Working with fractions, decimals and percentages together
A mixed operation has more than one step. We follow a clear order: do anything in brackets first, then × and ÷, and finally + and −, working from left to right.
Key idea
Order of work: Brackets → × ÷ → + −. Change fractions, decimals and percentages to the same form before adding or subtracting.
A worked calculation
Worked example
Find 0.2 + 0.3 × 2.
Do × first: 0.3 × 2 = 0.6.
Then add: 0.2 + 0.6 = 0.8.
So the answer is 0.8.
Now try ½ + ¼. Make the same denominator: ½ = 2/4, so 2/4 + 1/4 = ¾.
Changing forms
Remember that ½ = 0.5 = 50%, and ¼ = 0.25 = 25%. Changing to one form makes the sum easier and helps you avoid mistakes. For example, to add 50% + ¼, first write ¼ as 25%, then 50% + 25% = 75%. If you mix forms without changing them, you may add the wrong parts. Take your time and write each step neatly so it is easy to check.
Remember
- Multiply and divide before you add and subtract.
- Use the same form (all fractions or all decimals) before + or −.
- Always check: does the answer look sensible?