Domain 1: Number Sense

1/100

.01 = 1%

1/10

.1 = 10%

7/10

.7 = 70%

9/10

.9 = 90%

1 km

0.6 mile

1 gallon

4 quarts

place value

each position in any number written in decimal form i.e. ten thousandths, thousandths, hundredths, tenths, ones, tens, hundreds, thousands, ten thousands, etc.

mixed number

when a value is expressed using a whole number together with a proper fraction

1 meter

~ 1 yard

1 kilogram

~ 2.2 pounds

1 liter

~ a little over a quart

12 inches

1 foot

3 feet

1 yard

Metric ton

1,000 kg

1 mile (in yards)

1,760 yards

multiplying mixed numbers

1. multiply the whole number by the denominator of the fraction 2. add this to the numerator of the fraction 3. this is now your numerator & denominator stays the same 4. change answer back to mixed number (if improper) and reduce i.e. 3 1/3 x 2 1/4 becomes 10/3 x 9/4 = 90/12 = 7 6/12 = 7 1/2

square root rules

1. numbers multiplied under a radical (square root) equal the product of the two square roots 2. division is the same as multiplication 3. in addition and subtraction, the numbers must by combined under the radical before any computation of a square root

multiplying or dividing signed numbers (positive and negative numbers)

1. the product or quotient of two numbers with the same sign will produce a positive answer 2. the product or quotient of two numbers with opposite signs will produce a negative answer

deci

1/10 or .1

centi

1/100 or .01

milli

1/1000 or .001

deca

10

hecto

100

kilo

1000

1 square foot

144 square inches

1 pound

16 ounces

1 pint

2 cups

1 quart

2 pints

1 ton

2,000 pounds

1/5

2/10 = 0.2 = 20%

1/4

25/100 = .25 = 25%

1 yard

36 inches

1 bushel

4 pecks

1 mile (in feet)

5,280 feet

1/2

5/10 = .5 = 50%

1 year

52 weeks

3/5

6/10 = .6 =60%

3/4

75/100 = .75 = 75%

4/5

8/10 =.8 = 80%

1 square yard

9 square feet

Order of Operations

PEMDAS - parentheses, exponents, multiplication or division, addition or subtraction

prime numbers

a natural number greater than 1 and that only has 1 and itself as divisors (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.)

composite numbers

a natural number greater than 1 that is not a prime number

additive inverse

a value that, when added to any number, equals 0; any number added to its additive inverse also equals zero

natural numbers

aka counting numbers - the numbers you would naturally count by (i.e. 1, 2, 3, 4, 5, etc.); excludes 0

decimals

all numbers to the left of the decimal point are whole numbers and all numbers to the right are fractions with denominators of 10, 100, 1000, etc.

real numbers

all the rational and irrational numbers

integers

all the whole numbers together with their opposite negative number

rational numbers

all values that can be expressed in the form of a/b where a and b are integers and b does not equal 0; when expressed in decimals, the expression either terminates or has a repeating pattern

irrational numbers

all values that exist but aren't rational (i.e. √2 or π)

adding or subtracting mixed numbers

change the fraction to have least common denominator and add or subtract the fractions; remember to always add and subtract whole numbers too; you can borrow from the whole number to make fraction bigger for subtraction purposes

finding percent of a number

change the percent to a fraction or decimal then multiply

percentage change

change/starting point x 100% = percent change i.e. What is the percentage decrease of $500 item on sale for $400? Change = 500 - 400 = 100 100/500 x 100% = 1/5 x 100% = 20% decrease

improper fraction to a whole number or mixed number

divide the denominator into the numerator i.e. 24/3 = 8 i.e. 19/5 = 3 4/5

percent to fraction

divide the percent by 100

dividing fractions

invert the second fraction and multiply i.e. 1/6 ÷ 1/5 = 1/6 x 5/1 = 5/6

decimal to percent

move decimal point two places to the right

dividing decimals

move the decimal in the divisor over as many times until it is a whole number then move the decimal point in the dividend the same number of places i.e. 5 ÷ 1.25 becomes 500 ÷ 125 = 4

percent to decimal

move the decimal point two places to the left

distributive property

multiplication outside parentheses distributing over either addition or subtraction inside parentheses does not affect the answer (need to use with more than 1 operation)

multiplying decimals

multiply as usual then count total number of digits above the line which are to the right of the decimal and count that many over in your answer

fraction to percent

multiply by 100%

multiply fractions

multiply the numerators then multiple denominators; reduce your answer to lowest terms (you can reduce before multiplying or after)

mixed number to an improper fraction

multiply the whole number by the denominator, add the numerator, and then place that value over the denominator i.e. 6 2/5 = (5 x 6) + 2 = 32/5

whole numbers

natural numbers including 0

numerator

number above the bar in a fraction; tells you how many of the parts are being considered

denominator

number below the bar in a fraction; generally tells you how many equal parts something has been divided

proper fraction

numerator is smaller than the denominator

improper fraction

numerator is the same or more than the denominator

greatest common factor

the greatest factor in common for the numerator and denominator that you can use to reduce the value of the fraction i.e. 24/36 divided by 12 = 2/3

associative property

the grouping, without changing the order, does not affect the answer (addition and multiplication only)

least common multiple (least common denominator)

the least positive value that all the denominators will divide into without a remainder (used for adding and subtracting fractions together; helps you find common denominator)

communicative property

the order in which addition or multiplication is done does not affect the answer (addition and multiplication only)

square numbers

the results of taking integers and raising them to the 2nd power (squaring them or multiplying it by itself); i.e. 1, 4, 9, 16, etc.

cube numbers

the results of taking integers and raising them to the 3rd power (cubing them); i.e. 1, 8, 27, 64, 125, etc.

multiplicative inverse

value that when multiplied with any non-zero number equals 1; any non-zero number multiplied by its multiplicative inverse equals 1 (a x 1/a = 1)

identity number

value that, when added to another number or multiplied with another number, does not change the value of that number (for addition = 0, for multiplication = 1)

scientific notation

very large or very small numbers are written in this form; begins with a positive number greater than or equal to 1, but less than 10, multiplied by an integer power of 10 the exponent is positive for values greater than 1 and negative for values less than 1 i.e. 2,100,000 becomes 2.1 x 10^6 i.e. 0.000042 becomes 4.2 x 10^-5