# Unit 1 Study Guide

### By: Nasser M

## Number Sets

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

## Fraction To Decimals

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

- 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