A reliable method
For fractions, use a common denominator before adding. For standard form, place one nonzero digit before the decimal point. Find common factors or multiples only after identifying which is required.
The common trap
Adding denominators gives the wrong fraction sum. The highest common factor cannot exceed the smaller positive number.
Make the connection
Use prime factors to check a highest common factor and a lowest common multiple independently. Exact answers are especially useful on the non-calculator paper.
Common denominators versus common factors
To add 2/3 and 1/4, rewrite them as 8/12 and 3/12, giving 11/12. Adding numerators and denominators directly would give 3/7, which is even smaller than 2/3; that size check exposes the error. For the integers 12 and 18, the HCF is 6 but the LCM is 36. The first divides both numbers; the second is divisible by both. Using precise language prevents a correct factor calculation from answering a multiple question. Standard form is a separate representation skill: 36000=3.6×10⁴, with a coefficient between one and ten.
Transfer, explain and check
Find 5/6−1/4 and check its sign and size. Answer: 7/12. Then identify HCF(8,12)=4 and LCM(8,12)=24, explaining why the two operations cannot be exchanged.
Without a calculator, evaluate 3/6 + 4/3.
- Use denominator 6 for both terms.
- The numerator becomes 3+2(4)=11.
- Reduce the fraction if possible.
Compare the other answer choices
Add numerators and denominators directly.
Change the second denominator without scaling its numerator.
Multiply the fractions instead of adding them.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
Cambridge IGCSE Mathematics 0580