Adding and subtracting Fractions
Use the interactive below to represent two fractions with different denominators. Try setting one to be $\frac{1}{4}$14 and one to be $\frac{1}{5}$15. How can we add these together?
You might have noticed that adding or subtracting fractions uses our skills of finding Lowest Common Multiples, and Equivalent Fractions. You can apply those skills to add and subtract fractions without using the model.
Example
Evaluate: $\frac{3}{4}+\frac{2}{5}$34+25
Think: Find the LCM between $4$4 and $5$5 and find equivalent fractions. Then we will be able to add them, just like in the applet above.
Do: The LCM between $4$4 and $5$5 is $20$20.
| $\frac{3}{4}+\frac{2}{5}$34+25 | $=$= | $\frac{15}{20}+\frac{8}{20}$1520+820 |
| $=$= | $\frac{23}{20}$2320 |
Worked Examples
QUESTION 1
Evaluate $\frac{5}{9}-\frac{4}{9}$59−49.
Write your answer in its simplest form.
QUESTION 2
Evaluate $\frac{6}{35}+\frac{3}{7}-\frac{8}{7}$635+37−87.
Write your answer in its simplest form.
QUESTION 3
Evaluate $\frac{9}{10}-\frac{3}{7}$910−37.
Write your answer in its simplest form.
QUESTION 4
Evaluate $\frac{2}{3}+\frac{4}{5}-\frac{1}{2}$23+45−12.
Write your answer in the simplest form possible.