Adding and Subtracting Fractions with Unlike Denominators Calculator (with Steps)

To add or subtract fractions with unlike denominators, rewrite them over the least common denominator (LCD), combine the numerators, and simplify. This adding fractions with unlike denominators calculator does those steps for you and shows the full working for two or three fractions, including mixed numbers, whole numbers, and negatives. Below the calculator you will find practice questions and the method explained by hand.

How to use the Adding and Subtracting Fractions with Unlike Denominators Calculator

1. Type the first fraction, such as 3/4. Mixed numbers (1 1/2), negatives (-2/5), and whole numbers (3) also work.
2. Choose + or − and type the second fraction.
3. To work with three fractions, tick “Add a third fraction” and choose its sign.
4. Press Calculate or the Enter key. You get the answer in simplest form, as a mixed number when it is greater than 1, plus the decimal value.
5. Read the steps: the LCD (found with lists of multiples or with prime factors), the equivalent fractions, the combined numerator, and the simplifying.
6. Scroll to the Practice section to try new problems and check your answers.

How to add and subtract fractions with unlike denominators by hand

Fractions can only be added or subtracted when they count the same size of piece. Fourths and sixths are different sizes, so we first cut both into a size that fits each one evenly. That size is the least common denominator, the smallest number both denominators divide into.

The method has four steps:

1. Find the LCD. List multiples of each denominator until you reach a number on every list, or use prime factorization.
2. Rewrite each fraction. Multiply the numerator and denominator by the same number so the denominator becomes the LCD.
3. Add or subtract the numerators. The denominator stays the same.
4. Simplify. Divide the top and bottom by their greatest common factor, and write an improper fraction as a mixed number if you like.

Worked example 1: 5/6 + 3/8

Find the LCD. Multiples of 6: 6, 12, 18, 24. Multiples of 8: 8, 16, 24. The first number on both lists is 24, so the LCD is 24.

Rewrite. 24 ÷ 6 = 4, so 5/6 = (5 × 4)/(6 × 4) = 20/24. Next, 24 ÷ 8 = 3, so 3/8 = (3 × 3)/(8 × 3) = 9/24.

Add the numerators. 20/24 + 9/24 = 29/24.

Simplify. 29 is prime and does not divide 24, so 29/24 is already in lowest terms. Since 29 ÷ 24 = 1 remainder 5, the mixed number is 1 5/24.

Worked example 2: 5/6 − 1/10

Find the LCD. Multiples of 6: 6, 12, 18, 24, 30. Multiples of 10: 10, 20, 30. The LCD is 30.

Rewrite. 5/6 = (5 × 5)/(6 × 5) = 25/30 and 1/10 = (1 × 3)/(10 × 3) = 3/30.

Subtract the numerators. 25/30 − 3/30 = 22/30.

Simplify. The greatest common factor of 22 and 30 is 2. Dividing both by 2 gives 11/15.

If a problem contains a mixed number, change it to an improper fraction first. For example, 2 1/3 = (2 × 3 + 1)/3 = 7/3. Then follow the same four steps. If you need help finding an LCD for larger numbers, the least common denominator calculator lists the steps, and the simplify fractions calculator reduces any fraction to lowest terms.

Quick reference: LCDs for common denominator pairs

A useful shortcut: when one denominator is a multiple of the other (5 and 10), the larger one is the LCD. When the two denominators share no common factor (3 and 5), the LCD is their product.

Common mistakes to avoid

• Adding the denominators. 1/2 + 1/3 is not 2/5. The pieces are different sizes, so they must be renamed first: 3/6 + 2/6 = 5/6. A quick check shows 2/5 is smaller than 1/2 alone, which cannot be right.
• Changing only the denominator. To turn 3/4 into twelfths, multiply both parts by 3 to get 9/12. Writing 3/12 changes the value.
• Forgetting to simplify. 22/30 is correct in value, but most teachers expect 11/15.
• Losing a negative sign. Subtracting a negative is adding: 1/4 − (−1/2) = 1/4 + 2/4 = 3/4. When the second fraction is larger, the answer is negative: 1/3 − 5/6 = 2/6 − 5/6 = −3/6 = −1/2.
• Mixing up the whole number in a mixed number. Change 1 1/2 to 3/2 before finding the LCD, or handle the whole numbers and fraction parts separately and regroup carefully.

Where this fits in the curriculum

Adding and subtracting fractions with like denominators is taught in grade 4 (Common Core 4.NF.B.3). Unlike denominators come in grade 5: standard 5.NF.A.1 asks students to add and subtract fractions with unlike denominators, including mixed numbers, by replacing them with equivalent fractions that have like denominators. Standard 5.NF.A.2 applies the same skill to word problems. The skill comes back in pre-algebra and algebra when you add rational expressions, so a solid method now pays off later.

In daily life, unlike fractions appear in recipes (1/2 cup plus 1/3 cup), measurements in inches (5/8 in. minus 1/4 in.), and time (3/4 hour plus 1/6 hour).

Check your answer

Estimate with benchmark fractions before you trust a result. In 5/6 + 3/8, 5/6 is a little less than 1 and 3/8 is a little less than 1/2, so the sum should be a bit less than 1 1/2. Our answer, 1 5/24, fits. You can also compare decimals: 5/6 ≈ 0.833 and 3/8 = 0.375 add to about 1.208, and 29/24 ≈ 1.208. For more practice, try the adding and subtracting fractions practice page.

Adding and subtracting fractions practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

How do you add fractions with unlike denominators?

Find the least common denominator, rewrite each fraction as an equivalent fraction with that denominator, add the numerators, and keep the denominator. Then simplify. For example, 1/4 + 1/6 = 3/12 + 2/12 = 5/12.

Can I just multiply the denominators together?

Yes. The product of the denominators is always a common denominator, so the answer will be correct after you simplify. It is not always the least one, though. For 1/4 + 1/6, multiplying gives 24, while the LCD is 12, so using the LCD keeps the numbers smaller and the simplifying shorter.

Why can't you add the denominators?

The denominator names the size of the pieces, and the numerator counts them. Adding 1/2 and 1/3 does not make fifths. You have to cut both into sixths first, which gives 3/6 + 2/6 = 5/6.

How do you subtract fractions with unlike denominators when the answer is negative?

Use the same steps. After rewriting with the LCD, subtract the numerators and keep the sign. For example, 1/3 − 5/6 = 2/6 − 5/6 = −3/6, which simplifies to −1/2.

How do you add or subtract mixed numbers with unlike denominators?

The simplest way is to change each mixed number to an improper fraction, then find the LCD and combine. For 2 1/3 + 1 1/4, write 7/3 + 5/4 = 28/12 + 15/12 = 43/12 = 3 7/12. Students can also add the whole numbers and the fractions separately, regrouping if the fraction part becomes 1 or more.

How do I find the least common denominator quickly?

List multiples of the larger denominator and stop at the first one the smaller denominator divides evenly. For 8 and 12, the multiples of 12 are 12 and 24, and 24 is the first that 8 divides, so the LCD is 24. For larger numbers, use prime factorization.