IMMS MATHEMATICS TUTORIALS

Directed numbers Directed numbers are numbers that have a sign (positive or negative) associated with them.  They help us represent quantities that can have opposing directions or values.  Positive-directed numbers indicate a gain or movement in the positive direction, while negative-directed numbers represent a loss or movement in the negative direction. Directed numbers can be positive or negative numbers. These numbers are characterized by size (2 and 4.8) and direction (– or +). Positive numbers: +3, +1.5, +0.2, +2, … Negative numbers: – 3, – 1.5, -0.2, -21, … Remember: +3 is read as “positive three.” +1.5 is read as “positive one point five.” -3 is read as “negative three.” -0.2 is read as “negative zero point two.” Operations Involving Directed Numbers The following are the rules for dealing with addition, subtraction,  multiplication, and division of directed numbers. Addition There are two rules: 1. SAK (Same sign – Add – Keep the sign) Examples: (-2) + (-3) = -5...

I ndex A number or a variable may have an index. Index of a variable (or a constant) is a value that is raised to the power of the variable. The indices are also known as  powers or exponents . It shows the number of times a given number has to be multiplied. It is represented in the form: a m  = a × a × a ×……× a (m times) Here, a is the base and m is the index. The index says that a particular number (or base) is to be multiplied by itself, the number of times equal to the index raised to it. It is a compressed method of writing big numbers and calculations. Example:  2 3  = 2 × 2 × 2 = 8 In the example, 2 is the base and 3 is the index. Laws of Indices There are some fundamental rules or laws of indices which are necessary to understand before we start dealing with indices. These laws are used while performing algebraic operations on indices and while solving the algebraic expressions, including it. Rule 1:  If a constant or variable has index as ‘0’, then the...

Simplification Simplification of expressions: Simplification of expressions means rewriting the same algebraic expression with no like terms and in a compact manner. Making something simpler is making it less complex. The operations required to simplify things are done in a set order called BODMAS. Where, B = Bracket 0 = of D = Division M = Multiplication A = Addition S = Subtraction To simplify a fraction, reduce it to its most basic form. If a fraction's numerator and denominator only share the number one, it is said to be in its simplest form . The process of simplifying difficulties as we work to tackle fractional problems is essential. The value of the fraction won't change even after we simplify them. This indicates that the true fraction and the simplified fraction are two equivalent fractions . simple methods for simplifying fractions. Simplifying Fractions How to Simplify Fractions? Simplify Fractions Reducing a fraction to its simplest form is the definition of s...