Add, subtract, multiply or divide fractions with a simplified exact answer, decimal check and clear worked steps for Singapore learners.
Choose an example or type the known values, then calculate to see the answer and working.
Fractions describe equal parts of a whole, a measure or a ratio between quantities. This calculator keeps the answer exact, reduces it fully and shows the rule used for the selected operation. Enter signed whole-number numerators and non-zero denominators, then compare the first displayed transformation with your own paper method. The decimal is included as a reasonableness check, not as a replacement for the exact fraction.
Use this page when both quantities are written as fractions and the question asks for one arithmetic operation. It is especially useful for checking unlike denominators, cancellation before multiplication and the reciprocal used in division. Do not use it to decide which operation a word problem requires. First label what each fraction represents and check that the parts refer to compatible wholes.
The denominator tells how many equal parts form one whole. Thirds and fourths are different-sized parts, so they cannot be added directly. A common denominator renames both fractions using the same part size without changing their values.
Dividing a numerator and denominator by the same non-zero factor creates an equivalent fraction. Cancelling before multiplication keeps the numbers smaller; reducing after an operation confirms that the final numerator and denominator share no factor greater than one.
Dividing by a fraction is equivalent to multiplying by its reciprocal because the reciprocal converts the divisor into one. Check the direction carefully: 3/4 divided by 1/2 asks how many half-sized groups fit inside three quarters.
The denominators 3 and 4 are unlike, so twelfths provide a common part size.
Estimate the sign, scale, range or likely form of the answer before calculating. A prediction makes an input error easier to notice.
Rename 1/3 as 4/12 by multiplying its numerator and denominator by 4.
Rename 1/4 as 3/12 by multiplying its numerator and denominator by 3.
Add the numerators while keeping the common denominator: 4/12 + 3/12 = 7/12.
Check the size: 1/3 is about 0.33 and 1/4 is 0.25, so a result near 0.58 is sensible.
| Mistake | Why it fails | Better check |
|---|---|---|
| Adding denominators | Writing 1/3 + 1/4 as 2/7 combines unlike part sizes and changes the meaning. | Rename both fractions with one common denominator before adding numerators. |
| Using the wrong reciprocal | In fraction division, reversing the first fraction answers a different calculation. | Keep the first fraction and invert only the divisor, then multiply. |
| Converting to decimals too early | Rounded decimals can lose an exact relationship and introduce accumulated error. | Keep the fraction exact until the question specifically requires a decimal. |
The engine accepts a negative denominator, although standard form normally moves the sign to the numerator. A denominator of zero is never allowed because division by zero is undefined.
Convert each mixed number to an improper fraction first. That conversion makes the complete quantity explicit and lets the same four operation rules apply consistently.
Estimate with benchmarks such as one half or one whole, convert the final fraction to a decimal, and use the inverse operation where practical.
The result points to related practice, but the best next step depends on what the learner could explain without help.