Adding Fractions Calculator
Calculate adding fractions instantly with our math tool. Shows detailed work, formulas used, and multiple solution methods.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
a/b + c/d = (ad + bc) / bd
To add fractions, find a common denominator (bd or LCD), multiply each numerator by the other denominator, add the results, and simplify. For mixed numbers, first convert to improper fractions. The LCD method uses the Least Common Multiple of denominators for smaller numbers.
Worked Examples
Example 1: Adding Fractions with Different Denominators
Problem:Calculate 3/4 + 2/5
Solution:Step 1: Find LCD of 4 and 5\nLCD = LCM(4, 5) = 20\n\nStep 2: Convert to common denominator\n3/4 = (3 x 5)/(4 x 5) = 15/20\n2/5 = (2 x 4)/(5 x 4) = 8/20\n\nStep 3: Add numerators\n15/20 + 8/20 = 23/20\n\nStep 4: Convert to mixed number\n23/20 = 1 3/20\n\nDecimal: 1.15
Result:3/4 + 2/5 = 23/20 = 1 3/20 = 1.15
Example 2: Adding Mixed Numbers
Problem:Calculate 2 1/3 + 1 5/6
Solution:Step 1: Convert to improper fractions\n2 1/3 = (2 x 3 + 1)/3 = 7/3\n1 5/6 = (1 x 6 + 5)/6 = 11/6\n\nStep 2: Find LCD of 3 and 6\nLCD = 6\n\nStep 3: Convert and add\n7/3 = 14/6\n14/6 + 11/6 = 25/6\n\nStep 4: Convert to mixed number\n25/6 = 4 1/6\n\nDecimal: 4.1667
Result:2 1/3 + 1 5/6 = 25/6 = 4 1/6
Frequently Asked Questions
How do you add fractions with different denominators?
To add fractions with different denominators, you must first find a common denominator, which is a number that both denominators divide into evenly. The most efficient choice is the Least Common Denominator (LCD), found by calculating the Least Common Multiple (LCM) of the two denominators. Once you have the LCD, multiply each fraction numerator and denominator by the factor needed to reach the LCD. Then simply add the numerators while keeping the common denominator. Finally, simplify the result by dividing both numerator and denominator by their Greatest Common Divisor (GCD). For example, to add 2/3 + 3/4: LCD = 12, so 8/12 + 9/12 = 17/12.
How do you add fractions with the same denominator?
Adding fractions with the same denominator is straightforward: simply add the numerators together and keep the denominator unchanged. For example, 3/8 + 2/8 = 5/8. The reason this works is that the denominator tells you the size of each piece, and when pieces are the same size, you just count how many you have in total. After adding, check whether the result can be simplified by finding the GCD of the numerator and denominator. If the numerator is larger than the denominator, the result is an improper fraction that can be converted to a mixed number. For instance, 5/4 + 3/4 = 8/4 = 2 (a whole number).
How do you add mixed numbers (fractions with whole parts)?
To add mixed numbers, you have two approaches. The first method converts each mixed number to an improper fraction, then adds using the standard LCD method, and converts back. For example, 2 1/3 + 1 3/4: convert to 7/3 + 7/4, LCD = 12, so 28/12 + 21/12 = 49/12 = 4 1/12. The second method adds whole numbers and fractions separately: 2 + 1 = 3 for the wholes, and 1/3 + 3/4 = 4/12 + 9/12 = 13/12 = 1 1/12, then combine 3 + 1 1/12 = 4 1/12. Both methods yield the same answer, but the first is more systematic and less error-prone for complex problems.
How do you simplify a fraction after adding?
Simplifying (or reducing) a fraction means dividing both the numerator and denominator by their Greatest Common Divisor (GCD) to get the smallest equivalent fraction. To find the GCD, you can use the Euclidean algorithm: repeatedly divide the larger number by the smaller and take the remainder until you reach zero. The last non-zero remainder is the GCD. For example, to simplify 12/18: GCD(12,18) = 6, so 12/18 = 2/3. If the numerator is larger than the denominator, first convert to a mixed number by dividing the numerator by the denominator, with the quotient as the whole part and remainder as the new numerator. Always simplify as a final step to present answers in standard mathematical form.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy