Adding and subtracting algebraic fractions

When adding and subtracting fractions, we must ensure that we have the same denominator.

For adding and subtracting fractions:

Step 1

Multiply the two terms on the bottom to get the same denominator.

Step 2

Multiply the top number on the first fraction by the bottom number of the second fraction to get the new top number of the first fraction.

Step 3

Multiply the top number on the second fraction by the bottom number of the first fraction to get the new top number of the second fraction.

Step 4

Now add/subtract the top numbers and keep the bottom number so that there is now one fraction.

Step 5

Simplify the fraction if required.

Example

Calculate \(\frac{2}{5} + \frac{3}{7}\)

\(=\frac{2\times 7}{35}+\frac{3\times 5}{35}\)

\(= \frac{{14}}{{35}} + \frac{{15}}{{35}} = \frac{{29}}{{35}}\)

Now try the example questions that follow.

Question

Calculate \(\frac{2}{3} - \frac{y}{{18}}\)

Question

\(\frac{x}{y} + \frac{y}{x}\)

Question

\(\frac{2}{x} - \frac{5}{{x + 2}}\)

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Applying the four operations to algebraic fractionsAdding and subtracting algebraic fractions