Illinois Basic Skills Math Review

Front 1

What does = mean?

Back 1

is equal to

Front 2

What does ≠ mean

Back 2

is not equal to

Front 3

What does < mean?

Back 3

is less than

Front 4

What does > mean?

Back 4

is greater than

Front 5

What does ≥ mean?

Back 5

is greater than or equal to

Front 6

What does ≤ mean?

Back 6

is less than or equal to

Front 7

What does π mean?

Back 7

is pi, which equals 3.14

Front 8

What does AB mean?

Back 8

line segment AB

Front 9

What does AB mean?

Back 9

line AB

Front 10

What does ⊿ signify

Back 10

angle

Front 11

What does a/b or a:b signify

Back 11

ratio of ab

Front 12

Formula for Area of Square

Back 12

2
A=s

Front 13

Describe Area of Square Formula

Back 13

area of a square is
area = width × height
The width and height are by definition the same, formula is usually written as area = s2
where s is the length of one side. Formula bove should be spoken as "s raised to the power of 2", meaning s is multiplied by itself. But we usually say it as "s squared". This wording actually comes from the square. The length of a line s multiplied by itself, creates the square of side s. Hence "s squared".

Front 14

Formula for Perimeter of a Square

Back 14

Permeter = 4s

Front 15

Describe Perimeter of a square formula

Back 15

Like any polygon, the perimeter is the total distance around the outside, which can be found by adding together the length of each side. I the case of a square, all four sides are the same length, so the perimeter is four times the length of a side. Or as a formula:
perimeter = 4S where:
S is the length of any one side

Front 16

Define a circle

Back 16

A line forming a closed loop, every point on which is a fixed distance from a center point.

Front 17

Define center of a circle

Back 17

A point inside the circle. All points on the circle are equidistant (same distance) from the center point

Front 18

Define radius of a circle

Back 18

The radius is the distance from the center to any point on the circle. It is half the diameter. See Radius of a circle.

Front 19

Define diameter of a circle

Back 19

The distance across the circle. The length of any chord passing through the center. It is twice the radius. See Diameter of a circle.

Front 20

Define circumference of a circle

Back 20

The circumference is the distance around the circle. See Circumference of a Circle

Front 21

Define Area of a Circle

Back 21

The number of square units it takes to exactly fill the interior of a circle.

Front 22

Formula for area of a circle

Back 22

Given the radius of a circle, the area inside it can be calculated using the formula where: Area=πr2
R is the radius of the circle
π is Pi, approximately 3.142

Front 23

If you have the diameter of circle. How do you calculate the area?

Back 23

(πD^2)/4
where:
D is the diameter of the circle
π is Pi, approximately 3.142

Front 24

If you have the circumference of a circle. How do you calculate the area

Back 24

Area=C^2/4π
where:
C is the circumference of the circle
π is Pi, approximately 3.142

Front 25

Formula for Circumference of a circle

Back 25

Circumference=2 π r
where r is the radius

Front 26

Formula for Diameter of a circle

Back 26

Diameter = 2 r
r is the radius

Front 27

Definition of a rectangle

Back 27

A 4-sided polygon where all interior angles are 90°

Front 28

Properties of rectangle

Back 28

Opposite sides are parallel and congruent Adjust the rectangle above and satisfy yourself that this is so.
The diagonals bisect each other
The diagonals are congruent

Front 29

Formula for area of a rectangle

Back 29

Area=l w
l is length
w=width

Front 30

What is the perimeter of a rectangle

Back 30

The total distance around the outside of a rectangle

Front 31

Formula for perimiter of a rectangle

Back 31

Perimter = 2 ( l w )
where l is length and w is width

Front 32

Perminter of a circle is

Back 32

Like any polygon, the perimeter is the total distance around the outside, which can be found by adding together the length of each side. I the case of a rectangle, opposite sides are equal in length, so the perimeter is twice its width plus twice its height.

Front 33

Definition of a triangle

Back 33

A closed figure consisting of three line segments linked end-to-end.
A 3-sided polygon.

