Fraction Calculator

To add fractions with different denominators, first find the least common denominator, then rename both fractions with that denominator. For example, 1/3 + 1/4 uses LCD 12. Rename 1/3 as 4/12 and 1/4 as 3/12, then add the numerators: 4/12 + 3/12 = 7/12. The denominator stays 12 because the pieces are now the same size. Finally, check the GCF of 7 and 12. Since it is 1, the answer is already in lowest terms.

Subtracting fractions follows the same denominator rule as addition. If the denominators are different, find the LCD, rename both fractions, subtract the numerators, and simplify. For example, 5/6 - 1/4 uses LCD 12. Rename 5/6 as 10/12 and 1/4 as 3/12. Then subtract: 10/12 - 3/12 = 7/12. With mixed numbers, check whether the top fraction is large enough before subtracting. If it is not, borrow 1 from the whole number.

To multiply fractions, multiply numerator by numerator and denominator by denominator. A common denominator is not needed. For example, 2/3 x 3/4 gives 6/12, which simplifies to 1/2. You can also cross-cancel before multiplying: cancel 2 with 4 to get 1 and 2, then cancel 3 with 3 to get 1 and 1. The remaining multiplication is 1/1 x 1/2 = 1/2. Cross-cancellation keeps the numbers smaller.

To divide fractions, use Keep-Change-Flip. Keep the first fraction, change division to multiplication, and flip the second fraction. For example, 3/4 divided by 2/5 becomes 3/4 x 5/2. Multiply straight across to get 15/8, then convert if needed: 15/8 = 1 7/8. Flipping works because dividing by 2/5 asks how many two-fifths fit into the first value, which is the same as multiplying by its reciprocal, 5/2.

LCD means Least Common Denominator. It is the smallest denominator that two fractions can share. For 1/3 and 1/4, list multiples: 3, 6, 9, 12 and 4, 8, 12. The first shared multiple is 12, so the LCD is 12. You can also use prime factors. Since 3 and 4 share no factors, multiply them to get 12. The LCD is needed for addition and subtraction because you can only combine pieces of the same size.

To simplify a fraction, find the greatest common factor of the numerator and denominator, then divide both parts by it. For example, 12/18 has GCF 6. Divide the numerator and denominator by 6: 12 divided by 6 is 2, and 18 divided by 6 is 3. So 12/18 simplifies to 2/3. If the GCF is 1, the fraction is already in lowest terms and should not be reduced further.

Yes. Switch to Mixed number mode to enter values like 1 1/2 or 2 3/4 without converting them by hand. The calculator converts each mixed number to an improper fraction behind the scenes, performs the operation, and then shows the answer as a simplified fraction, mixed number, and decimal. For example, 1 1/2 + 2 1/4 becomes 3/2 + 9/4, then 6/4 + 9/4 = 15/4 = 3 3/4.

An improper fraction has a numerator greater than or equal to its denominator, such as 7/4 or 9/3. To convert an improper fraction to a mixed number, divide the numerator by the denominator. For 7/4, 7 divided by 4 is 1 remainder 3, so 7/4 = 1 3/4. To convert a mixed number back, multiply the whole number by the denominator and add the numerator. For 1 3/4, 1 x 4 + 3 = 7, so the improper fraction is 7/4.