### Some important things to know about fractions

• Fractions are 'related' if the denominator of one is a multiple of another. For example, the fractions $$\dfrac{1}{3} \text{and} \dfrac{5}{9}$$ have related denominators because 9 is a multiple of 3.
• When we add or subtract fractions we need to deal with fractions with the same denominator. Sometimes it is necessary to convert one or both of the fractions being added (or subtracted) to equivalent fractions with the same denominator.
• It is possible for two fractions to be equivalent even when the denominators are not obviously related and the equivalence is not immediately obvious. For example, $$\dfrac{17}{34} \text{and} \dfrac{5}{10}$$ are both equivalent fractions since they are both equal to $$\dfrac{1}{2}$$.