\displaystyle \dfrac{6x}{2}-\dfrac{7x}{2}	\displaystyle =	\displaystyle \frac{6x-7x}{2}	Subtract the numerators
	\displaystyle =	\displaystyle -\dfrac{x}{2}	Evaluate the subtraction

Example 2

Simplify the following: \dfrac{3x}{5}-\dfrac{x}{7}

Worked Solution

Create a strategy

Find a common denominator to add the fractions.

Apply the idea

5\times 7=35 so 35 is a common multiple of the denominators. So we need to multiply the numerator and denominator of each fraction by the other denominator.

\displaystyle \dfrac{3x}{5}-\dfrac{x}{7}	\displaystyle =	\displaystyle \frac{3x \times 7}{5 \times 7} - \frac{x \times 5}{7 \times 5}	Multiply fractions by the other denominator
	\displaystyle =	\displaystyle \frac{21x}{35}-\frac{5x}{35}	Evaluate the second fraction
	\displaystyle =	\displaystyle \frac{21x-5x}{35}	Subtract the numerators
	\displaystyle =	\displaystyle \frac{16x}{35}	Evaluate the subtraction

Example 3

Simplify the following: \dfrac{-3x-1}{6}+\dfrac{x+6}{6}

Worked Solution

Create a strategy

We can write the numerators together as a single expression over the common denominator.

Apply the idea

\displaystyle \dfrac{-3x-1}{6}+\dfrac{x+6}{6}	\displaystyle =	\displaystyle \dfrac{(-3x-1) + (x+6)}{6}	Add the numerators
	\displaystyle =	\displaystyle \dfrac{-3x+x-1+6}{6}	Collect like terms
	\displaystyle =	\displaystyle \dfrac{-2x+5}{6}	Subtract the numerator
	\displaystyle =	\displaystyle -\dfrac{2x+5}{6}	Simplify

Idea summary

The most important things to remember when adding and subtracting fractions:

We need like denominators.
We need to keep our fractions equivalent.

Outcomes

VCMNA331

Apply the four operations to simple algebraic fractions with numerical denominators.

1.01 Adding and subtracting algebraic fractions

Ideas

Addition and subtraction of algebraic fractions

Examples

Example 1

Example 2

Example 3

Outcomes

VCMNA331

What is Mathspace

About Mathspace