TEAS V- Math

Example of Arabic numerals

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

whole numbers

0,1,2,3,4, etc.

Equivalent decimal for 1/100,000

0.00001

Equivalent decimal for 1/10,000 (ten thousandths)

0.0001

Equivalent decimal for 1/1000 (thousandths)

0.001

Equivalent decimal for 1/100 (hundreths)

0.01

Equivalent decimal for 1/10 (tenths)

0.1

1 cm = how many inches

0.394 inch

1 # = how many kg

0.45 kg

1 yard = how many m's

0.914 m

1 quart = how many L

0.95 L

To find what fraction of the whole

1 (whole) is assumed when no # is given. Ex: 1-(1/5+1/10+1/40) change to common deno, add fractions then find common deno of 1/1-13/40=40/40-13/40=27/40

Convert Fraction to decimal

1) Divide the num by deno (works for all fractions) or 2)fractions whose deno is 10, the num becomes the digit in decimal number and the number of 0's in deno determines placement of decimal point.

Change Roman to Arabic numerals

1) Write from left to right 2) Begin with largest # 3) Subtract I, X or C values when placed to left of larger #

Change Arabic to Roman numerals

1) Write from left to right 2) change each place value to roman numeral 3)I, X and C can be written 2+ times but not followed by a larger # 4) Use I, X and C to left of larger # to indicate subraction 5) V, L and D are never used to the left of larger value and never used more than 1x

Steps to add or subtract fractions

1) convert mixed to proper/improper fractions 2)Find LCD 3)rewrite as an equivalent fraction with LCD as new deno 4) add or subtract numerators 5)simplify 6)change improper to Mixed

Steps for solving word percent problems

1)Change written statement into mathematical equation: of=mult, is= equal, decimal for percent should be used. 2)solve for the unknown, 3)rewrite statement and make sure answer is reasonable.

Steps to solve % problems

1)Change written statement to mathematical equation: of=multiplication, is=equal, decimal form of % should be used in the equation. 2)Solve for the unknown 3)rewrite the statement and make sure answer is reasonable

Steps to reconcile a checking or savings acct

1)Group deposits and add them 2)group the checks and add them 3)Add deposits to previous balance 4) subtract the checks 5)subtract the service charge 6)add the interest.

Convert from decimal to %

1)Multiply the decimal by 100. 2) Add % symbol. Or move the decimal point two places to the right and add % symbol.

Convert from % to decimal

1)Remove the % symbol. 2)Move the decimal point to the left two places. (like dividing by 100)

Steps to convert % to fraction

1)Remove the % symbol. 2)write the # in the num and write 100 in the deno. 3)simplify

Estimation

1)Round the first digit according to the following number 2)if # is 5 or greater round to next higher #, if # is 4 or less leave the # the same and change rest to 0's 3)Perform calculation

Convert fractions to percent

1)convert fraction to a decimal then convert decimal to % by mult by 100 and add % sign (works for all fractions). 2)Write the fraction as an equivalent fraction over 100 then write the num of this fraction with the % symbol (works for fractions whose deno can be written as power of 10)

to multiply fractions

1)convert mixed fraction to improper 2) simplify numerator with deno 3)multiply numerators 4)multiply denos 5)make sure fraction is simplified

to divide fractions

1)convert mixed fraction to improper 2)keep first fraction as is 3)change division sign to mult 4)reverse second fraction 5)simplify numerator with deno 6)multiply numerators 7)multiply denos 7)make sure fraction is simplified

to divide fractions

1)convert mixed fraction to improper 2)keep first fraction as is 3)change division sign to mult 4)reverse second fraction 5)simplify numerator with deno 6)multiply numerators 7)multiply denos 8)make sure fraction is simplified

Process to divide decimals

1)set divisor (deno, outside of div #) to a whole #. Ex 1.2 to 12. 2)Move decimal point in dividend same amount of spaces you moved the divisor decimal point 3)place decimal point above the dividend 4)Divide as if its a whole #

Value of Roman numeral M?

1,000

1 km = how many m/mile

1,000 m/ 0.62 mile

1 mile = how many km's

1,609 km

Converting an irrational decimal # to √

1. Determine if the # given is greater or less than the base square root. Ex: 2.236 is greater than √4 which is 2 and less than √9 which is 3, it could be √5 √6 √7 √8 since the # is closer to 2 than 3 most likely it's √5

How to calculate the square root of # that cannot be written as a square root √5

1. the first digit can be approximated by thinking what 2 base square roots the desired root is in between. Ex: √4=2 & √9=3 so first # is 2.___ 2. estimate by reasoning that since the # inside the √ is closer to 4 than 9 then it can be 2.1 or 2.2

1 L = how many quarts

1.06 quarts

10 to the 0 pwr is

1/ no prefix

Value of Roman numeral C?

