Maths-Decimals

Decimal Placement/Converting

- Value greater than 1, Move decimal to right till you get whole number.
- Number becomes numerator and 1 becomes denominator with the number of 0's that matches number of moves for decimal. = *Fraction*
- Value less than 1. Use whole number as numerator and the *Place value* of *last decimal Digit* as denominator. =*Fraction*

_____ ______ cannot be written as fractions or decimals becuase the number of decimal places is infinate and there is no recurring pattern of digits within the number.

ex. pi(∏) begins with 3.141592 and continues without repeating or terminating.

Irrational numbers

Are whole number grater than 1 that has only 2 factors; itself and 1; that is, a number that can be devided evenly by 1 and itself.

Prime numbers

Percentage Convert to/from Decimal

*TO* - Divide % by 100 then remove % symbol
*FROM* - Multiply by 100 then add % symbol

Divide % by 100

How do you convert a percent into a decimal?

Percentage Convert to/from Fraction

*TO* - Convert to decimal first (divide by 100) then put into simplest form
*FROM* - Convert to decimal (multiply to get 100 in denominator then divide by denominator) then put decimal into %

Fraction Convert to Decimal

Divide numerator by denominator

Order of Operations

-PEMDAS (No exponent for TEAS 6)
-Parentheses *FIRST*
-Multiplication and Division *SECOND* (Left to Right)
-Addition and Subtraction *THIRD* (Left to Right)

Compare and Order Rational Numbers

-*Rational Numbers*: -6 (-6/1), 5 (5/1), 100 (100/1)
-*Irrational Numbers*: Square root (any prime number), pi
-*Numeric Order*: Least to Greatest, Greatest to Least. Best in decimal form. Line them up vertically.
-*Fraction/Fraction Form*: 5 2/7 (put into decimal) Divide 2 by 7 to get .2857 which will equal 5.2857

Less than, IS fewer than
Less than or equal to, is at most, is no more than

>, _>_

Greater than, IS more than
Greater than or equal to, is at least, is no less than

=

Equal, equal to, is, was, were, will be, yields, becomes

Common Denominator

1. Find least on on multiple of denominator
2. Change each fraction to make their denominator the same as least common denominator
~List multiples of each denominator and find SMALLEST number
~Multiply numerator by multiple of LCD, Use LCD as denominator

Solve Equations in One Variable

Collecting all variable terms to *one* side of the equal sign and all the constants on the other side, using addition or subtraction. Once all like terms are combined, last step is to divide. Could also be multiplication by the reciprocal ( One divided by original number).

Extraneous

Incorrect
Story that is interesting containing details that aren't necessary to tell you what happened.

Erroneous

Irrelevant
Story might contain *conflicting* accounts of what happened due to having multiple observers.

Terms Related to Operations

Sum (+) , Difference (-) , Product (x) , Quotient ( / ) , Per 100 (#% _

Rational Numbers can be represented by?

By *fractions*
Includes: Whole Numbers, Positives/Negatives, Zero, and all decimals that either terminate or repeat.
~Irrational numbers will not concern us at this point

Solve Real World Problems with Percentage

Percent *LESS THAN OR EQUAL TO* 100%
~(50% -> 50 out of 100%)
Percent *MORE THAN* 100%
~(150% is 150 for each 100)

-Percent off sales tax, annual percent interest rate at a bank, annual percent gain or loss for a company or business, percent commission for sales person, percent depreciation of assets, percentages of ingredients in a mixture or recipe.

Sales Tax Equation

-Convert % to decimal then Multiply % times the Original Number (% x Original Price, Original Price + x = ST)

Percent Increase Equation

- Percent Increase
~ PI= new amount - original amount/ original amount X 100%

Percent Decrease Equation

PD = original amount - new amount/ original amount X 100%

Rounding Rules

- 5 or *LARGER*, round *UP* (decimals)
- 5 or *SMALLER*, Round *DOWN* (decimals)
- Numerator is *GREATER THAN OR EQUAL TO 1/2* the denominator, then round whole # *UP*
- Numerator is *LESS THAN OR EQUAL TO 1/2* the denominator, then round whole # *DOWN*

Proportions

Ratio in fraction form set equal to another ratio in fraction form.
~Example:
50mi/1cm = X/12.6cm (cross multiply) -> 50mi*x*12.6cm/1cm=X*x*12.6cm/12.6cm (cancel out 12.6cm on Num. and Den.) -> 50mi*x*12.6cm/1cm (cancel out cm) = X -> 630mi = X

Constant of Proportionality

Also known as *Rate of Change*
Ratio between two quantities
~Y=k*x (k is constant, y and X are direct proportion)
~One variable is always the product of the other and a constant, the two are said to be directly proportional.

Ratio/Rate Change

-Ratio: Simply just a fraction.
Once you add/attach WORDS (units) to fraction then it becomes a RATE.
- Example-
~Y2-Y1/X2-X1 rise over run
~Unit Rate - denominator HAS to be 1

Translate Phrases and Sentences into Expressions, Equations, and Inequalities

Sentence Fragments become *Expression* and Full Sentences becomes *Equations and Inequalities*.
-Examples:
*Expressions:* 3x-5 , , y , 3(2x+7)
*Equations:* 3x-5=70 , y=36 , 3(2x+7)=4x-9
*Inequalities:* x-5>70 , y

Bar Graph

Which graph is used to compare data (has scale)?

