Numbers

1
Numbers Operations

• CRCT review

2
Real Numbers

• All rational and irrational numbers all numbers
  that can be expressed as a decimal
• Rational Numbers Irrational Numbers
• natural numbers
• whole numbers
• integers

3
Natural Numbers

• aka counting numbers
• ex 1, 2, 3, 4,

4
Whole Numbers

• The natural numbers and zero
• ex 0, 1, 2, 3, 4,

5
Integers

• The set of whole numbers and their opposites
• ex -4, -3, -2, -1, 0, 1, 2, 3, 4

6
Rational Numbers

• A number that can be written as a/b, where a and
  b are integers and b doesnt equal 0.
• includes fractions, repeating/terminating
  decimals
• ex -1/4, 6/5, .0324, -3.272727

7
Irrational Numbers

• non-terminating and non-repeating decimals
• Cant be written as a/b
• ex 2.34567,
• All numbers that are not rational are irrational

8
Rational or Irrational?

• 1. -7.2
• 2. 1.004
• 3.
• 4.
• 5.

rational
rational
rational
rational
irrational
9
Absolute Value

• The distance a number is from 0
• 8
• 0
• 4
• -10

10
Comparing/Ordering Rational Numbers

• Write all numbers in the same form (all decimals,
  all fractions, or all percents)
• EX. Order the numbers from greatest to least

11
Adding Signed (/-) numbers

• 1. When numbers being added have the same sign,
  add the numbers and write the sign with the
  answer
• EX. 15 7 22 (-15) (-7)
  -22
• 2. When numbers being added have different signs
• -subtract the absolute values of the numbers
• -use the sign of the number with the higher
  absolute value.
• EX. -15 7 -8 (-7) 15 8

12
Subtracting Signed numbers

• Add the opposite
• Ex. -15 7 -22

13
Multiplying/Dividing signed numbers

• If there are an even number of (-), then the
  answer is ()
• EX. (-2)(3)(-4)
• If there are an odd number of (-), then the
  answer is (-)
• EX. (-2)(-3)(-4)

24
-24
14
Adding/Subtracting Fractions

• Must have a common denominator

3
12
10
12
15
Multiplying fractions

• Must write as improper fraction
• Multiply the numerators
• Multiply the denominators

16
Dividing Fractions

• Write as improper fractions
• When you have 2 fractions and you want to
  divide, flip the second fraction and multiply.

17
Adding/Subtracting Decimals

• Line up the decimals
• Add/subtract as normal
• Write the decimal point in the answer

18
Multiplying Decimals

• Multiply as normal (ignore the decimals)
• Count how many spaces over you need to place the
  decimal point in the answer

19
Dividing Decimals

• If the divisor (outside the house) has a decimal
  point in it, then you have to move the decimal to
  the end.
• Move the decimal point in the dividend (inside
  the house) the same number of places.