Front 34

What is the vertex of a triangle

Back 34

The vertex (plural: vertices) is a corner of the triangle. Every triangle has three vertices

Front 35

What is the base of a triangle

Back 35

The base of a triangle can be any one of the three sides, usually the one drawn at the bottom. You can pick any side you like to be the base. Commonly used as a reference side for calculating the area of the triangle. In an isosceles triangle, the base is usually taken to be the unequal side.

Front 36

What is the altitude of a triangle

Back 36

The altitude of a triangle is the perpendicular from the base to the opposite vertex. (The base may need to be extended). Since there are three possible bases, there are also three possible altitudes. The three altitudes intersect at a single point, called the orthocenter of the triangle. See Orthocenter of a Triangle.
In the figure above, you can see one possible base and its corresponding altitude displayed.

Front 37

Properties of an altitude of a triangle

Back 37

The point where the three altitudes of a triangle intersect. One of a triangle's points of concurrency.

Front 38

What is a median of a triangle

Back 38

The median of a triangle is a line from a vertex to the midpoint of the opposite side. The three medians intersect at a single point, called the centroid of the triangle.

Front 39

What is the area of a triangle?

Back 39

The number of square units it takes to exactly fill the interior of a triangle.

Front 40

What is the formula for area of a triangle

Back 40

Area=(ba)/2
Usually called "half of base times height", the area of a triangle is given by the formula below. b is the length of the base and a is the length of the corresponding altitude

Front 41

Methods for finding triangle area if you have all three sides

Back 41

Use Heron's formula:
A method for calculating the area of a triangle when you know the lengths of all three sides.
A= √ p (p-a) (p-b) (p-c)
p= half the perimeter, (a+b+c)/2

Let a,b,c be the lengths of the sides of a triangle. The area is given by:

where p is half the perimeter, or

Front 42

Method for finding triangle area if you have two sides and included angle

Back 42

Area= (a b sin c)/2
where
a and b are the lengths of two sides of the triangle
C is the included angle (the angle between the two known sides)

Front 43

Method for finding trianlge area if x,y coordinates of the vertices

Back 43

Area= A_x (B_y-C_y)+B_x(C_y-A_y)+C_x(A_y-B_y) / 2
where Ax and Ay are the x and y coordinates of the point A etc..

Front 44

Area of an equilateral triangle

Back 44

Area=(√3/4 ) s^2 where s is the length of any side of the triangle.

Front 45

What is a right triangle?

Back 45

A triangle where one of its interior angles is a right angle (90 degrees). Right triangles figure prominently in various branches of mathematics. For example, trigonometry concerns itself almost exclusively with the properties of right triangles, and the famous theorem by Pythagoras defines the relationship between the three sides of a right triangle:
a2 + b2 = h2
where h is the length of the hypotenuse
a,b are the lengths of the the other two sides
Attributes

Front 46

What is a hypotenus of a triangle?

Back 46

The side opposite the right angle. This will always be the longest side of a right triangle.

Front 47

What are the sides of a triangle?

Back 47

The two sides that are not the hypotenuse. They are the two sides making up the right angle itself.

Front 48

Can a right triangle be an isosceles?

Back 48

A right triangle can also be isosceles if the two sides that include the right angle are equal in length

Front 49

Can a right triangle be equilateral?

Back 49

A right triangle can never be equilateral, since the hypotenuse (the side opposite the right angle) is always longer than the other two sides.

Front 50

One angle of a right triangle is 41°. What are the other two?

Back 50

49° and 90°. The interior angles of any triangle always add up to 180°

Front 51

If you need to solve for the hypotenus of a right triangle, what formula do you use?

Back 51

h= √(a^2 + b^2) where a and b are the lengths of the two legs of the triangle, and
h is the hypotenuse

Front 52

If you need to solve for one leg and have hypotenus and one leg, what formula do you use?

Back 52

a= √(h^2 - b^2) where a is the leg we wish to find
b is the known leg
h is the hypotenuse.

Front 53

Explain the surface area of a sphere

Back 53

In general, the surface area is the sum of all the areas of all the shapes that cover the surface of the object.

Front 54

What is the formula to get the surface area of a sphere?

