Basic of Mathmatics

Intergers

Numbers that can be written as a fraction or a decimal

Counting Numbers that are positive or negative

If it has a decimal point w/ something after that or a fractional remainder, IT’S NOT AN ______

e.g. -3, -2, -1, 0, 1, 2, 3

Whole Number

Positive integers, no negative numbers

e.g. 0, 1, 3, 55, 600, 8000

The Distributive Property

tells us

A(B + C) = AB + AC

2 (30+ 55)

2(85)

= 170

Opposite of Distributing is Factoring

When you’re DISTRIBUTING, you’re MULTIPLYING several terms by the same number

When you’re FACTORING, you’re DIVIDING the same number out of a number of different terms

The Commutative Property of Addition and Multiplication

ORDER DOES NOT MATTER

A + B = B + A

A x B = B x A

Order is what the commutative property relates to

However, this isn’t true for subtraction and division

The Associative Property of Addition and Multiplication

GROUPING DOES NOT MATTER

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

A x (B x C) = (A x B) x C

Regardless of how you group them, you’ll get the same result

The Identity Property of Addition

ANY NUMBER + 0 = ITSELF

5 + 0 = 5

You can drop the zero because of the ______

The Identity Property of Multiplication

ANY NUMBER X 1 = ITSELF

3 × 1 = 3

You can drop the one because of the identity property of multiplication

The Additive Inverse Property

ANY NUMBER + ITS ADDITIVE INVERSE = 0

2 + -2 = 0

Positive and negatives will help us find the additive inverse

The Multiplicative Inverse Property

ANY NUMBER X ITS MULTIPLICATIVE INVERSE = 1

Any number x its ___________ = 1

6 × 1/6 = 1

Integer 6 think as 6/1

The ________ is the reciprocal of the fraction

Prime Number

Can be evenly divided by 1 and itself without a remainder

• You divide it by anything besides 1 in itself, you’ll get a decimal remainder

• Sometimes an odd number can be a ____ number

  • e.g. 2, 3, 5, 7, 11, 13

Any even number OTHER THAN 2, is automatically not a ____ number, but if it’s an odd number, it varies.

• e.g. 5 is ____, but 9 is not

Real Numbers

Anything that can exist in the real world

Most numbers on the exam will fall under this category

e.g. 12, 5/8, \sqrt{3 }

Rational Number

Any number that can be expressed as a ratio of two other numbers

• e.g. 1/2, 0.5, 12%, 1

Fractions, decimals, percentages, and integers

Fractions

(Type of rational number on test)

Top number → Numerator

________________________

Bottom Number → Denominator

Reduce 4/8 divided by 4/4 = ½ or 4/8 divided 2/2 = 2/4 divide again by 2/2 = ½

Convert Improper Fraction to a Mixed Number

The numerator larger than denominator

Find how many times denominator divides into the numerator = whole number

Multiply the whole number x denominator - that number from the numerator to get the numerator of the remainder

9/4 = how many times can 4 go into 9?

2→ whole number

4 × 2 = 8 → subtraction from numberator

9-8 = 1 → new numerator

Denominator always stays the same

2 ¼ → Answer

Mixed Number to an Improper Fraction

Multiply the whole number by the denominator

Then add that number to the numerator

Denominator won’t change!

2 ¼ → 2 × 4 = 8

8 + 1 → = 9

9/4 = Answer

Convert a Fraction into a Decimal

Divide the numerator by the denominator

2/4 = 2 divided by 4 = 0.5

Convert a Decimal into a Fraction

Move the decimal to the right of the last significant digit, the last non-zero digit. Every time we move the decimal, we change the number’s value by a unit of 10.

0.14

01.4

014.

Moved twice

10 × 10 = 100

14/100

However, many times when you move a decimal, that’s how many zeroes follow the one in your denominator

Percent Definition

Divided by 100

Per= divided by

Cent= centennial means 100

Percentage to Fraction

12% do what name, divide by 100

12/100, then divide by denominator

= 0.12

Decimal Definiton

Deci = 10

Imaginary Numbers

\sqrt{ -4} “square root of negtive 4”

you can’t have the square root of a negative number

Base 10 Number System and Place Value

Each place has a value of 10

Why when moving decimal point, change the numbers of value by units of 10

Each movement, left or right, changes the place value by a unit of 10

Why aren’t all numbers a base 10 system?

Computers use a binary system, meaning only 2 digits, 2 values in each digit

e.g. 0 and 1 and 10, 01

Ordering Fractions

Convert fractions into fractions with the common denominator

MULTIPLY ALL. THE DENOMINATORS YOU HAVE. It won’t always give you the least, but it’ll always give you common

Rules for Multiplying and Dividing Fractions

+ x + = +

- x - = +

- x + = -

Rounding and Estimating

What’s the difference between this set of numbers rounded to the nearest 10? and actual exact values

43.45 5 if the number in the ones place is 5 or greater, than tens place will go up one = 43.5

6.2 2 is in the tens place so = 6.2

7.48 4 is in the tenths place, 8 in the hundredths, so you’re answer is 7.5 (because decimal placement)

I34.547, the 5 is in the tenths place, the 4 is in the hundredths place, and the 7 is in the thousandths place.

• If you're rounding to the nearest tenth, look at the hundredths place (4).

• Since 4 is less than 5, the tenths place stays the same (5).

• The digits after the tenths place are removed.

So, 34.547 rounds to 34.5

19 this is already rounded

Algroithmic Opposites

Way we compute something

It’s the opposite of each other

e.g. roots and exponents

If you square something and then take the square root of it, you’re back to where you started

5² = 25 = srqrt{25} = 5²