Resources for Adding and Subtracting Fractions
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Adding and Subtracting Fractions Theory
![When adding or subtracting fractions, if the denominators are the same, then the numerators are added or subtracted. If the denominators are different then the lowest common denominator has to be determined.\\ \textbf{Example 1}\\[3pt] Simplify the following.\\ \textbf{i)} \(\dfrac{3}{7}+\dfrac{2}{7}\)\\ \textbf{ii)} \(\dfrac{3}{7}-\dfrac{1}{3}\)\\ \textbf{iii)} \(\dfrac{3}{7}+\dfrac{5}{14}\)\\ \textbf{Example 1 solution}\\ \textbf{i)} \(\begin{aligned}[t] \frac{3}{7}+\frac{2}{7} & =\frac{3+2}{7} \\ & =\frac{5}{7} \end{aligned}\)\\[3pt] \textbf{ii)} \(\begin{aligned}[t] \frac{3}{7}-\frac{1}{3} & =\frac{3}{3} \times \frac{3}{7}-\frac{7}{7} \times \frac{1}{3} \\ & =\frac{9}{21}-\frac{7}{21} \\ & =\frac{9-7}{21} \\ & =\frac{2}{21} \end{aligned}\)\\[3pt] \textbf{iii)} \(\begin{aligned}[t] \frac{3}{7}+\frac{5}{14} & =\frac{2}{2} \times \frac{3}{7}+\frac{5}{14} \\ & =\frac{6}{14}+\frac{5}{14} \\ & =\frac{11}{14} \end{aligned}\) \columnbreak When adding on subtracting mixed fractions, the whole numbers are added or subtracted and then the fractions are added or subtracted.\\ \textbf{Example 2}\\ Simplify the following:\\ \textbf{i)} \(2 \dfrac{1}{4}+3 \dfrac{1}{3}\)\hfill \textbf{ii)} \(3 \dfrac{1}{5}-2 \dfrac{1}{7}\)\hfill \textbf{iii)} \(3 \dfrac{1}{7}-2 \dfrac{1}{5}\)\\ \textbf{Example 2 solution}\\[3pt] \textbf{i)} \(\begin{aligned}[t] 2 \frac{1}{4}+3 \frac{1}{3} & =(2+3)+\frac{1}{4}+\frac{1}{3} \\ & =5+\frac{3}{3} \times \frac{1}{4}+\frac{4}{4} \times \frac{1}{3} \\ & =5+\frac{3}{12}+\frac{4}{12}=5 \frac{7}{12} \end{aligned}\)\\[3pt] \textbf{ii)} \(\begin{aligned}[t] 3 \frac{1}{5}-2 \frac{1}{7} & =(3-2)+\frac{1}{5}-\frac{1}{7} \\ & =1+\frac{7}{7} \times \frac{1}{5}-\frac{5}{5} \times \frac{1}{7} \\ & =1+\frac{7}{35}-\frac{5}{35}=1 \frac{2}{35} \end{aligned}\)\\[3pt] \textbf{iii)} \(\begin{aligned}[t] 3 \frac{1}{7}-2 \frac{1}{5} & =(2-2)+1\frac{1}{7}-\frac{1}{5} \\ & =\frac{7}{7}+\frac{1}{7}-\frac{1}{5} \\ & =\frac{8}{7}-\frac{1}{5} \\ & =\frac{5}{5} \times \frac{8}{7}-\frac{7}{7} \times \frac{1}{5} \\ & =\frac{40}{35}-\frac{7}{35}=\frac{33}{35} \end{aligned}\) \end{multicols}](/media/k45ofyd2/7928.png)
NSW Y8 Maths Fractions and Percentages Adding and Subtracting Fractions
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