Back 54

Surface Area of a Sphere =
4 pi r ^2

Front 55

What is the formula to get the volume area of a sphere?

Back 55

Volume= 4/3 pi r^3
Find the radius. Cube the radius. Multiply the previous answer by four thirds.Multiply the answer by π

Front 56

Definition of a cube?

Back 56

Definition: A solid with six congruent square faces. A regular hexahedron.

Front 57

What is the face of the cube

Back 57

Also called facets or sides. A cube has six faces which are all squares, so each face has four equal sides and all four interior angles are right angles.

Front 58

What is the edge of a cube?

Back 58

A line segment formed where two edges meet. A cube has 12 edges. Because all faces are squares and congruent to each other, all 12 edges are the same length

Front 59

What is a vertex of a cube?

Back 59

A point formed where three edges meet. A cube has 8 vertices

Front 60

Volume of a cube is

Back 60

The number of cubic units that will exactly fill a cube

Front 61

Define Rational numbers

Back 61

Definition: A rational number is a number that can be represented as a fraction , where m and n are integers and . The definition of rational number says that it must be a number that can be represented as a fraction of integers.

Front 62

Define Integers

Back 62

An integer is any whole number. An integer can be zero, greater than zero or less than zero. The integers greater than zero are the natural numbers.

Front 63

Define Fractions

Back 63

Fraction is an equal part of one whole object. Fraction can be represented as " p/q " where 'p' denotes the value called numerator and 'q' denotes the value called denominators

Front 64

Fraction Rules for Division by Zero in a Simple Fraction

Back 64

The denominator of any fraction cannot have the value zero. If the denominator of a fraction is zero, the expression is not a legal fraction because it's overall value is undefined

Front 65

Fraction Rules for Zero in the Numerator of a Simple Fractions

Back 65

A numerator is allowed to take on the value of zero in a fraction. Any legal fraction (denominator not equal to zero) with a numerator equal to zero has an overall value of zero.

Front 66

Fraction Rules for One Minus Sign in Simple Fractions

Back 66

If there is one minus sign in a simple fraction, the value of the fraction will be negative.

Front 67

Fraction Rules for More Than One Minus Sign in a Simple Fractions

Back 67

If there is an even number of minus signs in a fraction, the value of the fraction is positive.
If there is an odd number of minus signs in a simple fraction, the value of the fraction is negative.

Front 68

Fraction Rules for The Division Symbol in a Simple Fractions

Back 68

The Division Symbol - in a simple fraction tells the reader that the entire expression above the division symbol is the numerator and must be treated as if it were one number, and the entire expression below the division symbol is the denominator and must be treated as if it were one number.

Front 69

Fraction Rules for Properties of the Number 1

Back 69

Multiplying any number by 1 does not change the value of the number. Dividing any number by 1 does not change the value of the number..

Front 70

Fraction Rules for Different Faces of the Number 1

Back 70

The number 1 can take on many forms. 4 - 3 = 1 and 10 - 9 = 1 can be used as a substitution for the number 1 because they have a value of 1. When the numerator of a fraction is equivalent to the denominator of a fraction, the value of the fraction is 1. This only works when you have a legal fraction; i.e., the denominator does not equal zero. You can substitute one of these fractions for the number 1.

Front 71

Fraction Rule for Any Integer Can Be Written as a Fraction

Back 71

You can express an integer as a fraction by simply dividing by 1, or you can express any integer as a fraction by simply choosing a numerator and denominator so that the overall value is equal to the integer.

Front 72

Fraction Rule for Factoring Integers

Back 72

To factor an integer, simply break the integer down into a group of numbers whose product equals the original number. Factors are separated by multiplication signs. Note that the number 1 is the factor of every number. All factors of a number can be divided evenly into that number.

Front 73

Fraction Rule for Reducing Fractions

Back 73

To reduce a simple fraction, follow the following three steps:
1.Factor the numerator.
2.Factor the denominator.
3.Find the fraction mix that equals 1.

Front 74

Fraction Rule for Multiplying Simple Fractions

Back 74

To multiply two simple fractions, complete the following steps.
1. Multiply the numerators.
2.Multiply the denominators.
3.Reduce the results. (See Rule 10)
a.Factor the product of the numerators.
b.Factor the product of the denominators.
c.Look for the fractions that have a value of 1.

