Worked Examples

Don't start over from scratch — instead, walk back through your own scratch work one step at a time and compare it against the same step in the example. The first line where the two disagree is almost always where the actual mistake happened, even if the wrong answer only became obvious several lines later. Working backward from the answer this way finds the error far faster than redoing the whole problem.

Predicting first is the more useful habit, even though reading straight through feels faster. Cover everything below the problem statement, decide what the very next line of working should be, then reveal just that step and check yourself. It takes longer per example, but it tells you honestly whether you understand the method or have only recognized the numbers.

As a rough guide, once you can predict every step of an example correctly before revealing it, you're ready to try a similar problem unaided. That might happen after one example for an operation you already know reasonably well, or after several for one that still feels unfamiliar — the point where prediction stops being a guess is the real signal, not a fixed count.

After. Solving a problem by hand first — even slowly, even with mistakes — is what builds the skill; using the calculator afterward is what confirms whether it worked. Reaching for the calculator before attempting a step yourself turns it into an answer key instead of a checking tool, which teaches far less.

They cover one representative case for each of the four operations plus a plain conversion, which is enough to recognize the general method each time. They can't cover every specific combination of numbers you'll encounter, though — that's exactly what the calculator above is for: type in your own numbers and get the same style of step-by-step working for that specific problem.

Start with the operation symbol or word in the problem — plus, minus, times, or divided by — since that alone points to one of the four operation examples below. Then check whether the denominators already match (no extra step needed), differ (a common denominator comes first), or whether the problem is already a single improper fraction with no operation at all (the conversion example).