Add two fractions together.
Both fractions are put over a common denominator, then the numerators are added.
Sum: a/b + c/d = (a×d + c×b) ÷ (b×d)
A fraction addition calculator adds two fractions and returns the sum in lowest terms, with its decimal value. It shows the common denominator it used, how each fraction was rewritten, and the final reduction, so each line can be matched with the method taught in school.
Adding fractions is one of the first places where students discover that the rules for whole numbers do not carry over directly. It turns up in recipes that call for 3/8 of a cup and then another 5/12, in dividing work among people, and in measurements in inches. It also appears inside algebra, where adding rational expressions follows exactly the same logic with letters in place of numbers.
1. Write the fractions as a/b and c/d.
2. Choose a common denominator. The product b × d always works; the LCM of b and d gives the smallest one.
3. Rewrite each fraction over the common denominator by multiplying its top and bottom by the same number.
4. Add the numerators and keep the common denominator: a/b + c/d = (a × d + c × b) ÷ (b × d).
5. Reduce the result by dividing top and bottom by their HCF.
6. Convert an improper result to a mixed number if the question asks for it.
Multiplying the top and bottom of a fraction by the same non-zero number does not change its value, because you are multiplying by a form of 1. That lets you rewrite 3/8 as 36/96 and 5/12 as 40/96. Now both fractions count ninety-sixths, and the counts can be added: 36 + 40 = 76 ninety-sixths. Adding is only meaningful for pieces of the same size, just as you cannot add 3 metres and 5 feet until they share a unit.
When the denominators share a factor, as 8 and 12 share 4, the product b × d is larger than necessary. The LCM, 24, is the least common denominator. Using 24 gives 9/24 + 10/24 = 19/24 directly. Using 96 gives 76/96, which reduces by 4 to the same 19/24. The calculator uses the product and reduces at the end, which always reaches the same answer. By hand, the LCM keeps numbers smaller and reduces the risk of arithmetic slips.
To add mixed numbers such as 2 3/8 + 1 5/12, either add the whole parts and fraction parts separately and carry any whole number from the fraction sum, or convert both to improper fractions first. The second route is safer and is what you would enter here, as 19/8 + 17/12. For negative fractions, keep the sign in the numerator. Adding a negative fraction is the same as subtracting its positive, so the same formula handles both cases.
Sana's cake recipe needs 3/8 of a cup of sugar for the sponge and 5/12 of a cup for the frosting, and she wants the total before she measures.
Starting point: 3/8 + 5/12
Use a common denominator: 8 × 12 = 96
Rewrite both fractions: 36/96 + 40/96
Add the numerators: 36 + 40 = 76
Reduce to lowest terms: Divide both by their GCD of 4 → 19/24
Answer: Result 19/24
Adding tops and bottoms, as in 3/8 + 5/12 = 8/20.
Changing the denominator without changing the numerator by the same factor.
Stopping at 76/96 without reducing to lowest terms.
Adding the whole parts of mixed numbers but forgetting to carry when the fractions add up to more than 1.
Totalling recipe quantities measured in fractional cups.
Combining lengths in inches and fractions of an inch in carpentry and tailoring.
Adding fractional shares of work done by two people in time-and-work problems.
Class 6 and 7 fraction exercises and olympiad sums.
Why do I need a common denominator to add fractions?
The bottom number of a fraction shows how big each piece is. You cannot add halves and thirds directly, until both are changed to the same size of piece.