Mixed Fraction Calculator

This Mixed Fraction Calculator helps you add, subtract, multiply, and divide mixed fractions in seconds. Simply enter your values, and the calculator will instantly show the result with a clear step-by-step explanation. It is perfect for students, teachers, or anyone who wants to solve mixed fraction problems quickly and accurately.

To make things even easier for you, the calculator operates on your mixed numbers and gives you the answer in mixed fraction form, improper fraction form, and as a decimal form. This way, you can choose the best answer that matches your needs.

How to Use the Mixed Fraction Calculator

Want to add, subtract, multiply, or divide two mixed fractions quickly? Just follow these steps for instant results, with a clear, step-by-step explanation.

1. Enter the first mixed number
2. Select the operation (+, −, ×, ÷) you want to perform from the dropdown
3. Enter the second mixed number
4. Click the “Calculate” button to get instant results.

You can also click the step-by-step explanation section to see how the mixed fractions were added, subtracted, multiplied, or divided.

What is a Mixed Fraction?

A mixed fraction, or mixed number, combines a whole number and a proper fraction to represent a quantity greater than one. For example, in the mixed fraction $2\frac{1}{4}$, the “2” is the whole number part, and “$\frac{1}{4}$” is the fraction part. The whole number shows complete units, while the fraction shows a part of another unit.

This is different from an improper fraction, where the numerator is larger than the denominator. Thus, learning how to add, subtract, multiply, or divide fractions is useful for solving real-world measurement problems, such as construction, cooking, or tailoring, where amounts are rarely whole numbers.

➕ Adding Mixed Fractions

Adding mixed fractions becomes easy when you break it into simple steps. Follow these steps to add two mixed numbers by hand:

1. Convert each mixed number into an improper fraction
2. Find a common denominator
3. Add the fractions
4. Simplify the result

Example 1. Adding Mixed Numbers

Add $1\frac{2}{6} + 2 \frac{1}{4}$

Solution

Step 1. Convert each mixed number into an improper fraction

To convert a mixed fraction into an improper fraction, multiply the whole number by the denominator, then add the numerator. You can also use a mixed number to an improper fraction calculator.

Thus, $1\frac{2}{6}$ becomes $\frac{8}{6}$

Similarly, $2 \frac{1}{4}$ becomes $\frac{9}{4}$

Step 2. Find the common denominator

From the two improper fractions, we see that the denominators are 6 and 4, which are different.
So, we find the least common denominator (LCD).

The smallest common multiple of 6 and 4 is 12.

To convert $\frac{8}{6}$​ to a fraction with a denominator of 12, we multiply both the numerator and denominator by 2 since 12÷6 = 2

Thus, $\frac{8}{6} =\frac{16}{12}$

Similarly, to convert $\frac{9}{4}$ to a fraction with a denominator of 12, we multiply both the numerator and denominator by 3 since 12÷4 = 3.

Thus, $\frac{9}{4} = \frac{27}{12}$

Step 3. Add the two fractions

Since both fractions have the same denominator, we add the numerators together and retain the denominator.

Thus, $\frac{16}{12} + \frac{27}{12} =\frac{16+27}{12}$

=$\frac{43}{12}$

Step 4: Simplify the Result

Since the answer is improper, we need to convert it back to a mixed fraction.

Thus, $\frac{43}{12} = 3\frac{7}{12}$

Want to quickly convert any improper fraction to a mixed fraction? Use the improper to mixed fraction calculator.

You can confirm the results using the mixed fraction calculator. Just enter the first mixed fraction, select the addition operator (+), and enter the second mixed fraction. On clicking the “Calculate” button, the calculator will yield similar results, as shown below:

➖ Subtracting Mixed Fractions

Subtracting mixed fractions follows a similar process to addition. Just follow these simple steps:

1. Convert each mixed number into an improper fraction
2. Find a common denominator
3. Subtract the fractions
4. Simplify the result

Example 2. Subtract Mixed Numbers

Subtract $3\frac{1}{2} – 1\frac{2}{3}$

Solution

Step 1. Convert each mixed number into an improper fraction

To convert a mixed fraction into an improper fraction, multiply the whole number by the denominator, then add the numerator.

