Calculate with signs, fractions, decimals and parentheses
Choose a suitable exact or decimal calculation · Apply parentheses and operation order · Check the sign and size of an answer
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Integer arithmetic
- Equivalent fractions
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Choose a suitable exact or decimal calculation
- Apply parentheses and operation order
- Check the sign and size of an answer
Order and signs
Calculate parentheses first, then powers, then multiplication/division from left to right, then addition/subtraction from left to right. Multiplication does not always come before division. Subtracting a negative adds its opposite; products or quotients of two negatives are positive.
For fractions, add with a common denominator, multiply numerators and denominators, and divide by multiplying by the non-zero divisor's reciprocal. A zero divisor is never allowed.
Choose and check
Keep fractions exact when they simplify cleanly. For decimals, align place values for addition and track decimal places in multiplication. Estimate before calculating: 19.8 × 0.51 should be close to 20 × 0.5 = 10, not 1000.
Sources for this lesson
Pause and explain
For 12 ÷ 3 × 2, which operation comes first?
Worked example
Calculate −3 + 2(5 − 8)² ÷ 3.
Show the worked solution
- The parentheses give −3, whose square is 9.
- Multiply/divide left to right: 2 × 9 ÷ 3 = 6.
- Add −3 to get 3.
Answer 3.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Calculate −7 − (−3) + 2².
Give me a hint
Treat the subtraction and power separately.
Compare my reasoning
- −7 − (−3) = −4.
- 2² = 4, so −4 + 4 = 0.
0.
Look for these in your work
- Use the opposite of −3
- Respect the power
Calculate 3/4 + 2/3 and (3/4) ÷ (2/3).
Give me a hint
Use twelfths for addition and a reciprocal for division.
Compare my reasoning
- 9/12 + 8/12 = 17/12.
- (3/4)(3/2) = 9/8.
17/12 and 9/8, respectively.
Look for these in your work
- Use a common denominator
- Invert only the divisor
Three notebooks cost 2.40 each; a 20 payment covers them. Find the change and give an estimate check.
Give me a hint
Calculate the total before subtracting.
Compare my reasoning
- 3 × 2.40 = 7.20.
- 20 − 7.20 = 12.80; a rough total of 3 × 2.50 = 7.50 suggests change around 12.50.
Change 12.80; the estimate supports its size.
Look for these in your work
- Keep currency units
- Check a reasonable magnitude
Common mistakes
- Do not square a negative without identifying the parentheses.
- Do not add fraction denominators.
What can you explain now?
For 12 ÷ 3 × 2, which operation comes first?
Compare with the explanation
Divide 12 by 3, then multiply by 2.
The operations have equal priority and are performed left to right.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
For 12 ÷ 3 × 2, which operation comes first?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.