Number Sense

each movement to the left or right changes the place value by a unit of __

10

what place is the 4,7,9,8, and 6?

1247.986

4: tens

7: ones

9: tenths

8: hundredths

6: thousandths

Real Numbers

can exist in the real world/all rational and irrational numbers

no square root of negative numbers

12, 5/8, √3, 0, -4, -1/2, 3.14

Integers

all whole numbers, both positive and negatives, no fractions or decimals

0,1,2,-1,-2

Whole Numbers

0 and positive integers

0,1,2,3,4….

Prime Numbers

can only be divided by one and itself without a remainder

2, 3, 5, 7, 11, 13, 17…

Rational Numbers

any number that can be expressed as a ratio of two integers, can be expressed as decimals, fractions or %, decimal must be repeating or terminate

1, 58, 0.5, 4 1/2, 10%, 0.1343434, √4, -1/4

Natural Numbers

counting numbers: 1, 2, 3, 4

the numbers by which you would normally count by, does not include 0 or negatives

Irrational Numbers

all values that exist but are not rational

π: 3.14159265…..

√ 2: 1.41421356…..

both have no termination or repeating pattens

Composite Number

natural number greater than one, not a prime number

6, 4, 9, 10, 12, 14….

Square Numbers

result when numbers are multiplied by themselves

1, 4, 16, 25, 36, 49

Cube Numbers

Result of raising integers to the third power (cubing them). First 7 positive cube numbers are: 1, 8, 27, 64, 125, 216, 343

When estimating and rounding…

drop numbers that are 4 or less

round up numbers 5 or greater

Order of Operations

Please Really Excuse My Dear Aunt Sally

parentheses

roots & exponents

multiplication & division

addition & subtraction

What is the easiest way to compute 31×4?

30×4 =120

+

1×4=4

124

How to divide fractions

flip second fraction, then multiply

How to multiply fractions

multiply across, no need for common denominator

how to add or subtract fractions

need to find common denominators

what you do to bottom, must do to the top

z² means…

z^-2means…

z x z

1/z x z

In scientific notation, there can only be _______ before the decimal point

one digit

write 472,000,000 in scientific notation

4.72 × 10⁸

write 0.0000000472 in scientific notation

4.72 × 10^-8

Common Factor

a common factor is a number by which two other numbers are both divisible

ex: what are the greatest common factors of 40 and 60?

1, 2, 4, 5, 10, 20

*do not use factor trees to find common factors unless you are only seeing common prime factors

How to calculate for: what % of 8 is 2?

x/100 × 8/1=2

Distributive Property

A(B+C)=AB + AC

A(B-C)=AB-AC

*the opposite of distributing is factoring

Commutative Property

the order in which multiplication or addition is done does not effect the answer

ab=ba

a+b=b+a

*not included in subtraction or division

Associative Property

In addition and multiplication, grouping does not matter

A+(B+C)=(A+B)+C

A x (BxC)=(AxB) x C

Identity Property of Addition

any number plus 0 equals itself

4+0=4

Identity Property of Multiplication

any number times 1 equals itself

4×1=4

Additive Inverse Property

any number plus its additive inverse = 0

4+ -4 = 0

Multiplicative Inverse Property

any number times its multiplicative inverse =1

4 × ¼ = 1

2/3 × 3/2 = 1