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Coefficients as Fractions

Coefficients as Fractions

The number at the start of a term - for example, the number 3 at the start of `3x`, is known as a coefficient. The coefficient of `5x^3` is 5. But the coefficient need not necessarily be an integer; it may be a fraction or a decimal.

Example 1

Simplify `frac(1)(2)``a` + `frac(1)(3)``a`

`frac(1)(2)``a + ``frac(1)(3)``a`

Because the terms are the same (`a`), the terms can be added together

`= ``frac(3)(6)``a + ``frac(2)(6)``a`

`= ``frac(5)(6)``a`

Answer: `frac(5)(6)``a`

Example 2

Multiply `frac(1)(2)``b` and `4b`

`frac(1)(2)`` xx 4 xx b xx b = 2b^2`

Answer: `2b^2`

See also Adding and Subtracting Fractions and Multiplying Fractions