1. to make Math really make sense
Math Resource
Helpful hints
to make Math really make sense

2. Decimals
(parts)
Whole Numbers
Place Value

3. Types of Numbers Real Numbers: numbers found on a number line
Integers: numbers (positive and negative) that don’t have decimals
Whole Numbers: positive integers, including O,
Odd Numbers: any number that ends in 1,3,5,7,9
Even Numbers: any number that ends in 0,2,4,6,8
Consecutive Numbers: in a natural row (3,4,5)

4. More Numbers
Rational numbers: any number that can be expressed as a fraction (3 = 3/1, 2/3, 0.25)
Irrational numbers: numbers that dont make sense - repeating decimals, go on forever (∞, π)
Prime numbers: only factors of 1 and itself (2,3,5,7,11, . . )
Composite numbers: three or more factors (4,6,8,9,10, . . )

5. Sieve of Erasthosenes Composite Numbers -
Prime Numbers - in yellow/gold
Composite Numbers -
crossed out
First five Prime Numbers
2, 3, 5, 7, 11

6. Written Numbers
Standard form: written with digits (individual numbers)
Expanded form: broken into place values *
*(2x10 000)+(3x1 000)+(4x100)+(5x10)+6
Scientific Notation: making very large or very small numbers easier to deal with
= 2.34 X 10 5th power
x 10 -5th power

7. Adding Positive and Negative Numbers
1.) Same signs - just add and keep same sign ( = -5)
2.) Different signs - subtract smaller from larger and keep sign of larger digit
( = -1)
Subtraction: “add the opposite” then follow addition rules
-3 -(-2) = -3 + (+2) = -1

8. Multiplying and Dividing Positive and Negative Numbers
Same signs = positive answers
Different signs =
negative answers
(+)(+) = +
(-)(-) = +
(+)(-) = -
(-)(+) = -
(-5)(-6) = +30
(+4)(-5) = -20

9. Multiplication Term to Know
Multiples - like skip counting, groups of numbers with common number - can go on forever (4,8,12,16, )
Factor: numbers when multiplied make a product (when finding factors start on outside and work in (1, )
Product - the answer to a multiplication problem
factor X factor = product
Least (or lowest) Common Multiple (LCM) - comparison of two numbers
4,8,12,16,20
5,10,15,20 LCM =20
Greatest Common Factor (GCF) - comparison of two numbers factors
6: (1,2,3,6)
9: (1,3,9) GCF = 3

10. LCM =20
LCM =20
How to Multiply
Traditional Method
Alternate Method

11. Divisibility Rules 2 - any even number
3 - digits add up to a multiple of 3
4 - last two digits divisible by 4
5 - ends in 5 or 0
6 - divisible by both 2 and 3
8 - last 3 digits divisible by 8
9 - digits add up to a multiple of 9
10 - end in 0

12. Dividend / divisor = Quotient
How to Divide
Dividend / divisor = Quotient
Traditional Method
Alternate Method

13. division or multiplication
Order of Operations
3 + (2+1) x 4 =
3² + 3 x 4 =
9 + 3 x 4 = =
= 21
BEDMAS =
brackets
exponents
division or multiplication
addition or
start at Left side
then move to right

14. Exponents
Exponent is the small number that tells how many times the base multiplies itself
Base: large number that is multiplying itself
Together the base and exponent are know as Power
3 to the power of 4 = 3 x 3 x 3 x 3 = 81
Positive exponents = positive whole numbers
Negative exponents = fractions or decimals
Power of 10 - positive exponents tell how many zeros behind the 1
Negative exponents tell how many zeros in front of the 1 including the 0 before the decimal.

15. Squared Numbers
Squared numbers are numbers that have both factors the same (6 x 6 = 36)
Perfect squared numbers have an ODD number of factors (1,2,3,4,6,9,12,18,36) = 9 factors
Radical sign : answers can be positive or negative
6² = (6)(6) = ² (-6)(-6) = 36
Know the common squared numbers!!
2 x 2 = x 3 = x 4 = 16
5 x 5 = x 6 = x 7 = 49
8 x 8 = x 9 = x 10 = 100
11 x 11 = x 12 = x 13 = 169
14 x 14 = x 15 = 225

16. Finding Squared numbers
Guess and Check
1) find the nearest square numbers that it lies between
2) Find the square roots
3) Guess which root is it closer to
4) Check with multiplication if your guess is correct
5) Guess and try again if not close
Formula Based Method
1) Find the nearest square number without going over
2) Subtract the closest square number from the square number you are dealing with
3) Divide that answer by 2 times the square root of the closest square number
4) Add that answer to the nearest square root to get the final answer)

17. Fractions - Terminology
Numerator = top part of the fraction
Denominator = bottom part of the fraction 2 3
Improper Fraction = numerator larger than denominator 3 2 1
Mixed Number = whole number with fraction 2 3
Reciprocal = “flipping the fraction”
Inverse operation = opposite operation

18. Improper Fraction to Mixed number
1.) Denominator goes into numerator = whole number
2.) Remainder = new numerator
3.) Denominator stays the same

19. Mixed number to improper number
1.) Denominator x whole number
2.) Add the numerator to find the new numerator
3.) Denominator stays the same

20. Adding and Subtracting Fractions
1.) Fractions must have COMMON DENOMINATORS
2.) Add numerators together
3.) common denominator stays the same
4.) Change to lowest terms

21. Formulas to know and love!
Area of a rectangle/square/parallelogram
A = b x h or A = l x w
Area of a triangle
A = (b x h)/2
Area of a Circle
A = πr²

22. Pythagorean Theorem

23. Pythagorean Theorem Hypotenuse - side opposite the right angle
Legs - sides of the triangle that make up the right angle
used only on
Right angle triangles