Arithmetic and General Math Calculators

How the arithmetic calculators work

Each calculator keeps numbers exact for as long as possible. Fractions stay as fractions, a repeating decimal is never rounded in the middle of a calculation, and the final answer is reduced to lowest terms. When a decimal is useful, for example in a percentage problem about prices, it is shown next to the exact value rather than instead of it.

Every result comes with the method a teacher would expect to see: the common denominator and the equivalent fractions, the prime factorization behind a greatest common factor, or the equation that turns a percentage question into a single multiplication. Before an answer is displayed, it is checked by an independent calculation, so a step that looks right but leads to a wrong result is caught.

Where these skills are used

Fractions and percentages appear long after primary school. Adding rational expressions in algebra uses the same least common denominator as adding $\frac{1}{4} + \frac{1}{6}$, and probability answers are usually fractions. Percent change is the language of discounts, interest rates, test scores and population growth, and the greatest common factor is the first step whenever an algebraic expression is factored.

If you are revising, try a problem by hand first, then enter it and compare each line of your working with the solution. The difference usually points to the exact rule that needs another look.

Mental estimates are the best check on any arithmetic answer. Before you calculate $\frac{3}{4} + \frac{5}{6}$, notice that both fractions are a little less than $1$, so the sum must be a little less than $2$; an answer of $\frac{8}{10}$ is then clearly wrong, because it is smaller than either fraction on its own.