Lesson 1 - 5 Flashcards
(95 cards)
1
Q
The numbers 1,2,3,4,5……make up a set of _________
A
Whole numbers
2
Q
Whole numbers along with ________,________,________, and ________ form a mathematical system.
A
Addition
Subtraction
Multiplication
Division
3
Q
The system that is made up of Whole numbers and mathematical operations is called
A
The Decimal System
4
Q
The Latin word “decem” means
A
10
5
Q
The decimal system has only 10 symbols, what are they called?
A
Digits
6
Q
The decimal system is said to have a base of _______
A
10
7
Q
The value of any digit in a particular number is determined by
A
The position it occupies in the number
8
Q
Each position in a number represents what?
A
Power of 10
9
Q
What are the three forms to express a number?
A
Standard form
Expanded form
Word form
10
Q
The rounding of numbers depends on the
A
Accuracy that is desired
11
Q
What are the three rules for rounding?
A
Step 1: identify the digit in the place you want to round to.
Step 2: Look at the digit to the right, if it is 5 or greater, increase the digit in the place being rounded by one ( round up). Otherwise, keep that digit the same ( round down).
Step 3: write zeros in the places to the right of the digit that was rounded.
12
Q
The “+” symbols is the sign used for
A
Addition
13
Q
Numbers being added are the
A
Addends
14
Q
The result of addition is called the
A
Sum
15
Q
When one or more of the numbers being added has more than one digit, you must
A
Align the numbers so that all the ones digits are in a column and so on.
16
Q
The number being subtracted is called
A
Subtrahend
17
Q
The number from which you are subtracting is called
A
Minuend
18
Q
The result of subtraction is
A
The difference
19
Q
Multiplication is way to express
A
Repeated addition
20
Q
Various symbols are used to indicate multiplication. What are they?
A
X- an X
• - a raised dot
()- enclosing parentheses
21
Q
The number being multiplied is known as an
A
Multiplicand
22
Q
The number by which you are multiplying is
A
The multiplier
23
Q
The multiplicand and the multiplier are
A
Factors
24
Q
The answer in multiplication is the
A
Product
25
The product of 1 and any number is
Is that number
26
The product of zero and any number is
Zero
27
When the product has 2 digits the product of each of its digits and the multiplicand is
A partial product
28
What is the process used to separate a group into equal parts?
Division
29
Division is the ______ ______ of multiplication
Inverse operation
30
The number being divided is called
Dividend
31
The number by which you are dividing
Divisor
32
The answer of division is called
The quotient
33
The result of the last subtraction in division is called
The remainder
34
Zero divided by any number (except zero) is
Zero
35
Division of any number by zero is
Undefined
36
Any number divided by 1 is
That number
37
Every number has an opposite except
Zero
38
Opposites are the same distance from
Zero on the number line
39
________ are composed of the counting numbers and their opposites, together with zero
Integers
40
The absolute value of a number is
The distance from zero on the number line
41
The absolute value is defined as a distance, it is always
Non negative
42
To add two or more numbers that have the same sign
Add their absolute values, the sum has the same sign as the addends
43
To add two numbers that have different signs?
Subtract the lesser absolute value from the greater absolute value. The sum (difference) has the sign of the number with the greater absolute value
44
Subtracting integers a helpful hint to remember
Do not change the sign of the first number. Change subtraction to addition, and change the sign of the second number
- 5 - 2=
- 5 + (-2)=
45
To multiply two numbers that have the same sign,
Multiply the absolute values. The product is positive
46
To multiply two numbers that have different signs
Multiply the absolute values. The product is negative
47
The product of any number and zero is
Zero
48
To divide numbers that have the same sign
Divide the absolute value. The quotient is positive
49
To divide the numbers that have different signs
Divide the absolute value. The quotient is negative
50
What is Algebra?
The study of operations and relationships among numbers, often using symbols to represent numbers.
51
What are variables?
Symbols that represent numbers
52
What is an expression?
A number, a variable, or a combination of numbers, variables and operations.
53
What is purpose of the order of operations?
A lost of steps to be followed for finding the value of an expression.