Front 75

Fraction Rule for MULTIPLICATION :multiply a whole number and a fraction

Back 75

To multiply a whole number and a fraction, complete the following steps.
1.Convert the whole number to a fraction. (See Rule 8)
2.Multiply the numerators.
3.Multiply the denominators.
4.Reduce the results. (See Rule 10)
a.Factor the product of the numerators.
b.Factor the product of the denominators.
c.Look for the fractions that have a value of 1.

Front 76

Fraction Rule for MULTIPLICATION: multiply three or more simple fractions

Back 76

1.Multiply the numerators.
2.Multiply the denominators.
3.Reduce the results. (See Rule 10)
a.Factor the product of the numerators.
b.Factor the product of the denominators.
c.Look for the fractions that have a value of 1.

Front 77

Fraction Rule for Dividing Simple Fractions to divide one fraction by a second fraction

Back 77

Convert the problem to multiplication and multiply the two fractions.
1.Change the ÷sign to × and invert the fraction to the right of the sign.
2.Multiply the numerators.
3.Multiply the denominators.
4.Reduce the results. (See Rule 10)
a.Factor the product of the numerators.
b.Factor the product of the denominators.
c.Look for the fractions that have a value of 1.

Front 78

Fraction Rule for DIVISION to divide a fraction by a whole number

Back 78

convert the division process to a multiplication process, and complete the following steps.
1.Convert the whole number to a fraction
2.Change the ÷sign to × and invert the fraction to the right of the sign.
3.Multiply the numerators.
4.Multiply the denominators.
5.Reduce the results. (See Rule 10)
a.Factor the product of the numerators.
b.Factor the product of the denominators.
c.Look for the fractions that have a value of 1.

Front 79

Fraction Rule for DIVISION to divide three or more fractions

Back 79

1.Change the ÷signs to × sign and invert the fractions to the right of the signs.
2.Multiply the numerators.
3.Multiply the denominators.
4.Reduce the results. (See Rule 10)
a.Factor the product of the numerators.
b.Factor the product of the denominators.
c.Look for the fractions that have a value of 1.

Front 80

Fraction Rule for BUILDING FRACTIONS
To build a fraction is the reverse of reducing the fraction

Back 80

Instead of searching for the 1 in a fraction so that you can reduce, you insert a 1 and build.

Hint 80

convert 1 into a fraction like 4/4

Front 81

Fraction Rule for ADDITION To add fractions

Back 81

the denominators must be equal. Complete the following steps to add two fractions.
1.Build each fraction so that both denominators are equal.
2.Add the numerators of the fractions.
3.The denominators will be the denominator of the built-up fractions.
4.Reduce the answer.

Front 82

Fraction Rule for SUBTRACTION To subtract

Back 82

he denominators must be equal. You essentially following the same steps as in addition.
1.Build each fraction so that both denominators are equal.
2.Combine the numerators according to the operation of subtraction or additions.
3.The denominators will be the denominator of the built-up fractions.
4.Reduce the answer.

Front 83

Order of Operations, what do you do first

Back 83

Multiplication and division must be completed before addition and subtraction

Front 84

Order of Operations Parentheses

Back 84

Expressions in parenthesis are treated as one number and must be calculate first.
esis

Front 85

Order of Operations If parentheses are enclosed in other parentheses

Back 85

Work from the inside out.

Front 86

Order of Operations when no parentheses exist

Back 86

The division symbol has the same role as the parenthesis. It instructs you to treat the quantity above the numerator as if it were enclosed in a parenthesis, and to treat the quantity below the numerator as if it were enclosed in yet another parenthesis.

Front 87

Order of Operations for Complex Rules for converting complex fractions to simple

Back 87

Describe how to convert 3/(1/2) to simple fraction. To manipulate complex fractions, just convert them to simple fractions and follow rules 1 through 23 for simple fractions.