100

1 foot equals how many inches

12 inches

1 pound equals how many ounces

16 oz

1 pint equals how many cups

2 cups

1 kg = how many pounds

2.2 pounds

1 inch = how many cm

2.54 cm

1 oz = how many grams

28 g

1 yard equals how many feet

3 feet

1 gallon = how many L

3.785 L

1 oz = how many mL

30 mL

1 m = how many inches

39.37 inch

1 gallon equals how many quarts

4 qts

Perimeter of a Rectangle

4 sides - Length x2 + Width x2 or add all sides

1 tsp = how many mL

5 mL

1 mile equals how many feet

5, 280 feet

Value of Roman numeral L?

50

Value of Roman numeral D?

500

1 cup equals how many ounces

8 oz

Calculation for Take home pay

Beginning salary - deductions (add all deductions first) = take home pay. Also Gross pay-deductions = take home pay

Order rational number by size (decimals and fractions together)

Either conver all fractions to decimals or convert all decimals to fractions.

Order rational number by size with 3 denos

Find least common deno and re-write. Example using smaller deno to find LCD.

Unit of metric measure for weight and abbreviation

Gram/g

Unit of metric measure for volume and abbreviation

Liter/L

Example of Roman numerals

M, D, C, L, X, V, I

Order of Operations

P(parenthesis) E(exponents) M(mult) D(div) A(add) S(subtract)

Equation for reconciling checking/savings acct

Previous balance+deposits-checks-service charge+interest=reconciled account

Rate of change example

Set a ratio for student A, then for student B, subtract both results and that would be the final result

Order rational numbers by size (for decimals)

Start with the greatest place value 0.778 - 0 is in the one's place 7 is in the 10's place. 0 is the greatest place value. Until one number is greater than the following.

What are the three types of % problems?

To find the whole, part or percent

Define Rational #

a real number that can be written as a fraction, terminating decimal (0.25) or repeating decimal (0.2121)

Solve proportions

by using cross products

Prefix for centi and power of 10

c/ 10 to the -2nd pwr = 1/100

Either in mult or div if you find a mixed number...

change it to an improper fraction

Prefix for deci and power of 10

d/ 10 to the -1 pwr = 1/10

Prefix for deka and power of 10

d/10 to the 1st pwr = 10

Converting from decimal to fractions

decimal number expressed becomes the numerator, the number of decimal places to the right of the decimal determines the value of the denominator. Simplify

divisor is the same as

denominator and goes in the outside of div sign

Order rational number by size (fractions)

find a common deno for the fraction and rewrite. The greatest numerator is the greatest fraction.

English measurement system

foot, yard, mile, cup, pint, quart, gallon, pound, ton

Prefix for hecto and power of 10

h/10 to the 2nd pwr = 100

The number after the word "to" in a ratio problem

is the denominator.

Define part

is the new value

what is rate of change?

it uses proportions to determine the difference in completion times for a given task

Prefix for kilo and power of 10

k/10 to the 3rd pwr = 1,000

LCD

least common deno= least # that both deno's divide into evenly. Start by mult the biggest deno by 1, 2, 3, etc until the other deno is also divided evenly by it

Prefix for milli and pwr of 10

m/ 10 to the -3rd pwr = 1/1,000

Unit of metric measure for length and abbreviation

meter/m

Metric measurement system

meters, liters, grams

Calculation for event planning

multiply the # of people attending by each of the itmes they will receive and add those results together. If everyone attending will receive the same items then add all the items first, then multiply by the number of people.

formula for percent increase

new value-original value/original value, then multiply by 100

Define Real #'s

number that appears on the number line as either a rational or irrational #.

Define Irrational #

numbers that cannot be written as fractions. Ex: square roots, cube roots and pi, not all roots are irrational

dividend is the same as

numerator and goes in the inside of div sign

Define whole

original value, value that existed first

formula for percent decrease

original value-new value/original value, then multiply by 100

Percent correct in a test

part/whole, multiplied the quotient by 100 and % symbol

Remember

read carefully, negative signs,

In dividing decimals

remove 0's before the decimal point after the decimal has been moved, rewrite division problem.

Determine cost of a given set of items

select items to be purchased and add their prices. When it is an item with pounds, multiply the amount of items x weight of item x price per pound.

To determine approximate decimal equivalent for cube or square root

the number has to be between two roots, Ex cube root of 8 is 2 and cube root of 27 is 3. look at inside the root sign to see which root the # is in between. Cube root of 10 is between 8 and 27 but closer to 8 thus 2.15. You can search for "algorithm methods"

Simplify means

the only common # is 1

calculate profit

total income - total expenses

Define proportion

two ratios that are equal. The numerators should be in the same unit as well as the denominators.

Define ratio

use to express a relationship between two quantities. Can be written as fractions, with colons or with words. Are always written in the simplest form. Keep the order of the ratio

Ex: Divide 0.05 into 0.710

write as you see it; 5 outside and 71.0 in the inside