Math 1101-03

Front 1

Natural Numbers are also known as what? How do you describe them in set notation?

Back 1

Natural numbers are also known as counting number

Set notation is as follows: {1,2, 3}

Front 2

Whole numbers is a set of numbers plus what?

Back 2

Zero 0

Front 3

What is the set of integers?

Back 3

The set of integers adds the opposites of natural numbers to the set. {—3,-2,-1,0,1,2,3...}

Front 4

The set of integers is made up of three distinct subsets.

Back 4

1. Negative Integers

2. Zero

3. Positive integers

Front 5

How is the set of rational numbers is written?

Back 5

The set of rational numbers is written as {m/n|m and n are integers and n is not equal to zero.

Front 6

Are rational numbers fractions?

Back 6

Yes. The definition that rational numbers are fractions or quotients containing integers in both the numerator and denominator and the denominator is never zero.

Front 7

Is every natural number, whole number, and integer a rational number?

Back 7

Yes, every natural number, whole number, and integer is a rational number with a denominator of 1.

Front 8

Can any rational number be expressed as a decimal?

Back 8

Yes, because they are fractions, any rational number can also be expressed in decimal form. Any rational number can be represented as either :

A terminating decimal 15/8 = 1.875

Or a repeating decimal: 4/11= 0.36363636...=.36 repeating symbol over the .36

Front 9

Is zero a rational number?

Back 9

Yes, any natural number, whole number, and integer is a rational number. Zero is a whole number.

Front 10

What are irrational numbers?

Back 10

Irrational numbers are numbers that can not be written as fractions.

Front 11

How are Irrational numbers described in a set?

Back 11

h/h is not a rational number

Front 12

The set of rational and irrational numbers make up what is known as what?

Back 12

Real numbers: given any number n, we know that n is either rational or irrational. It cannot be both. The set of rational and irrational numbers makes up what is known as real numbers.

Front 13

Real numbers can be divided into three subsets, what are they?

Back 13

1. Negative numbers

2. Zero

3. Positive numbers

Each subset includes fractions, decimals, and irrational numbers according to their algebraic sign (+/-). Zero is neither positive or negative.

Front 14

What integer is neither positive or negative?

Back 14

Zero

Front 15

What is a real number line?

Back 15

A real number line is a set of real numbers visualized on a horizontal number line with an arbitrary point chosen as “0”, with negative numbers to the left and positive numbers to the right. A fix unit distance is then used to mark off each integer (or other basic value) on either side of 0. Any real number corresponds to a unique position on the number line. The converse is also true any number line corresponds to exactly one whole number. This is known as one-to-one correspondence.

Front 16

Classification of numbers fall into six sets of numbers, what are they?

Back 16

1)The set of natural numbers used for counting {1,2,3...} 2)The set of whole numbers is the serving natural plus zero. 3)The set of integers adds negative natural numbers to the set of whole numbers.4.)The set of rational numbers includes fractions written as {m/n|m and n are integers and n doesn’t equal to zero. 5)The set of irrational numbers is a set of numbers that are not rational, non repeating, and are non terminating. {h/h is not a rational number}6. Real numbers which is included all of the above

Front 17

When we multiply a number by itself, we square it or raise it to a power of 2. 4 to the 2nd power is 4 x 4= 16. We can raise any number to any power. This expression is known as wha kind of notation?

Back 17

Exponential notation

Front 18

In the exponential notation the exponent is read as nth power. The number is called what in this case?

Back 18

The base. 4 to the 2nd power. 4 is the base and 2 is the exponent.

Front 19

To evaluate a mathematical expression, we perform the various operations in a certain order known as what?

Back 19

Order of operations

Front 20

What is PEMDAS?

Back 20

The order of operations for mathematical expressions. Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Front 21

For some activities we perform, the order of operations does not matter, but the order of other operations does. Explain.

Back 21

For example it doesn’t matter if we put the left or right shoe on first, how ever it does matter whether we put on shoes or socks first. The same thing is true for order of operations in mathematics.

Front 22

Explain the principal behind Commutative properties for real numbers.

Back 22

The commutative property of addition states that numbers may be added in any order without affecting the sum.

Front 23

Explain the commutative property principal for multiplication.

Back 23

The commutative property principal for multiplication states that the numbers may be multiplied in any order without affecting the product.

Front 24

Do subtraction and division have commutative properties?

Back 24

No. 17-5 is not the same as 5-17. Similarly, 20/5 is not the same as 5/20

Front 25

Explain the principal behind Associative Properties of multiplication.

Back 25

The associative property of multiplication tells us that it doesn’t matter how we group numbers when multiplying. We can move grouping symbols to make the calculator easier and product remains the same.

Front 26

Explain the associative property for addition.

Back 26

The associative property for addition tells us that numbers may be grouped differently without affecting the sum. This property can be especially helpful with negative integers.

Front 27

Are subtraction and division associative?

Back 27

No.

Front 28

Explain the Distributive property.

Back 28

The distributive property combines both both addition and multiplication (and is the ONLY property to do so)

4[12+(-7)] = 4(12) + 4(-7)

=48+(-28)

=20

Front 29

Distributive property is multiplication distributed over addition. Is the reverse true? Is there a special case?

Back 29

The reverse is not true.