Front 88

Order of Operations for Complex Fractions
To multiply two complex fractions

Back 88

convert the fractions to simple fractions and follow the steps you use to multiply two simple fractions.
(3/4)/(1/2) X 8/(3/16)

Front 89

Complex Fractions To multiply add or subtract two complex fractions

Back 89

Convert the fractions to simple fractions and follow the steps you use to add or subtract two simple fractions.
(((1/2) + (1/3))/((1/4)+(1/5))) + (4/27)

(1/2

Front 90

Compund fraction is sometimes called

Back 90

a mixed number

Front 91

Converting Decimals to Fractions

Back 91

Divide the fraction by 1, and then multiply the result by 1 in a form that will remove the decimal. Convert 2.3 to fraction
(2.3/1) x 1 =(2.3/1) x (10/10) = 23/10

Front 92

Converting percentages to fractions

Back 92

Recall that 1%=1/100=0.01
go over

Front 93

Place value for Ones (units) position

Back 93

1.87954 , to the left of the decimal.

Front 94

Place value for tenths

Back 94

tenths are one place right of the decimal

Front 95

Place value for hundreths

Back 95

hundreths are 2nd place right of the decimal

Front 96

Place value for thousandths

Back 96

thousandths are 3rd place value right of the decimal

Front 97

Place value for ten thousandths

Back 97

ten thousandths are 4th place value right of the decimal

Front 98

Place value for hundreth thousandths

Back 98

hundreth thousandths are the 5th place value right of the decimal

Front 99

Place value for the millioneths

Back 99

millioneths place value is the 6th place value right of the decimal

Front 100

What is the Whole number portion of a decimal

Back 100

The whole number portion of a decimal number are those digits to the left of the decimal place.

Front 101

What is the Expanded Form of a Decimal Number

Back 101

The expanded form of a decimal number is the number written as the sum of its whole number and decimal place values.
Example:
3 + 0.7 + 0.06 + 0.002 is the expanded form of the number 3.762.

Front 102

Adding Decimals

Back 102

To add decimals, line up the decimal points and then follow the rules for adding or subtracting whole numbers, placing the decimal point in the same column as above.
When one number has more decimal places than another, use 0's to give them the same number of decimal places.
Example:
76.69 + 51.37
1) Line up the decimal points: 76.69 +51.37
2) Then add.

Front 103

Subtracting Decimals

Back 103

To subtract decimals, line up the decimal points and then follow the rules for adding or subtracting whole numbers, placing the decimal point in the same column as above.
When one number has more decimal places than another, use 0's to give them the same number of decimal places.
Example:
18.2 - 6.008
1) Line up the decimal points.18.2
- 6.008
2) Add extra 0's, using the fact that 18.2 = 18.200
18.200- 6.008
3) Subtract.

Front 104

Comparing Decimal Numbers

Back 104

Symbols are used to show how the size of one number compares to another. These symbols are < (less than), > (greater than), and = (equals). To compare the size of decimal numbers, we compare the whole number portions first. The larger decimal number is the one with the lager whole number portion. If the whole number parts are both equal, we compare the decimal portions of the numbers. The leftmost decimal digit is the most significant digit. Compare the pairs of digits in each decimal place, starting with the most significant digit until you find a pair that is different. The number with the larger digit is the larger number. Note that the number with the most digits is not necessarily the largest.

Front 105

Rounding Decimal Numbers

Back 105

To round a number to any decimal place value, we want to find the number with zeros in all of the lower places that is closest in value to the original number. As with whole numbers, we look at the digit to the right of the place we wish to round to. Note: When the digit 5, 6, 7, 8, or 9 appears in the ones place, round up; when the digit 0, 1, 2, 3, or 4 appears in the ones place, round down.
Examples:
Rounding 1.19 to the nearest tenth gives 1.2 (1.20).
Rounding 1.545 to the nearest hundredth gives 1.55.
Rounding 0.1024 to the nearest thousandth gives 0.102.
Rounding 1.80 to the nearest one gives 2.
Rounding 150.090 to the nearest hundred gives 200.
Rounding 4499 to the nearest thousand gives 4000.

