Unit 1 Study Guide

By: Nasser M

Number Sets

Natural Numbers: Any number that's not 0, a fraction, a decimal, or a negative.

Ex: 1,2,3,4,5,6


Whole Numbers: Any number that's not a fraction, decimal, or a negative.

Ex: 0,1,2,3,4,5,6


Integers: Any number that's not a fraction or a decimal.

Ex: -1,0,1,2


Rational Numbers: Any number that's not irrational.

Ex: 1.5, 7/4, -2, 0, 5


Irrational Numbers: A number that goes on forever, but never repeats.

Ex: 3.14 or Pi

Big image

Fraction To Decimals

To turn A fraction to a decimal, simply divide the numerator by the denominator.

Ex: 2/4 4(2.0 4x5=20 Answer: .5

Operations With All Rational Numbers

ADDITION: Integers (positive + Positive= Positive) (Positive+Negative=negative) If the negative number is Bigger

Ex: 9+ -12= -3 Ex: 12+ -9= 3

Decimals: negative + negative = negative) (positive + negative= negative) (+ + + = +)

Ex: 9.2+10.8= 20.0 Ex: -9.5+ -7.0 = -16.5 Ex: -9.0 - 3.0 = -12 Ex: -9.5 - (-9.5) = 0

Fractions:

  • Find common Denominator
  • Turn to mixed fraction
  • Simply add together
  • Turn to proper fraction

SUBTRACTION: (negative-negative=positive) (negative-Positive=negative)

Positive-negative=positive) (positive-positive=negative)

Integers: Ex: -18 - (-12)= -6 Ex: 18 - 6= 12 Ex: -20 - (-40)= 20 EX: 2-2=0

Decimals: Ex: -4.7 + -5.3= -10 EX: -5.1 - 5 = -10.1 Ex: 5 - (-10) = 15 -4.7 - (-4.7) = 0

Fractions:

  • Find common Denominator
  • Turn to mixed fraction
  • Subtract straight across
  • Turn to proper fraction

MULTIPLICATION: (Positive x Positive= positive) (Negative x Negative= positive)

(Negative x Positive= Negative)

Integers: 2*-11= -22 3*3= 9 -9*-10= 90

Decimals: EX: 5.4 x 13= 54 x 130 = 7020 = 70.20

  • 2.4 x 7 = 24 x 70
  • 2.44 x 7 = 244 x 700
Fractions:

  • Convert all mixed numbers to improper fractions.


  • Flip second fraction EX: 2/4 x 5/4 = 2/4 x 4/5

  • Multiply the numerators.


  • Multiply the denominators.


  • Reduce your final answer.



DIVISION: (negative/negative=positive) (positive/negative=negative) (posititve/+=+)

Decimals: 4.8/0.02= 480/2 = 240

Integers: (Same rules as multiplying integers) 16/-4= -4

Fractions: 4/5 / 1/2 = 4/5 x 2/1

  • flip second fraction
  • Multiply numerator
  • multiply denominators
  • reduce or simplify answer

Scientific Notation

Big image
  • Number to left of decimal has to be 1 or more, or 10 or less
  • if Negative then move decimal to left -2.0 x 10(3) = .0002
  • If positive then move decimal to right Ex: 2.0 x 10 (3) = 2000.0