Pre-Algebra is an important branch of mathematics, which prepares students for algebra course in higher classes. It is a common name for a course in middle school mathematics and is generally taught between the fourth and eighth grades students. The main objective of pre-algebra is to prepare students for the study of algebra. |

Absolute Value |
Absolute value of a real number x is the non negative value of x without regard to its sign. |

Expression | A number sentence that does not have an equal sign. |

Quotient | Expressed as the number of times the divisor divides into the dividend. |

Fraction |
Represents a part of a whole. A rational number expressed in the form $\frac{a}{b}$, where a is known as the numerator and b as the denominator. |

Term | The parts that make up an expression that are separated by '+' and '-' signs. |

Variable | A symbol that represents a quantity in a mathematical expression. |

Least Common Multiple | The smallest multiple of two or more numbers have in common. |

Exponents | Exponents are shorthand for repeated multiplication of the same thing by itself. |

Polynomials | Expression constructed from variables and constants using mathematical operations. |

Percentage | Is a number or ratio as a fraction of 100 |

Integer | A number that can be written without a fractional or decimal component. |

Decimal numbers | A number that contains a decimal point. Example 2.5, 25.545 etc., |

Real line | A line with a fixed scale so that every real number corresponds to a unique point on the line. |

Cartesian Coordinates | The usual coordinate system, originally described by Descartes, in which points are specified as distances to a set of perpendicular axes. Also called rectangular coordinates. |

X-Coordinate | Also known as the abscissa, the first number in an ordered pair. |

Y-Coordinate | Also known as the ordinate, the second number in an ordered pair. |

Curriculum for pre-algebra is given below.

__Decimals__- Naming Decimals
- Rounding Decimals
- Operations on Decimals
- Converting Between Fractions and Decimals

__Fractions__- Reducing Fractions
- Converting Between Improper Fractions and Mixed Fractions
- Multiplying Fractions and Mixed Numbers
- Dividing Fractions and Mixed Numbers
- Finding Common Denominators
- Arithmetic Operations on Fractions and Mixed Numbers
- Comparing Fractions

__ Integers__

- Definition and examples
- Integers and Absolute value
- Rules for integers
- Subset of integers
- Compare and order integers
- Comparing Integer Values
- Operations on Integers
- Introducing Exponents

**Ratio and Proportion **

- Ratio Definition
- Proportion definition
- How to calculate ratio and proportion?
- Difference between Ratio and Proportion

__Polynomials__- Degrees of polynomials
- Finding roots of polynomials
- Types of polynomials
- Operations on polynomials
- Simplify polynomials
- Factorization

- Roots of polynomials

**Percentage**- How do u find percentages
- Convert decimals to percentage
- Convert percentages to fractions
- Percentage increase, Percentage decrease
- Percentage change
- Percentage difference equation
- Weighted average percentage
- Gross profit percentage formula
- Percentage relative error
- Cumulative frequency percentage

**Whole Numbers**- Whole numbers definition
- Properties
- Operations on whole numbers
- Rounding whole numbers
- Adding fractions with whole numbers
- Multiplying mixed fractions with whole numbers

Given below are some of the basic pre-algebra formulas:

- (a + b)$^{2}$ = a$^{2}$ + b$^{2}$ + 2ab
- (a - b)$^{2}$ = a$^{2}$ + b$^{2}$ - 2ab
- a$^{3}$ + b$^{3}$ = (a + b)(a$^{2}$ - ab + b$^{2}$)
- Area of a Square = Side x Side
- Area of a triangle = $\frac{1}{2}$ (Base x Height)
- Perimeter of Square = 4 x Side
- Area of a rectangle = Length x Breadth
- Perimeter of a rectangle = 2 (Length + Breadth)
- Circumference of the Circle = 2$\pi$ r, r = radius of the circle
- Quadratic formula: The standard equation of ax$^{2}$ + bx + c = 0, a$\neq$ 0 is x = $\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

- Percentage Increase = $\frac{\text{Increase}}{\text{Original Price}}$ x 100%
- Percentage decrease = $\frac{\text{Decrease}}{\text{Original Number}}$ x 100%

### Solved Examples

**Question 1:**Solve 5x + 150 = 0.

**Solution:**

Given equation is 5x + 150 = 0

Put all the variables aside and value on the other side.

5x = -150

Divide both sides by 5, to find the value of 'x'.

$\frac{5x}{5}$ = $\frac{-150}{5}$

x = -30

Put all the variables aside and value on the other side.

5x = -150

Divide both sides by 5, to find the value of 'x'.

$\frac{5x}{5}$ = $\frac{-150}{5}$

x = -30

**Question 2:**Find the value of 'x' in 2x + 4 = 16.

**Solution:**

**Given:**2x + 4 = 16

2x = 16 - 4

2x = 12

Divide both sides by 2, to find the value of 'x'.

$\frac{2x}{2}$ = $\frac{12}{2}$

x = 6

**Question 3:**In an exam, Melody finished $\frac{9}{10}$ of the math problems, while Christine did $\frac{2}{5}$ of her math problems. Who did a greater fraction of math problems?

**Solution:**

**Given:**Melody finished $\frac{9}{10}$ of the math problems.

In terms of percentage, it is 90%.

Christine finished $\frac{2}{5}$ of the math problems.

In terms of percentage, it is 40%.

Compare the whole number parts which is in percentages.

As 90 is greater than 40 (90 > 40), Melody completed greater fraction of her math problems.