Front 106

Multiplying Decimal Numbers

Back 106

Multiplying decimals is just like multiplying whole numbers. The only extra step is to decide how many digits to leave to the right of the decimal point. To do that, add the numbers of digits to the right of the decimal point in both factors. We can multiply 4032 by 4 to get 16128. There are three decimal places in 4.032, so place the decimal three digits from the right:
4.032 × 4 = 16.128

Front 107

Dividing Whole Numbers, with Remainders

Back 107

4934 ÷ 6. Use long division.So the answer is 822 with a remainder of 2, written 822 R2.
To double-check that the answer is correct, multiply the quotient by the divisor and add the remainder:
(822 × 6) + 2 = 4932 + 2 = 4934.

Front 108

Dividing Whole Numbers, with Decimal Portions

Back 108

Find 32 ÷ 6 to the nearest whole number.
32 ÷ 6 = 5 r2. 6 is the divisor; 2 is the remainder.
2 is closer to 0 than 6, so round down. The answer is 5.

Front 109

Dividing Decimals by Whole Numbers

Back 109

To divide a decimal by a whole number, use long division, and just remember to line up the decimal points:
When rounding an answer, divide one place further than the place you're rounding to, and round the result. Add 0's to the right of the number being divided, if necessary.
To round 0.16666 . . . to the nearest thousandth, we take 4 places to the right of the decimal point and round to 3 places. Here, we round 0.1666 to 0.167, the answer.

Front 110

Dividing Decimals by Decimals

Back 110

To divide by a decimal, multiply that decimal by a power of 10 great enough to obtain a whole number. Multiply the dividend by that same power of 10. Then the problem becomes one involving division by a whole number instead of division by a decimal.
Example:
0.144 ÷ 0.12
Multiplying the divisor (0.12) and the dividend (0.144) by 100, then dividing, gives the same result.
The answer is 1.2.

Front 111

Exponents (Powers of 2, 3, 4, ...)

Back 111

Exponential notation is useful in situations where the same number is multiplied repeatedly.
The number being multiplied is called the base, and the exponent tells how many times the base is multiplied by itself.

Front 112

Exponent Special Cases

Back 112

A number with an exponent of two is referred to as the square of a number.
The square of a whole number is known as a perfect square. The numbers 1, 4, 9, 16, and 25 are all perfect squares.
A number with an exponent of three is referred to as the cube of a number.
The cube of a whole number is known as a perfect cube. The numbers 1, 8, 27, 64, and 125 are all perfect cubes.
Note:
A number written with an exponent of 1 is the same as the given number.
231 = 23.

Front 113

Factorial Notation n!

Back 113

The product of the first n whole numbers is written as n!, and is the product
1 × 2 × 3 × 4 × … × (n - 1) × n.
Examples:
4! = 1 × 2 × 3 × 4 = 24
11! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11 = 39916800
When dividing factorials, note that many of the numbers cancel out!
The number 0! Is defined to be 1.

Front 114

Square Roots

Back 114

The square root √n=r of a whole number n is the number r with the property that r × r = n.
Since the square root of a whole number n is the number r with the property that r × r = n, we always have (√n)^2=rxr=n

We write this as

.

Front 115

Deductive Thinking

Back 115

Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a "top-down" approach. We might begin with thinking up a theory about our topic of interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. This ultimately leads us to be able to test the hypotheses with specific data -- a confirmation (or not) of our original theories

Front 116

Inductive thinking

Back 116

Inductive reasoning works the other way, moving from specific observations to broader generalizations and theories. Informally, we sometimes call this a "bottom up" approach (please note that it's "bottom up" and not "bottoms up" which is the kind of thing the bartender says to customers when he's trying to close for the night!). In inductive reasoning, we begin with specific observations and measures, begin to detect patterns and regularities, formulate some tentative hypotheses that we can explore, and finally end up developing some general conclusions or theories.
nductive reasoning, by its very nature, is more open-ended and exploratory, especially at the beginning.

Front 117

Order of Operations
PEMDAS

Back 117

Parentheses
Exponents
Multiplication & Division which ever comes first
Addition & Subtraction-which ever comes first

Front 118

Associative Property for Addition

Back 118

If (a+b) +c=a=(b+c) states that as long as the only operation is addition, then you can move the parentheses and it will not change the value of the expression.