Thus, $3\frac{1}{2} = \frac{7}{2}$

Similarly, $1\frac{2}{3} = \frac{5}{3}$

Step 2. Find the common denominator

The denominators are 2 and 3, which are different. So, we find the least common denominator (LCD).

The smallest common multiple of 2 and 3 is 6.

To convert $\frac{7}{2}$ to a fraction with a denominator of 6, multiply both the numerator and denominator by 3 since 6÷2=3:

Thus, $\frac{7}{2} = \frac{21}{6}$

Similarly, to convert $\frac{5}{3}$ to a fraction with a denominator of 6, multiply both the numerator and denominator by 2 since 6÷3=2.

Thus, $\frac{5}{3} = \frac{10}{6}$

Step 3. Subtract the two fractions

Since both fractions now have the same denominator, subtract the numerators and retain the denominator.

Thus, $\frac{21}{6} – \frac{10}{6} = \frac{21-10}{6}$

= $\frac{11}{6}$

Step 4. Simplify the Result

Since the answer is an improper fraction, we need to convert it back to a mixed fraction.

Thus, $\frac{11}{6} = 1\frac{5}{6}$

Alternatively, you can easily subtract the two mixed fractions using the mixed fraction calculator. Just enter the two mixed numbers, select the subtraction operator (-), and click the “calculate” button. The calculator will yield similar results as shown below.

✖️ Multiplying Mixed Fractions

Multiplying mixed fractions is very straightforward once you convert the mixed numbers into improper fractions. To multiply mixed numbers manually, just follow these steps:

1. Convert each mixed number into an improper fraction
2. Multiply the resulting improper fractions using the formula: $\frac{a}{b} \times \frac{c}{d} = \frac{a\times c}{b\times d}$
3. Simplify the result

Example 3. Multiply Mixed Numbers

Multiply $2\frac{1}{3} \times 1\frac{3}{4}$

Solution

Step 1. Convert each mixed number into an improper fraction

To convert the mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.

Thus, $2\frac{1}{3} = \frac{7}{3}$ and $1\frac{3}{4} = \frac{7}{4}$

Step 2. Multiply the fractions

Multiply the fraction using the formula $\frac{a\times c}{b\times d}$

Thus, $\frac{7}{3} \times \frac{7}{4} = \frac{7 \times 7}{3 \times 4}$

= $\frac{49}{12}$

Step 3. Simplify the Result

Since the result is an improper fraction, we need to convert it back to a mixed fraction.

Thus, $\frac{49}{12} = 4\frac{1}{12}$

Alternatively, you can quickly find the same results using the mixed number calculator. Just enter the two mixed fractions, select the multiplication operator (x), and click Calculate. The calculator returns similar results, as shown below.

➗ Dividing Mixed Fractions

Dividing mixed fractions involves converting them into improper fractions and then multiplying the first improper fraction by the reciprocal of the second improper fraction. Therefore, to divide two mixed numbers manually, follow these steps:

1. Convert each mixed number into an improper fraction
2. Rewrite the division as multiplication using the reciprocal. In other words, flip the second fraction and multiply. That is $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b}\times \frac{d}{c}$
3. Multiply the fractions
4. Simplify the Result

Example 4. Divide Mixed Numbers

Divide $3\frac{1}{3}\div 1\frac{2}{5}$

Solution

Step 1. Convert each mixed number into an improper fraction

Converting $3\frac{1}{3}$ to an improper fraction gives $\frac{10}{3}$

Similarly, converting $1\frac{2}{5}$ to improper gives $\frac{7}{5}$

Step 2. Rewrite using the reciprocal

Here, we need to rewrite the division as multiplication by flipping the second fraction.

Thus, $\frac{10}{3} \div \frac{7}{5} = \frac{10}{3} \times \frac{5}{7}$

Step 3. Multiply the fractions

Thus, $\frac{10}{3} \times \frac{5}{7} = \frac{10 \times 5} {3 \times 7}$

= $\frac{50}{21}$

Step 4. Simplify the result

Since the answer is improper, we need to convert it back to a mixed fraction.

Thus, $\frac{50}{21} = 2\frac{8}{21}$

Want to multiply these two mixed numbers quickly? Using the mixed fraction calculator, enter the two mixed numbers, select the operator (÷), and click calculate. The calculator returns similar results as shown below.

Frequently Asked Questions