Area

What is the amount of space inside a 2 dimensional shape

Line Graph

Which graph is used to show data INCREASE or DECREASE over time (has legend)?

Pictograph

Which graph shows pics or symbols to show data (legend)?

Pie Chart

Which graph is a diagram to compare parts as a whole (labeled,legend)?

Histogram

What graph is like a bar graph with grouped data that is touching?

Stem and leaf plot

This graph outlines groups of data that fall into range (small to large, left=stem, right=leaf)

Scatter plot

This graph functions with data, finding simple regression.
4 different types: positive, negative, nonlinear exponential, nonlinear quadratic

Mean

Which measure of tendency is when you add all #, then divide by how many # there are? Also known as the average.

Median

Which measure of tendency is when you put the middle # of ordered (Least to Greatest) list, and if # are even, then the 2 middle # averaged out?

Mode

Which measure of tendency is the number that occurs the most and can be more than one?

Range

Which measure of tendency is when you subtract the minimum value from maximum value?

Outlier

What is a data point that is distinctly separated from other values and is considered unexpected value? This value "lies outside" (is much smaller or larger than) most of the other values in a set of data

Data trend

What is the term for the general tendency of numbers in a set?

Symmetry

Which shape of distribution is divided at the center with each side having half the data?

Unimodal

Which shape of distribution has a single clear peak?

Bimodal

Which shape of distribution has TWO clear peaks?

Bell Shaped

Which shape of distribution has a single peak at the center?

Skewed Right

Which shape of distribution has fewer observations on the right (towards higher values)?

Skewed Left

Which shape of distribution has fewer observations on the left (towards lower values)?

Uniform distribution

Which shape of distribution has observations in a data set that are spread equally across the range of the distribution?

Covariance

What is the term that explains the way two variables change together?

Dependent Variable

What kind of variable depends on at least one other variable?

Independent Variable

What kind of variable determines the value of another variable?

Length

Which geometric quantity is measured with ruler or tape measure?

Length

Inches, feet, yard, miles, centimeters, meter, and kilometers are all units of?

C=2 x PIE x r

How is the circumference (distance around a circle) calculated?

Pie x r squared

How do you find the area of a circle?

Length of half a circle

What does this formula cover?
C=2 PIE r then multiply by the fraction central angle measure/360

Perimeter

What is the term for the distance around a 2 dimensional shape?

Add all the sides

How do you find the perimeter of a shape?

Subtract the width and height of the other sides.

How do you find the perimeter of a shape that is missing a side?

A= l x l

What is the formula for a square?

A= l x w

What is the formula for a rectangle?

A= 1/2 x b x h

What is the formula for a triangle?

A= h x b

What is the formula for a parallelogram?

A= 1/2 x h x (b1 + b2)

What is the formula for a trapezoid?

A= PIE x R squared

What is the formula for a circle?

A= 1/2 x d1 x d2

What is the formula for a rhombus?

Conversion factor

What is the term for the number used to multiply or divide to change from one value to another?

3 feet

How many feet is 1 yd (yard)?

5280 ft

How many feet is 1 mi (mile)?

28 grams

How many grams in 1 oz (ounce)

8 oz

How many oz in 1 cup

16 oz

How many oz in 1 pint

2 pints

How many pints in 1 quart

4 quarts

How many quarts in 1 gal (gallon)

16 oz

How many oz in 1 Ib

1 fluid oz

How many oz in 2 tsp

8 fluid oz

How many oz is 1 glass?

King Henry Died By Drinking Chocolate Milk

Height

What is measure from top to bottom?

Length

What is the measurement of something from end to end?

Base

What measurement is the bottom of the figure?

Width

What is the distance from side to side?

Order of operations

PEMDAS
Please Excuse My Dear Aunt Sally.
1- Parenthesis
2- Exponents
3- Multiplication and Divison (left to right)
4- Addition and Substraction (left to right)

Convert decimal to percent by

Multiplying by 100 then move decimal two places to the right.

Convert percent to decimal by

Divide by 100 then move decimal two places to the left.

Convert decimal to a fraction by

(make sure fraction is in reduced form.) Multiply by 1,000. Then reduce fraction.

A number is divisible by 4 if _________

the last two digits of that number is divisible by 4. Example: 516.
The last two numbers are 16. 16 is divisble by 4. 16÷4=4; therefore, 516 is divisible by 4. 516÷4= 129

milli means

one-thousand of something

1 liter (L)

1,000 mL

Milimeter- mm (household approximation)

thickness of a dime

Centimeter- cm (household approximation)

the width of an average pinkie finger

Meter- m
(household approximation)

the average adult is 1.5-2m tall

Kilometer-km (household approximation)

the average adult walks 1 km in about 15 minutes

Gram- g (household approximation)

the weight of one asprin tablet

Kilogram- kg (household approximation)

a 5 pound bag of sugar weighs just over 1kg

Degrees Celsius -

zero is freezing ❄, 10 is not, 20 is warm and 30 is hot 🔥

Less than

<

Greater than

>

Irrational number

a number that cannot be expressed as terminating or repeating decimals.

Rational number

a number that can be expressed as a fraction