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| 5.1 |
Variables and Algebraic Expression |
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| Variable: |
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| Definition |
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A quantity whose value is unknown and not fixed, which can represent any value.
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- Letters can be used to represent variables.
- A variable has a fixed value if the represented quantity is always constant at any time.
- A variable has a varied value if the represented quantity changes over time.
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| Example |
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The travelling time taken by Sofea from her house to the school every day.
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\(k\) represents the travelling time taken by Sofea from her house to the school every day.
\(k\) has a varied value because the travelling time of Sofea changes every day.
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| Algebraic expression: |
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| Definition |
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An expression that combines a number, variable or other mathematical entity with an operation.
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- Examples: \(k,\, y+2,\, \dfrac{z}{3},\, 12rst\)
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| Determine the values of algebraic expressions: |
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- The value of an algebraic expression can be determined by substituting the variables with the given values.
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| Example |
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Given that \(x = 3 \) and \(y = 2\).
Calculate the value of \(8x – 5y + 7\).
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\(\begin{aligned} &\space8x – 5y + 7 \\\\&= 8(3) – 5(2) + 7 \\\\&=24-10+7 \\\\&=21. \end{aligned}\)
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| The terms and the coefficients in an expression: |
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- Term is every quantity in an expression involving a \(+\) or \(-\) sign.
- In an algebraic expression, a number is also considered as a term.
- Algebraic term is a term that contains one variable.
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| Example |
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State the terms in \(2pq-7y-3\).
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Algebraic terms: \(2pq,\,7y\) and \(3\)
\(2pq\) is the product of the number \(2\) and the variables \(p\) and \(q\).
Meanwhile, \(7y\) is the product of the number \(7\) and the variable \(y\).
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- The algebraic term that consists of one variable with the power \(1\) is called a linear algebraic term.
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- Coefficient is the factors in a product.
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| Examples |
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In the term \( –8xy^2\), state the coefficient of:
(i) \(-x\)
(ii) \(xy^2\)
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(i)
\(-8xy^2=8y^2\times(-x) \)
The coefficient of \(-x\) is \(8y^2\).
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(ii)
\(-8xy^2=(-8)\times xy^2 \)
The coefficient of \(xy^2\) is \(-8\).
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| Like terms: |
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| Definition |
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Contain the same variables with the same power.
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- Example: \(4k\) and \(\dfrac{1}{12}k\)
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| Unlike terms: |
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| Definition |
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Contain different variables or the same variables with different powers.
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| Examples |
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(i) \(2x\) and \(9m\)
Variables \(x\) and \(m\) are different.
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(ii) \(x\) and \(6x^2\)
The powers of the variable \(x\) are different.
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