Addition and Subtraction Revision Notes for Grade 12 NSC Matric Mathematics

Addition and Subtraction

Understanding like terms

Like terms are algebraic terms that have exactly the same variable parts. This means they must contain the same variables raised to the same powers. Understanding this concept is essential for algebraic addition and subtraction.

For terms to be considered "like terms," they must have:

The same variables (such as x, y, or a)
The same exponents on those variables

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Understanding Like Terms Through Examples:

$3x$ and $5x$ are like terms (both contain x to the power of 1)
$2x²$ and $-7x²$ are like terms (both contain x to the power of 2)
$3x$ and $5y$ are not like terms (different variables)
$2x²$ and $4x$ are not like terms (different powers of x)

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Key rule: Only like terms can be combined through addition and subtraction. Unlike terms cannot be simplified further.

Combining like terms through addition and subtraction

When you add or subtract like terms, you combine their coefficients (the numerical parts) while keeping the variable part unchanged. This process is called collecting like terms or simplifying expressions.

The process works as follows:

Step 1: Identify like terms in the expression
Step 2: Add or subtract the coefficients of like terms
Step 3: Keep the variable part exactly the same

Let's examine some key examples:

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Worked Example: Simple Addition

$3x + 5x = 8x$

Here, both terms contain the same variable x, so we add the coefficients: $3 + 5 = 8$ .

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Worked Example: Addition with Negative Coefficients

$-3a + 10a = 7a$

The coefficients are $-3$ and $+10$ , which combine to give $7$ .

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Worked Example: Complex Polynomial Simplification

$4x² + 7x - 2x² - 3x$

Step 1: Group like terms together

$(4x² - 2x²) + (7x - 3x)$

Step 2: Simplify each group

$= 2x² + 4x$

Adding and subtracting algebraic fractions

When working with algebraic fractions, the same principles apply as with numerical fractions. You must find a common denominator before adding or subtracting.

The process for algebraic fractions involves:

Step 1: Find the lowest common denominator
Step 2: Rewrite each fraction with this common denominator
Step 3: Add or subtract the numerators
Step 4: Keep the common denominator unchanged

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Worked Example: Simple Fraction Addition

$\frac{5}{6} + \frac{7}{12}$

The common denominator is 12: $\frac{5}{6} = \frac{10}{12}$

Therefore: $\frac{10}{12} + \frac{7}{12} = \frac{17}{12}$

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Worked Example: Fractions with Variables

$\frac{2}{x} + \frac{3}{2x}$

The common denominator is $2x$ : $\frac{2}{x} = \frac{4}{2x}$

Therefore: $\frac{4}{2x} + \frac{3}{2x} = \frac{7}{2x}$

Worked examples from exam-style questions

Let's work through some typical exam questions step by step.

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Worked Example: Question 1

Simplify $7y + 3y - 5y$

Step 1: All terms contain the variable y, so they are like terms.

Step 2: Combine the coefficients: $7 + 3 - 5 = 5$

Answer: $5y$

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Worked Example: Question 2

Simplify $2x² + 4x - 3x² + 6$

Step 1: Group like terms: $(2x² - 3x²) + 4x + 6$

Step 2: Simplify: $-x² + 4x + 6$

Answer: $-x² + 4x + 6$

Common exam tips and traps

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Exam Tips:

Always check that terms are truly "like terms" before combining
Be careful with negative signs when subtracting
For fractions, ensure you find the correct common denominator
Show your working clearly by grouping like terms together

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Common Traps to Avoid:

Don't combine unlike terms (e.g., $x²$ and $x$ cannot be combined)
Don't forget to apply negative signs correctly
Don't change the variable part when combining coefficients
Don't rush the fraction addition process - always find the common denominator first

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Key Points to Remember:

Like terms have identical variable parts and can be combined through addition and subtraction
Only coefficients change when combining like terms - the variable part stays the same
Group like terms together to make simplification easier and reduce errors
Algebraic fractions follow the same rules as numerical fractions - find a common denominator first
Check your work by ensuring unlike terms haven't been incorrectly combined

Addition and Subtraction (Grade 12 NSC Matric Mathematics): Revision Notes