A reliable method
Write fractions with a shared denominator before addition. In a calculation with several operations, evaluate grouping and powers before multiplication, division, addition, and subtraction. Keep intermediate values exact.
The common trap
Adding denominators changes the size of the pieces. For example, one third plus one third is two thirds, because the pieces are still thirds.
Check and transfer
A rough estimate should agree with the sign and size of an exact result. Use that estimate to catch a misplaced sign or decimal before accepting an answer.
Worked comparison: why the alternative fails
Compare 1/3 + 1/6 with (1 + 1)/(3 + 6). The first is 3/6 = 1/2; the second is 2/9 and changes the size of the pieces. Rewriting in sixths preserves the original lengths.
Transfer and explain
Try 3/4 + 1/8 before revealing the result: 7/8. Explain why the denominator is not 12.
A repair uses 2/6 meter of wire and another 3/4 meter. What total length, in meters, is used?
- Both measurements use meters, so add the fractions.
- Use twelfths: 4/12 + 9/12.
- The requested value is 13/12. Check its units and meaning against the original question.
Compare the other answer choices
Add numerators and denominators separately instead of using equal-sized parts.
Count only the first length of wire.
Multiply the lengths 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.
GED Mathematical Reasoning overviewSiyavula Grade 10 mathematics foundation reference