ATI TEAS 6 Math - Compare & Order Rational Numbers Algebra (M1.3,M1.4)
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 %
Percentage Convert to/from Decimal
*TO* - Divide % by 100 then remove % symbol *FROM* - Multiply by 100 then add % symbol
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*
Percent Increase Equation
- Percent Increase ~ PI= new amount - original amount/ original amount X 100%
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*
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
Sales Tax Equation
-Convert % to decimal then Multiply % times the Original Number (% x Original Price, Original Price + x = ST)
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)
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
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
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.
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
Tom is saving money to go to a concert. From his part-time job, he is able to save $18.50 per week. His older bro gave him $25 to start with. If W= number of weeks, which of the following expressions represents the number of weeks until Tom has saved at least $235? A. 8.50W + 25 = 235 B. (25 + 18.50)W >- 235 C. 12.50W + 25 >- 235 D. 12.50W + 25 < 235
C. 12.50W + 25 >- 235
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).
which of the following is 25% of 680 pounds? A. 1,700 pounds B. 510 pounds C. 68 pounds D. 170 pounds
D. 170 pounds
The success rate for a salesperson is 1 out of 8 calls. At this rate, how many sales would the salesperson expect to get out of 32 calls? A. 8 B. 256 C. 0.128 D. 4
D. 4
Fraction Convert to Decimal
Divide numerator by denominator
=
Equal, equal to, is, was, were, will be, yields, becomes
>, _>_
Greater than, IS more than Greater than or equal to, is at least, is no less than
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.
<, _<_
Less than, IS fewer than Less than or equal to, is at most, is no more than
Percent Decrease Equation
PD = original amount - new amount/ original amount X 100%
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.
Write in increasing order: -5,5 2/3, 0.523 Increasing order is defined as: When numbers increase from lower to higher.
Put fraction in decimal form 5 2/3 →(2÷3)= .66667 =5.667 1. ⁻5 2. 0.523 3. 5 2/3
Which of the following, list the numbers in Decreasing order -2, -0.2,2 2/10, 2? Decreasing number is: when number are arranged in order from Higher to Lower A. -2, -0.2, 2, 2 2/10 B. 2 2/10, 2, -2, -02 C. -2, 2, -0.2, 2 2/10 D 2 2/10, 2, -02,-2
Put fraction in decimal form: 2 2/10= 2÷10 2÷10 =.2 carry the 2 next to .2 to make ( 2.2) B. 2 2/10, 2, -2, -0.2
Which of the following is an expression to compare 8.33 and 8 2/3 ? A. 8.33 > 8 2/3 B. 8 2/3 > 8.33 C. 8.33 = 8 2/3 D. 8 2/3 < 8.33
Put fraction in decimal form: 8 2/3 2÷3= .6667 carry the 8 from fraction 8.667 which makes 8 2/3 greater B. 8 2/3 > 8.33
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
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<36 , 3(2x+7)_<_4x-9
Terms Related to Operations
Sum (+) , Difference (-) , Product (x) , Quotient ( / ) , Per 100 (#% _<_ 100%), Is or Of (#% _>_ 100%)
