Unit 4: Adding & Subtracting Common Fractions
Topic B: Subtracting Common Fractions
Good News!
There is only one new thing to learn in this topic. Everything else uses skills and knowledge you already have.
Let’s look at subtraction:
Example A
The shaded part [latex]\left(\dfrac{4}{5}\right)[/latex] is the amount that you are starting with.
Now cross out (pretend you are taking away) 3 shaded parts [latex]\left(\dfrac{3}{5}\right)[/latex].
Example B
Draw a pizza.
- Slice it into 8 equal pieces.
- Draw pieces of pineapple on 5 pieces.
- What fraction of the pizza has pineapple? [latex]\dfrac{5}{8}[/latex]
- Cross out 2 pineapple pieces to show they have been eaten.
- How much of the pineapple pizza is left?
- [latex]\begin{array}{rrl}&\dfrac{5}{8}&\text{(amount you started with)}\\-&\dfrac{2}{8}&\text{(amount eaten, "taken away")}\\ \hline&\dfrac{3}{8}&\text {of the pizza is left with pineapple on it}\end{array}[/latex]
Common fractions must have the same denominator when you subtract one from the other. Subtract the numerators and keep the same denominators.
Exercise 1
Subtract to find the difference.
TIP: Express the difference in lowest terms.
- [latex]\begin{array}{rr}&\dfrac{3}{5}\\-&\dfrac{1}{5}\\\hline&\dfrac{2}{5}\end{array}[/latex]
- [latex]\begin{array}{rrrr}&\dfrac{7}{8} &&\\-&\dfrac{3}{8}&&\\ \hline &\dfrac{4}{8}&=&\dfrac{1}{2}\\ \end{array}[/latex]
- [latex]\begin{array}{rr}&\dfrac{2}{3}\\-&\dfrac{1}{3}\\ \hline&\end{array}[/latex]
- [latex]\begin{array}{rr}&\dfrac{5}{9}\\-&\dfrac{2}{9}\\ \hline&\end{array}[/latex]
- [latex]\begin{array}{rr}&\dfrac{6}{7}\\-&\dfrac{1}{7}\\ \hline&\end{array}[/latex]
- [latex]\begin{array}{rr}&\dfrac{3}{4}\\-&\dfrac{1}{4}\\ \hline&\end{array}[/latex]
- [latex]\begin{array}{rr}&\dfrac{3}{2}\\-&\dfrac{1}{2}\\ \hline&\end{array}[/latex]
Answers to Exercise 1
- [latex]\dfrac{1}{3}[/latex]
- [latex]\dfrac{1}{3}[/latex]
- [latex]\dfrac{5}{7}[/latex]
- [latex]\dfrac{1}{2}[/latex]
- [latex]\dfrac{2}{2}[/latex] = 1
You know how to find the least common denominator (LCD) and to rewrite fractions in an equivalent form using the LCD.
You must use those skills when you wish to subtract fractions with different denominators.
Example C
[latex]\dfrac{4}{5}-\dfrac{3}{10} =[/latex]
Denominators are 5 and 10. The least common multiple is 10, so the least common denominator is 10.
[latex]\begin{array}{rrrr}&\dfrac{4}{5}\left(\dfrac{×2}{×2}\right) =&\dfrac{8}{10}&&\text{Write equivalent fractions using the LCD}\\ -&\dfrac{3}{10}=&\dfrac{3}{10} &&\text{Subtract the numerators}\\ \hline&=&\dfrac{5}{10}\left(\dfrac{÷5}{÷5}\right)&=\dfrac{1}{2}&\text{Simplify the answer.}\end{array}[/latex]
Exercise 2
Subtract and simplify the answers.
- [latex]\begin{array}{rr}&\dfrac{5}{6}\\-&\dfrac{2}{3}\\ \hline&\dfrac{1}{6}\end{array}[/latex]
- [latex]\begin{array}{rr}&\dfrac{5}{6}\\-&\dfrac{2}{3}\\ \hline&\dfrac{1}{6}\end{array}[/latex]
- [latex]\begin{array}{rr}&\dfrac{1}{4}\\-&\dfrac{1}{12}\\ \hline&\end{array}[/latex]
- [latex]\begin{a