Adding Fractions Calculator

Adding fractions calculator at a glance#

How do you add fractions?#

When fractions have matching denominators, you simply add the numerators while keeping the denominator unchanged. If the denominators are different, you'll need to rewrite each fraction with a common denominator first, then add the numerators and simplify. For instance, for 3/4 plus 1/6, the least common denominator is 12. So the sum becomes 9/12 plus 2/12, which is 11/12.

How do you use the adding fractions calculator?#

Enter your fractions separated by a plus sign, like 3/4 + 1/6, and click Calculate. You can add not just two fractions but also a long list of them. The result will be in its simplest form, displayed both as a fraction and a mixed number if it's larger than 1.

What is 4/6 + 4/8?#

The sum 4/6 plus 4/8 equals 7/6, or as a mixed number, 1 1/6. The least common denominator of 6 and 8 is 24. So the sum becomes 16/24 plus 12/24, which equals 28/24. This simplifies to 7/6 after dividing both parts by 4.

Adding fractions with the same denominator#

When denominators are the same, each piece is already the same size, so all you do is count them. For example, 5/12 plus 5/12 results in 10 twelfths, or 10/12, which simplifies to 5/6. The calculator's preloaded example adds 5/12 eight times, yielding 40/12, which the calculator then reduces to 10/3, or 3 1/3.

Never add denominators together. Adding straight across for 1/2 plus 1/2 gives 2/4, which equals only half, not one whole. Denominators define the piece size, and adding fractions doesn't alter that size.

Adding fractions with unlike denominators#

This is a common area for mistakes, but the calculator handles it for you. Consider 3/4 + 1/6. Fourths and sixths aren't the same size, so you need to convert both into pieces of a common size before combining them.

1. Begin by finding the least common denominator. The least common multiple of 4 and 6 is 12, thus the LCD is 12.
2. Rewrite each fraction using the LCD. Dividing 12 by 4 gives 3, so 3/4 becomes 9/12. Similarly, 12 divided by 6 equals 2, turning 1/6 into 2/12.
3. Add the numerators while retaining the denominator: 9/12 + 2/12 equals 11/12.
4. Simplify if possible. As 11 and 12 share no factor other than 1, the final answer is 11/12.

Splitting each fourth into 3 pieces and each sixth into 2 pieces results in both fractions being expressed in twelfths. Then 9 twelfths added to 2 twelfths equals 11 twelfths. OpenStax Prealgebra 2e explains the same four steps for combining fractions with different denominators: find the LCD, convert each fraction, add, and then simplify the outcome.

If finding the LCD is the hard part, the least common denominator calculator can determine it for any set of fractions.

Shortcut: multiply the denominators#

You can bypass the LCD by multiplying the denominators. For a/b + c/d, the sum is (a × d + b × c) / (b × d). For 3/4 + 1/6, this works out as (3 × 6 + 4 × 1) / (4 × 6) = 22/24. This approach always works, but often requires simplification, as 22/24 reduces to 11/12. The simplifying fractions calculator can take care of that final step.

Adding three or more fractions#

Use a single common denominator for all fractions involved. In the case of 1/2 + 1/3 + 1/4, the LCD of 2, 3, and 4 is 12, so the total is 6/12 + 4/12 + 3/12 = 13/12, which simplifies to 1 1/12. In the calculator, keep adding plus signs: 1/2 + 1/3 + 1/4.

Subtracting fractions#

Subtracting fractions works the same way, except you subtract numerators once the denominators match. 3/4 minus 1/6 results in 9/12 minus 2/12, which equals 7/12.

Since the calculator only uses plus signs, input the fraction you're subtracting as a negative. Enter 3/4 + -1/6. The result will be 7/12, the same as subtracting. A negative numerator can be placed anywhere in your list.

Adding whole numbers and mixed numbers#

The calculator reads fractions only, so whole numbers and mixed numbers need to be converted into fractions first.

• A whole number is placed over 1. To add 3 + 2/5, input 3/1 + 2/5. The sum then is 17/5, or 3 2/5.
• Convert a mixed number into an improper fraction. Multiply the whole number by the denominator and add the numerator: 2 1/2 becomes 5/2 and 1 3/4 turns into 7/4.

So 2 1/2 + 1 3/4 should be entered as 5/2 + 7/4. With the LCD of 4, this becomes 10/4 + 7/4 = 17/4, or 4 1/4. Manually, you can also add the whole numbers and the fractions separately: 2 + 1 = 3, and 1/2 + 3/4 = 5/4 = 1 1/4, so the total is 4 1/4. When handling two mixed numbers at a time, including subtraction, the mixed number calculator takes them as they're written.

Where adding fractions comes up#

Cooking#

Measuring cups are often marked in halves, thirds, and quarters. Adding 1/2 cup of milk to 2/3 cup results in 3/6 + 4/6 = 7/6 cups, slightly more than 1 cup.

Measuring lengths#

Inches on tape measures and rulers are divided into halves, quarters, eighths, and sixteenths. Stack a 3/4 inch board on a 5/8 inch board and you'll have 6/8 + 5/8 = 11/8 inches of height, or 1 3/8 inches, approximately 3.5 cm.

Time#

Adding a quarter of an hour to a third of an hour calculates as 1/4 + 1/3 = 3/12 + 4/12 = 7/12 of an hour, which is 35 minutes.

Common fraction sums#

These are sums people often look up, worked over the least common denominator.

Sources#

• OpenStax, Prealgebra 2e, section 4.5: Add and Subtract Fractions with Different Denominators

Frequently asked questions#

Do you add the denominators when adding fractions?#

No. Only numerators are added. Denominators must match first, and the shared denominator remains the same in the result.

Can you add fractions without finding the least common denominator?#

Yes. Any common denominator works, and the product of the denominators can serve as one. For 4/6 + 4/8, using 48 results in 32/48 + 24/48 = 56/48, which simplifies to 7/6. The LCD keeps calculations smaller.

How do you add a fraction and a whole number?#

Place the whole number over 1, then proceed with addition. 2 + 1/2 becomes 2/1 + 1/2 = 4/2 + 1/2 = 5/2, which is 2 1/2. Type 2/1 + 1/2 into the calculator.

How do you subtract fractions with this calculator?#

Input a negative fraction to subtract. Typing 3/4 + -1/6 results in 7/12, which is the same as 3/4 minus 1/6.

Why does the calculator show two answers?#

The two forms represent the same value. For instance, 10/3 is an improper fraction, while 3 1/3 is a mixed number. When the sum is smaller than 1, both sides reflect the same fraction.

How do you add fractions with variables?#

Apply the same common denominator rule. In the case of 1/x + 1/(2x), the LCD is 2x, so the sum is 2/(2x) + 1/(2x) = 3/(2x). Since the calculator only works with numbers, do sums with variables by hand.