 87°F, what was the change in high temperatures? -19°F 19°F 15°F -15°F

-15°F.

Subtract. −7 − 12 =

-19.

Subtract. -11 - (-6) =

-5.

Subtract. 3 - 9 =

-6.

|1| is equal to:

1.

The process for adding two numbers with the same sign is as follows:

1. Add the numbers, regardless of their sign 2. Give the sum the same sign as the addends

The following phrases can be used to represent 7:

1. The absolute value of 7 2. Seven above zero 3. Positive seven 4. The opposite of -7 5. The absolute value of -7

Rules for exponents:

1. The base of an exponential expression is the factor that is multiplied by itself. The exponent tells you how many times to multiply the base by itself. The power of the expression is the result after it is simplified. 2. A negative base taken to an even power is positive. 3. A negative base taken to an odd power is negative. 4. If there are no parentheses around a negative base, then just the power is negative, not the actual base.

Rules for multiplying integers:

1. The product of two numbers with the same sign is positive. 2. The product of two numbers with different signs is negative.

Rules for dividing integers:

1. The quotient of two numbers with the same sign is positive. 2. The quotient of two numbers with different signs is negative. 3. Division by zero is undefined.

Rules for adding integers:

1. When adding two integers with the same sign, add the numbers and keep the sign. 2. When adding two integers with different signs, find the difference between the numbers and keep the sign of the number that has the larger absolute value.

Symbols that can make the following statement true. -15______ -19

1. ≠ 2. ≥ 3. >

Symbols that can make the following statement true. |-8| _________ |8|

1. ≥ 2. ≤ 3. =

An example of the Identity Property of Addition is:

11 + 0 = 11.

An example of the Commutative Property of Addition is:

11 + 1 = 1 + 11.

An example of the Identity Property of Multiplication is:

11(1) = 11.

|11| is equal to:

11.

Subtract. 15 - (-4) =

19.

An example of the Associative Property of Multiplication is:

2(11 · 1) = (2 · 11) 1.

An example of the Commutative Property of Multiplication is:

2(11) = 11(2).

|-2| is equal to:

2.

Asia contains both the highest and lowest known points on earth. Mt. Everest is a little over 29,000 feet above sea level, and the shore of the Dead Sea is about 1,370 feet below sea level. What is the approximate difference in elevation between the two points? 29,370 feet 27,630 feet 30,370 feet 28,370 feet

30,370 feet.

|-4| is equal to:

4.

|-9| is equal to:

9.

Set

A collection or group of objects.

Venn diagram

A diagram that shows the relationships between sets.

Point

A dot that marks a location on a graph.

Number Line

A line that graphically represents all numbers.

Natural Number

A number belonging to the set made up of the counting numbers: 1, 2, 3, and so on.

Integer

A number belonging to the set made up of the whole numbers and their opposites.

Whole Number

A number belonging to the set made up of zero and the natural numbers.

Rational number

A number that can be written as a ratio in fraction form.

Real number

A number that can be written as an infinite decimal.

Positive Number

A number that is greater than zero.

Negative Number

A number that is less than zero.

Irrational number

A number that, when in decimal form, does not terminate or repeat.

Addend

A number to be added.

Factor

A number to be multiplied.

Zero pair

A pair of numbers whose sum is zero.

Associative property

A property of the real numbers that states that how numbers are grouped in a sum or product does not change the value.

Commutative property

A property of the real numbers that states that the order in which numbers are added or multiplied does not change the value.

Subset

A set whose elements belong to a given set.

Element

An object that belongs to the set; also called a member.

True or False? A negative number with a larger numeral is a larger number.

False.

True or False? |-3| ≤ 0

False. |-3| (3) is greater than 0.

True or False? |-2| ≥ |-3|

False. |-3| (3) is greater than |-2| (2).

True or False? |-4| < |4|

False. |-4| (4) is greater than |4| (-4).

Jackie solved the following problem by doing the work shown. Which statement best describes her answer? (8 - 10) - 5 = 8 - (10 - 5) = 8 - 5 = 3 Her answer is incorrect because she tried to use the commutative property with subtraction. Her answer is incorrect because she tried to use the associative property with subtraction. Her answer is correct. Her answer is incorrect because she tried to use the identity property with subtraction.

Her answer is incorrect because she tried to use the associative property with subtraction.

Rule for multiplying and dividing integers:

If the integers have the same signs the answer is POSITIVE, If the integers have different signs the answer is NEGATIVE.

Key point:

If there are no parentheses around the base, only the number, not the sign, is multiplied. After multiplying, the sign is applied to the power.

Infinite

Increasing or decreasing without end

Some real numbers are:

Integers.

The natural numbers are a subset of all of the following sets except the:

Irrational Numbers.

No integers are:

Irrational.

The number π (3.14/Pi) is:

Irrational.

Some integers are:

Natural numbers.

Inverse operations

Opposite operations that undo one another.

To which sets does 5/8 belong.

Rational numbers and Real numbers.

All rational numbers are:

Real numbers.

Inequality

Statement showing a relationship between numbers that are not necessarily equal; uses the symbols >, <, ≥, ≤, or ≠.

Absolute Value

The distance from zero on the number line.

Additive identity

The number 0; when added to any number, the value of the number does not change.

Multiplicative identity

The number 1; when multiplied by any number, the value of the number does not change.

Dividend

The number being divided.

Divisor

The number of parts that the dividend is being divided into.

Base

The number that is repeated as a factor in an exponential expression

Undefined

The quotient of any number and zero.

Sum

The result of adding two or more numbers.

Quotient

The result of dividing two numbers.

Product

The result of multiplying two or more numbers.

Difference

The result of subtracting two numbers.

Exponent

The superscript number in an exponential expression; tells how many times a factor is repeated

Power

The value of a base and exponent; also the exponent itself

Rule:

To find the sum of two numbers with different signs, find the difference of their absolute values, and give the result the same sign as the number with the larger absolute value.

True or False? All integers are rational numbers.

True.

True or False? |1| > -1

True. 1 is greater than -1.

True or False? The terms power and exponent are used interchangeably.

True. The term power can also refer to the exponent itself. For example, the expression 2 5 is often read as "two to the fifth power." Although the word power was originally intended to represent the value of the base and exponent, over time, the words power and exponent became interchangeable.

True or False? |1| = 1

True. They're equal.

Opposite Numbers

Two numbers that are the same distance from zero on the number line but in opposite directions.

All natural numbers are:

Whole numbers.

Anything multiplied or divided by zero equals:

Zero!

Distributive property

a(b + c) = ab + ac, or a(b - c) = ab - ac