54
What is the Order of Operations
```
Complete all calculations of
Parentheses
Exponents
Multiplication & Divisions (Left to right)
Addition & Subtraction (Left to right)
In that order
```
55
What are grouping symbols? There are 4
Parentheses
Brackets
Absolute value signs
Fraction bar
56
What is the Commutative Property of Addition
Changing the order of addends does not change the sum
57
What is the Commutative Property of Multiplication?
Changing the order of factors does not change the product
58
The Associative Property of Addition
Changing the grouping of addends does not change the sum
59
The Associative Property of Multiplication states
Changing the grouping of factors does not change the product
60
The Distributive Property of Multiplication over Addition states
Multiplying the sum by a number gives the same result as multiplying each addend by the number and then adding the products
61
The Identity Property for Addition
Sum of Zero and any number is that number
62
Identity Property for Multiplication
Product of any number and one, is that number
63
Multiplication Property of Zero
The product of any number and zero is zero
64
The opposite of a number is called
The additive inverse
65
The opposite of a number is formed by
Multiplying that number by -1
66
The reciprocal of any number except zero is called
The multiplicative inverse of the number
67
The reciprocal of a number is formed
By writing the number as a fraction and then inverting the fraction
68
The property of Additive Inverses states
The sum of a number and it’s opposite is zero
69
The property of Multiplicative Inverses states
That the product of any number, except zero, and it’s reciprocal is 1
70
Algebraic expressions consist of
Terms
71
A term can be ________, ________, or ______________
A number
A variable
A product of a number and variable
72
In an expression, terms are separated by
Addition and subtraction symbols
73
The numerical factor in a term is called
The coefficient
74
A decimal is
A number that contains a decimal point
75
The decimal point ________
Separates the whole number from the part of the number less than a whole
76
To compare decimals ______
Write them so they each have the same number of decimal places.
77
What are the steps to multiplying decimals? (3)
1. Multiply as you would whole numbers
2. Find the sum of the decimal places in the factors
3. . insert a decimal point so that the number of decimal places in the product is the sum in step 2
78
What are the steps to divide decimals? (3)
1. Move the decimal point in the divisor to the right until the divisor becomes a whole number
2. Move the decimal point in the dividend to the right the same number of places that was moved in the divisor. Place decimal point in the quotient directly above.
3. Divide
79
Steps to convert a decimal to a fraction or mixed number
A decimal number less than one, use the word form. First part of the word form is the numerator, the second part is the denominator. Then simplify
80
A _______is a special ratio that compares a number to 100 using the symbol _______.
Percent
| %
81
You can convert between decimals and percents by _________
moving the decimal point
82
How do you convert a Percent to a Decimal? 75%
Move the decimal point 2 places to the left
| 75%=.75
83
How to convert Percent to a Fraction? 75%
1. Recognize the decimal point location
2. The denominator is the largest place value after the decimal point
3. Simplify when possible
75%=.75= Seventy-five hundredths= 75/100=3/4
84
How to convert a Decimal to a Percent? .75
Move the decimal point 2 places to the right.
| .75=75%
85
How to convert a decimal to a fraction? .75
Make .75 into a fraction with 100 as the denominator
| Simplify the fraction when possible
86
How to convert a fraction to a decimal? 3/4
Divide the numerator by the denominator
87
How to convert a Fraction to a Percent?
Convert to a decimal
| Convert to a percent
88
How to solve percent problem with Proportions? 27% is how much of $2100
```
1. Create a Part/Whole Fraction
Part/Whole=Part/Whole
27/100 = N/2100
2. Reduce and Cross multiply
3. Solve for N
```
89
An _________ is a mathematical sentence that states that two expressions are equal.
equation
90
To solve an equation you must _________ and how?
1. find the value(s) of the variable that makes the equation true
2. Isolate the variable
91
The value that makes the equation true is called a _________
solution
92
If a variable is multiplied by a number, you can _______ or _______ to isolate the variable
1. Divide by that number
| 2. Multiply by the reciprocal
93
If the variable is raised to an even power, the equation will have
Two distinct solutions
94
If the variable is raised to an odd power, the variable will have
one solution
95
To isolate a variable with a radical symbol you must
Write the variable without a radical. Isolate the variable by raising both sides of the equation to the Index power.
