The language of algebra
Objective. Use variables, terms, coefficients and constants correctly.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Algebra uses letters called variables to stand for numbers that can change or are currently unknown. A term is a single number, variable, or product of numbers and variables, such as 5x or 3. A coefficient is the number multiplying a variable, so in 7y the coefficient is 7, while a constant is a term with no variable attached, like the 4 in x+4. An expression such as 3x+2y−5 combines several terms using addition or subtraction, without an equals sign, unlike an equation.
Worked example
In the expression 6x + 3y − 7, identify the coefficients and the constant term.
- 1Find the term attached to x: 6x, so the coefficient of x is 6.
- 2Find the term attached to y: 3y, so the coefficient of y is 3.
- 3Find the term with no variable: −7.
- 4This −7 is the constant term.
Answer: Coefficients 6 and 3; constant term −7
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Start practisingCommon mistake. Pupils often confuse a coefficient with a constant, thinking the 4 in 4x is a separate number term rather than part of the term 4x. Point out that a coefficient always sits attached to a variable.
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