6 + (3 x 5) is not equal to (6+3) x (6+5) —-6+15 isn’t 9 x 11

21 isn’t equal to 99

There is a special case of the distributive property when a sum of terms is subtracted:

12-(5+3) we can turn this from a subtraction into an addition of opposites 12+(-1) x (5+3)

Front 30

What is Identity property of addition

Back 30

States that there is a unique number called additive identity (0) that when added to a number results in original number

Front 31

Identity property of multiplication

Back 31

Identity property of multiplication states that there is a unique number, called the multiplication identity (1) that when multiplied by a number results in the original number

Front 32

Inverse properties are what

Back 32

Inverse properties of addition states that for every real number a there is a unique number called the additive inverse or opposite denoted by -a that when added to the original number results in the additive identity of 0.

Front 33

What is the inverse property of multiplication?

Back 33

The inverse property of multiplication holds for all real numbers except 0 because the reciprocal of 0 is not defined. The property states that, for every real number a there is a unique number called the multiplicative inverse (or reciprocal) denoted 1/a that when multiplied by original number = 1. 1/a x a/1 = 1

Front 34

What are five properties of real numbers?

Back 34

Commutative Property, Associative Property, Distributive Property, Identity Property, Inverse Property

Front 35

When evaluating algebraic equations is a collective of _______and ______ joined together by algebraic operations of addition subtraction multiplication and division.

Back 35

When evaluating algebraic equations there is a constant (which does not vary) and a variable (which does vary). In naming variables we ignore the exponent or radicals containing the variable.

Front 36

The exponent tells us what?

Back 36

The exponent tells us how many factors of the base to use regardless of whether that base is a constant or a variable

Front 37

Any variable in an algebraic expression may take on or be assigned different values. When that happens....

Back 37

The value of the algebraic expression changes.

Front 38

What does it mean to evaluate an algebraic expression?

Back 38

To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with a given value, then simplify the resulting expression using order of operations. If the algebraic expression contains more than one variable replace each variable with its assigned value and simplify the expression as before.

Front 39

What is an equation?

Back 39

An equation is a mathematical statement indicating that two expressions are equal. The expressions can be numerical or algebraic.

Front 40

What is the etymology of the word algebra?

Back 40

late Middle English: from Italian, Spanish, and medieval Latin, from Arabic al-jabr ‘the reunion of broken parts’, ‘bone-setting’, from jabara ‘reunite, restore’. The original sense, ‘the surgical treatment of fractures’, probably came via Spanish, in which it survives; the mathematical sense comes from the title of a book, ‘ilm al-jabr wa'l-muqābala ‘the science of restoring what is missing and equating like with like’, by the mathematician al-Ḵwārizmī (see algorithm).

Front 41

Is an equation inherently true or false?

Back 41

No. It is a proposition. The values that make the equation true, the solutions, are found using properties of real numbers and other results. For example: 2x + 1 = 7 has the unique solution of 3 bc when we substitute 3 for x we get a true statement.

Front 42

What is a formula?

Back 42

A formula is an equation expressing a relationship between constant and variable quantities.

Front 43

What is the most common examples of a formula?

Back 43

The most common example is the formula for finding Area of a circle. A=pi r squared

A=πr2

Front 44

What is an example of how mathematicians, scientists and economists commonly encounter Very large and very small numbers?

Back 44

Pixels are the smallest unit of light to date that can be perceived on a digital camera a camera might record an image 2,048 pixels by 1536 pixels which is a very high resolution picture. It can also perceive a color depth gradation of 48 bits per frame and can shoot 24 frames per second so the maximum number of bits of information used to film a one hour (3600) digital film is then an extremely high number . 2.048 x 1536 x 48 x 24 x 3600 on a calculator groves us 1.3045963E13 or approx. 1.3 X 10 to 13 power bits of info

Front 45

What is the product rule of exponents?

Back 45

When multiplying exponents with the same base we write the result as the common base and the sum of the exponents this is the product rule of exponents.

X 3rd times X 4th power =

X • X •X (X•X•X•X)

Or X to the 7th power

The exponent of the product is the sum of the exponents of terms.

Front 46

What is the quotient rule of exponents?

Back 46

The quotient rule of exponents is when dividing exponential expressions with the same base, we write the result with that common base and the difference of the exponents.

Y to 9th divided by Y to the fifth is Y to the 4th

Front 47

What is the power rule of exponents?

Back 47

The power rule of exponents is if you have (X to the 2nd) cubed

Then multiply the exponents 2x3=6

X to the 6th power

Front 48

Using the zero exponent Rule of Exponents

Back 48

Return to the quotient rule exponents when bases are divided we take the difference of the exponents m-n but condition is it is never zero. But what if m=n? T the 8th divided by T the 8th isn’t zero under this rule it is 1. T the zero power is 1.

Front 49

What is the power of the product rule of exponents?

Back 49

Pq to the 3rd power is

Same as P to the 3rd times Q

3rd power

Front 50

What is the Pythagorean Theorem?

Back 50

A to 2nd power plus B to the 2nd power equals C to the second power

Front 51

What is a radical?

Back 51

The symbol housing the Radicand (number under the symbol) in a square root expression

Front 52

What is the principal square root?

Back 52

The principal square root is a non negative number and when multiplied by itself equals a. The square root obtained using a calculator is the principal square root.

Front 53

What is a radical expression?

Back 53

The principal square root of a is written as the radical expression of the radical with the number under it which is the product of the principal square root multiples by itself

Front 54

What common math rules can you apply to simplify square roots?

Back 54

The product Rule and quotient rule

Front 55

What is the negative exponent rule?

Back 55

A negative exponent is the how many times the inverse coefficient is divided. 3 to negative 2 power is 1/3 squared or 1/9th