How do you add fractions with different denominators?

To add fractions with different denominators: 1) Find the least common denominator (LCD). 2) Convert each fraction to an equivalent fraction with the LCD. 3) Add the numerators. 4) Simplify if possible. Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.

How do you multiply fractions?

To multiply fractions, multiply the numerators together and multiply the denominators together: (a/b) x (c/d) = (a*c)/(b*d). Then simplify the result. Example: 2/3 x 3/4 = 6/12 = 1/2.

Fraction Calculator

Add, subtract, multiply, and divide fractions with step-by-step solutions.

Result

Step-by-Step Solution

How to Calculate Fractions

This calculator handles all four basic fraction operations and shows detailed step-by-step solutions so you can learn the process.

Adding and Subtracting Fractions

To add or subtract fractions, you need a common denominator. Find the least common denominator (LCD) of both fractions, convert each fraction to an equivalent fraction with that denominator, then add or subtract the numerators.

Example: 1/3 + 1/4. The LCD of 3 and 4 is 12. So 1/3 = 4/12 and 1/4 = 3/12. Therefore 4/12 + 3/12 = 7/12.

Multiplying Fractions

Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together, then simplify. (a/b) × (c/d) = (ac)/(bd). Example: 2/3 × 3/4 = 6/12 = 1/2.

Dividing Fractions

To divide fractions, multiply by the reciprocal (flip the second fraction): (a/b) ÷ (c/d) = (a/b) × (d/c). Example: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3 = 2 2/3.

Simplifying Fractions

To simplify (or reduce) a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For example, 12/18: GCD(12, 18) = 6, so 12/18 = 2/3.

Converting Between Fractions and Decimals

To convert a fraction to a decimal, divide the numerator by the denominator: 3/4 = 0.75. To convert a decimal to a fraction, express the decimal as a fraction over a power of 10 and simplify: 0.625 = 625/1000 = 5/8.

Frequently Asked Questions

Find the least common denominator (LCD), convert each fraction, add the numerators, and simplify. Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.

Multiply numerators together and denominators together: (a/b) x (c/d) = (ac)/(bd). Then simplify. Example: 2/3 x 3/4 = 6/12 = 1/2.

Multiply by the reciprocal of the second fraction: (a/b) / (c/d) = (a/b) x (d/c). Example: 2/3 / 1/4 = 2/3 x 4/1 = 8/3 = 2 2/3.

Divide both numerator and denominator by their greatest common divisor (GCD). Example: 12/18 — GCD is 6, so 12/18 = 2/3.

A mixed number combines a whole number and a fraction, like 2 1/3. It represents an improper fraction (where the numerator is larger than the denominator). 2 1/3 = 7/3.