Front 119

Associative Property for Multiplication

Back 119

If (axb)x c =a x (b x c) as long as the only operation is multiplication, you can move the parentheses around and it doesn't change the value of the expression

Front 120

Does Associative property work for subtraction

Back 120

No, this only works for addition and multiplication

Front 121

Does associative property work for negative numbers?

Back 121

Yes, example -2+(4+5)=(-2+4)+5

Front 122

Commutative Property for Addition

Back 122

for all numbers a+b=b+a
addresses the numbers on both sides move back and forth. In addition, whether it is written as 4+5 or 5+4, you will get the same value for both expressions.

Front 123

Commutative Propertty for Multiplication

Back 123

For all numbers a x b=b x a

Front 124

Is there a commutative property for subtraction or division

Back 124

No

Front 125

Opposite of a number can be found by

Back 125

Just multiply by -1 , if you see a -(7), the - stands for (-1), so you would write it as (-1)(7)

Front 126

Percent means

Back 126

Percent means per hundred

Front 127

Convert fraction to a percent

Back 127

ivide the numerator by the denominator. Then move the decimal point two places to the right (which is the same as multiplying by 100) and add a percent sign. .625 .625 x 100 = 62.5 or 62.5%
------
8 )5.000
4 8
---
20
16
--
40
40

Front 128

To change a percentage to a fraction,

Back 128

divide it by 100 and reduce the fraction or move the decimal point to the right until you have only integers:
10% = 10/100 = 1/10
62.5% = 62.5/100 = 625/1000
625/1000 = 125/200 = 25/40 = 5/8

Front 129

Percent to Decimal

Back 129

Percent-to-decimal conversions are easy; you mostly just move the decimal point two places. The way I keep it straight is to remember that 50%, or one-half, of a dollar is $0.50. In other words, you have to move the decimal point two places to the left when you convert from a percent (50%) to a decimal (0.50). Some more examples are:

Front 130

Percent to Fraction

Back 130

Percent-to-fraction conversions aren't too bad. This is where you use the fact that "percent" means "out of a hundred". Convert the percent to a decimal, and then to a fraction;Now you can reduce the fraction:

Front 131

Ratios

Back 131

Ratios tell how one number is related to another number.
A ratio may be written as A:B or A/B or by the phrase "A to B". A ratio of 1:5 says that the second number is five times as large as the first.

Front 132

How to Determine a Ratio

Back 132

Example: Determine the ratio of 24 to 40.
○ Divide both terms of the ratio by the greatest common factor (24/8 = 3, 40/8=5)
○ State the ratio. (The ratio of 24 to 40 is 3:5)

Front 133

How to determine proportions

Back 133

A proportion is an equation which states that two ratios are equal.
When the terms of a proportion are cross multiplied, the cross products are equal.
Cross multiplication is the multiplication of the numerator of the first ratio by the denominator of the second ratio and the multiplication of the denominator of the first ratio by the numerator of the second ratio.

Front 134

If one term of a proportion is not known, how to determine proportion

Back 134

cross multiplication can be used to find the value of that term. x / 3 = 70 /10
x * 10 = 70 * 3
10x = 210
10x/10 =210/10
x = 21

Front 135

Find the mean proportional of –3 and –12.

Back 135

(-3)/x=x/12
(-3)(12)=x^2
-36=x^2
Since it is a negaative number.You cannot square it.You cannot solve it.

Front 136

Find the unknown value in the proportion: 2 : x = 3 : 9.

