\displaystyle \dfrac{1}{3}	\displaystyle =	\displaystyle \dfrac{1 \times 2}{3 \times 2}	Multiply the numerator and denominator by 2
	\displaystyle =	\displaystyle \dfrac{2}{6}

Idea summary

Equivalent fractions look different but have the same value.

You need to multiply or divide both the numerator and the denominator of a fraction by the same number to work out the equivalent fraction.

Add and subtract fractions with different denominators

This video shows how to add and subtract fractions by finding common denominators.

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Find the value of \,\dfrac{3}{5}+\dfrac{3}{4}.

Worked Solution

Create a strategy

We need to find the smallest common multiple of the denominators.

Apply the idea

The smallest common multiple of 5 and 4 is 20 since 5\times 4 =20. So the least common denominator of the two fractions is 20.

We need to multiply both the numerator and denominator of \dfrac{3}{5} by 4 to get a denominator of 20.

\displaystyle \dfrac{3}{5}	\displaystyle =	\displaystyle \dfrac{3\times 4}{5\times 4}	Multiply numerator and denominator by 4
	\displaystyle =	\displaystyle \dfrac{12}{20}

We need to multiply both the numerator and denominator of \dfrac{3}{4} by 5 to get a denominator of 20.

\displaystyle \dfrac{3}{4}	\displaystyle =	\displaystyle \dfrac{3\times 5}{4\times 5}	Multiply numerator and denominator by 5
	\displaystyle =	\displaystyle \dfrac{15}{20}

Now we can use these equivalent fractions in the addition.

Idea summary

Before we add or subtract fractions, we must first make sure that the fractions have the same denominator.

5.10 Add and subtract fractions