Fraction calculator with steps

• Fractions: 3/4
• Mixed numbers: 1 1/2 (whole number, space, fraction)
• Negative numbers: -2/3
• Whole numbers and decimals: 5 or 0.25

The calculator uses the lowest common denominator (the LCM of the denominators), which keeps numbers small.

Convert mixed numbers to improper fractions first: $2\tfrac{1}{3} = \tfrac{7}{3}$ (multiply the whole number by the denominator and add the numerator). Do the calculation, then convert back if the question wants a mixed number. Adding the whole numbers and fractions separately works for addition, but it's easy to go wrong with subtraction and doesn't work for multiplication or division.

• Adding the bottoms: $\tfrac{1}{3} + \tfrac{1}{4} \neq \tfrac{2}{7}$. The pieces must be the same size first.
• Flipping the wrong fraction when dividing: only the second fraction (the divisor) is flipped.
• Forgetting to simplify: divide top and bottom by their HCF.

See also: how to divide fractions, how to multiply fractions and how to simplify fractions.

Fraction questions often hide inside wording:

• "Of means multiply": $\tfrac{3}{5}$ of 40 is $\tfrac{3}{5} \times 40 = 24$.
• "How many … in …" means divide: how many $\tfrac{1}{4}$-litre cups in $2\tfrac{1}{2}$ litres? $2\tfrac{1}{2} \div \tfrac{1}{4} = 10$.
• Fraction of a fraction: $\tfrac{2}{3}$ of the class are girls and $\tfrac{1}{4}$ of the girls wear glasses, so $\tfrac{2}{3} \times \tfrac{1}{4} = \tfrac{1}{6}$ of the class are girls with glasses.

In non-calculator papers, show each step: common denominators, multiplying out and simplifying usually earn method marks even if the final answer slips.