Back 136

2 : x = 3 : 9
First, I convert the colon-based odds-notation ratios to fractional form:
.
Then I solve the proportion:

9(2) = x(3)
18 = 3x
6 = x

Front 137

Find the unknown value in the proportion: (2x + 1) : 2 = (x + 2) : 5

Back 137

(2x + 1) : 2 = (x + 2) : 5
First, I convert the colon-based odds-notation ratios to fractional form:
Then I solve the proportion:

5(2x + 1) = 2(x + 2)
10x + 5 = 2x + 4
8x = –1
x = –1/8

Front 138

Terms are

Back 138

When numbers are added or subtracted

Front 139

Factors are

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When numbers are multiplied,

Front 140

12 inches =

Back 140

1 foot ft ES

Front 141

3 feet=

Back 141

1 yard -yd ES

Front 142

1760 yards =

Back 142

1 mile mi ES

Front 143

Metric
kilometer km

Back 143

1000 meters m

Front 144

Metric
hectometer hm

Back 144

100 meters m

Front 145

decameter dam

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10 meters m

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meter m=

Back 146

1 meter m

Front 147

decimeter dm =

Back 147

1/10 meter m

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centimeter cm=

Back 148

1/100 m

Front 149

millimeter mm

Back 149

1/1000 meter m

Front 150

Conversion from English to Metric
1 inch=

Back 150

2.54 centimeters

Front 151

Conversion from English to Metric
1 foot=

Back 151

30 centimeters

Front 152

Conversion from English to Metric
1 yard=

Back 152

0.9 meters

Front 153

Conversion from English to Metric
1 mile=

Back 153

1.6 kilometers

Front 154

Measurements of Weight (ES)
28 grams=

Back 154

1 ounce oz

Front 155

Measurements of Weight (ES)
16 ounces oz=

Back 155

1 pound lb

Front 156

Measurements of Weight (ES)
2000 pounds lbs

Back 156

1 ton t short ton

Front 157

Measurements of Weight (ES)
1.1 ton t

Back 157

1 ton t

Front 158

Measurements of Weight Metric
kilogram kg=

Back 158

1000 grams g

Front 159

Measurements of Weight Metric
gram g =

Back 159

1 gram g

Front 160

Measurements of Weight Metric
milligram mg=

Back 160

1/1000 gram g

Front 161

Conversion of Weight from ES to Metric
1 ounce=

Back 161

28 grams g

Front 162

Conversion of Weight from ES to Metric
1 pound=

Back 162

0.45 kilograms kg or
45 grams

Front 163

Measurement of Volune ES
8 fluid ounces oz=

Back 163

1 cup c

Front 164

Measurement of Volune ES
2 cups c=

Back 164

1 pint pt

Front 165

Measurement of Volune ES
2 pints pt=

Back 165

1 quart qt

Front 166

Measurement of Volune ES
4 quarts qt=

Back 166

1 gallon gal

Front 167

Measurement of volume MS
kiloliter kl=

Back 167

1000 liters

Front 168

Measurement of volume MS
liter l=

Back 168

1 liter l

Front 169

Measurement of volume MS
milliliter ml=

Back 169

1/1000 liters ml

Front 170

Conversion of volume from ES to MS
1 teaspoon tsp=

Back 170

5 milliliters ml

Front 171

Conversion of volume from ES to MS
1 fluid ounce oz=

Back 171

15 milliliters ml

Front 172

Conversion of volume from ES to MS
1 cup c=

Back 172

0.24 liters l

Front 173

Conversion of volume from ES to MS
1 pint pt=

Back 173

0.47 liters l

Front 174

Conversion of volume from ES to MS
1 quart qt=

Back 174

0.95 liters l

Front 175

Conversion of volume from ES to MS
1 gallon gal=

Back 175

3.8 liters

Front 176

Measurement of time:
1 second=

Back 176

1 second

Front 177

1 minute=

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60 seconds

Front 178

1 hour=

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60 minutes

Front 179

1 day=

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24 hours

Front 180

1 week=

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7 days

Front 181

1 year=

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365 days

Front 182

1 century-

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100 years

Front 183

symbol ' represents

Back 183

feet

Front 184

symbol " represents

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inches

Front 185

Scientific notation

Back 185

convenient method for writing very large and very small numbers

Front 186

Two factors of scientific notation are:

Back 186

1. First factor is a numbe between 1 and 10. numbers
2. The 2nd factor is the power of 10. This notation is a shorthand for expressing large/small

Front 187

10^n is

Back 187

ten multiplied by itself

Front 188

What is a square unit?

Back 188

1 square foot =144 sq inches

Front 189

1 square yard=

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9 square feet

Front 190

1 square yard=

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1296 sqaure inches