Fractions and Exact Arithmetic
Carry out combined fraction operations accurately and give a fully simplified exact result.
How to study National 5 Mathematics
Secure one operational skill at a time, connect it to neighbouring techniques, then apply it in unfamiliar contexts with complete working and a checked conclusion.
Core concepts
Concept 1
Addition and subtraction require a common denominator; multiplication and division use factor cancellation and reciprocals.
Exam cue: Convert mixed numbers and copy operation signs before calculating.
Concept 2
Mixed numbers should normally be converted to improper fractions before multiplication, division or combined operations.
Exam cue: Use the least practical common denominator for addition or subtraction.
Concept 3
Order of operations and exact simplification matter in both calculator and non-calculator work.
Exam cue: Cancel common factors and simplify the final numerator and denominator.
Risk pitfalls and guardrails
Adding denominators.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Taking the reciprocal of the wrong fraction in division.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Converting an exact fraction to a rounded decimal unnecessarily.
Guardrail: Keep sufficient accuracy through intermediate work and round only the final requested result.
Memory anchors
Add fractions
Use a common denominator, then combine the numerators.
Subtract fractions
Use a common denominator and protect the subtraction sign.
Multiply fractions
Multiply numerators and denominators, cancelling factors where possible.
Divide fractions
Multiply by the reciprocal of the divisor.
Mixed number
Convert to an improper fraction before combined work.
Exact finish
Reduce the final fraction fully unless another form is required.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Calculate 3/4 + 5/6, giving the answer as a fully simplified fraction.
Calculate 7/8 − 5/12.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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