How to add and subtract mixed fractions, step by step
Use improper fractions and a common denominator, then reduce and check the answer.
What to calculate
A mixed number contains a whole part and a fraction. Convert a b/c to (a × c + b)/c before operating. For addition or subtraction, find a common denominator, rewrite both numerators and combine them. Finally divide numerator by denominator to return to a mixed number if useful. You may simplify at intermediate steps, but keep the equivalence clear. A fraction calculator is helpful for checking, while the written method shows where a sign or denominator error occurred.
Worked example
Calculate 2 1/3 + 1 3/4. Convert to 7/3 + 7/4. The least common denominator is 12, so the expression becomes 28/12 + 21/12 = 49/12 = 4 1/12. For subtraction, 2 1/3 − 1 3/4 = 28/12 − 21/12 = 7/12. As a sense check, 2.33 plus 1.75 is slightly above four, while their difference is slightly above one half.
Common mistake
Do not add denominators: 1/3 + 1/4 is 7/12, not 2/7. Also check the order when subtracting; reversing the terms changes the sign. The least common denominator can simplify work, but any common multiple gives the same answer after reduction. If the fractions represent measurements, retain their units and round only after the exact fraction calculation.
How to use the result
Use the fraction calculator to compare the exact answer with a decimal and the percentage calculator only if a percent is genuinely needed. Ratios are another way to describe relationships but are not interchangeable with adding fractional quantities. Work one line at a time so that a mixed number, an improper fraction and the simplified result remain traceable.
Related tools and reading
For a different stepwise number pattern, read arithmetic sequence terms and sums.