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Pre-Algebra

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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.

There are various sub topics, which are the parts of the Pre-Algebra which starts from solving the equation and may go up till the geometry problems.

Pre-Algebra Topics

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Given below are the important pre-algebra topics:

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.

Pre-Algebra Curriculum

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Curriculum for pre-algebra is given below.

Decimals
  • Naming Decimals
  • Rounding Decimals
  • Operations on Decimals
  • Converting Between Fractions and Decimals
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

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

Pre-Algebra Formulas

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In prealgebra, we use a set of formulas to solve complex problems.
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%

Pre-Algebra Problems

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Given below are some of the prealgebra problems.

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

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.