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OBJECTIVES

At the completion of this unit, students will be able to:

1. What is the Algebra & list its branches.
2. Define the elementary algebra.
3. Mathematical operations.
4. Self practice.

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Define the algebra

Objective no 01

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• Algebra is a branch of mathematics that deals with solving equations and finding the values of variables (Symbols (like x or y) that represent unknown values).

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• It can be used in different fields such as physics, chemistry, Nursing research and economics to solve problems.

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• Algebra is not just solving equations but also understanding the relationship between numbers and variables. e.g. Combinations of numbers and variables (3x + 5).

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Branches of Algebra

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Algebra is divided into different sub-branches such as;

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• Elementary algebra
• Advanced algebra
• Abstract algebra
• Linear algebra
• Commutative algebra.

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Elementary algebra

Objective no 02

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• Elementary Algebra is the branch of Algebra that covers the traditional topics studied in a modern elementary algebra course.

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• Arithmetic includes numbers along with mathematical operations like +, -, x, ÷.

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• But in algebra, the numbers are often represented by the symbols and are called variables such as x, a, n, y.

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• The elementary algebra practiced in classes 7, 8 or sometimes 9, where basics of algebra are taught.

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Mathematical operations

Objective no 03

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• Mathematical operations are procedures that take numbers or expressions as input and produce a result.

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• The four fundamental mathematical operations are:
1. Addition (+)
2. Subtraction (-)
3. Multiplication (× or *)
4. Division ( ÷ or / )

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Addition

• Addition which describes adding two or more numbers together to get their sum.
• Addition is indicated by a plus sign ( + ).

Example#1: 2 + 3 = 5

Example#2: 9 + 11 = 20

Example#3: 10 + 3 = ?

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Subtraction

• Subtraction finds the difference between two numbers.
• Subtraction is indicated by a minus sign ( - ).

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Example#1: 5 - 2 = 3

Example#1: 8 - 2 = 6

Example#1: 52 - 7 = ?

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Multiplication

• Multiplication: Repeats a number a specified number of times.
• Multiplication is indicated by a times sign or the dimension sign ( x or * ).

Example#1: 4 × 5 = 20

Example#2: 11 × 9 = 99

Example#1: 8 × 4 = ?

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Multiplication by 10, 100 & 1000…

• Use zeros to make up places, where necessary.
• If the answer is a whole number, the decimal point may be omitted.

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Example:

(i) 0.36 x 10 = 0.3 . 6 = 3.6 Or 03.6 3.6

(ii) 0.36 x 100 = 0.36.0 = 36 Or 36.0 36

(iii) 0.36 x 1000 = 0.360. = 360 Or 360.0 360

Division

• Division: Shares a number into equal parts.
• Multiplication is indicated by a times sign or the dimension sign ( ÷ or / ).

Example#1: 10 ÷ 2 = 5

Example#2: 100 ÷ 4 = 25

Example#3: 1000 ÷ 50 = ?

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Division by 10, 100 & 1000…

• Use zero to make up places, where necessary.
• Write a zero before the decimal point (for numbers less than one)

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Example:

1. 37.8 10 = 3 .7 . 8 = 3.78 Or 37.8 3.78
2. 37.8 / 100 = 0. 37 . 8 = 0.378 Or 37.8 0.378
3. 37.8 / 1000= 0. 037 . 8 = 0.0378 Or 37.8 0.0378

Other mathematical operations

1. Exponentiation (^ or **): Raises a number to a power.

Example: 2^3 = 81.

2. Root extraction (√): Finds the root of a number.

Example: √16 = 41.

3. Modulus (%): Finds the remainder of division.

Example: 17 % 5 = 21.

4. Floor (⌊) and Ceiling (⌈): Round numbers down or up to the nearest integer.

Example: ⌊3.7⌋ = 3, ⌈3.7⌉ = 41.

5. Absolute value (| |): Removes negative signs.

Example: |-4| = 4.

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• These operations form the foundation of arithmetic and are used extensively in various mathematical disciplines.
• Would you like to explore specific operations or practice problems?

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Advanced algebra

Algebra 2 is advanced algebra, which is practiced at the high school level. Advanced algebra will help you to go through the other parts of algebra such as:

• Equations with inequalities
• Matrices
• Solving system of linear equations
• Polynomial Equation
• Polynomials and expressions with radicals
• Sequences and series
• Rational expressions
• Trigonometry
• etc

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Abstract Algebra

• Abstract algebra deals with algebraic structures like the fields, groups, modules, rings, lattices, vector spaces, etc.

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Linear Algebra

• Linear algebra is a branch of algebra that deals with the study of planes and lines.
• The important topics covered in linear algebra such as;
• Linear equations
• Vector Spaces
• Relations
• Matrices and matrix decomposition
• Relations and Computations.

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Commutative algebra

• Commutative algebra is a branch of math that focuses on commutative rings, where multiplication works the same way as regular numbers like (a × b = b × a).
• Commutative algebra is useful in many areas of math, helping us study equations and shapes in algebraic geometry and other fields.

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SELF PRACTICE

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1. 0.68 X 10 =
2. 0.975 X 100 =
3. 3.7 X 1000 =
4. 68/10 =
5. 2.29/100 =
6. 51.4/1000 =
7. 5.62 X 10 =
8. 77 X 100 =
9. 825 X 1000 =

10. 916/10 =
11. 67.2/100 =
12. 387/1000 =
13. 0.2 X 100 =
14. 0.046 X 100 =
15. 0.0147 X 1000 =
16. 8.94/10 =
17. 0.707/100 =
18. 307/1000 =

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If you have any…!

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Questions…?

or

Confusion…?

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Good luck

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