Mixed Fraction Calculator – Add, Subtract, Multiply & Divide Instantly
Mixed Fraction Calculator is an online tool designed to simplify arithmetic operations involving mixed fractions. Whether you’re adding, subtracting, multiplying, or dividing mixed fractions, this tool provides accurate results instantly while offering step-by-step breakdowns for better understanding.
Most online mixed fraction calculators only support operations between two fractions, with only 10% allowing up to five fractions. However, CalculationClub.com offers a unique mixed fraction calculator that enables calculations with an unlimited number of mixed fractions, making it a powerful and versatile tool for all your fraction-solving needs.
With this tool, you can effortlessly compute operations between two or more mixed fractions, such as 1 $\frac{2}{5}$ + 2$\frac{3}{4}$ or 3$\frac{2}{5}$ ÷ 1$\frac{1}{4}$. Whether you’re a student solving math problems, a professional requiring precise calculations, or someone aiming to master mixed fractions, this calculator is designed to be fast, user-friendly, and highly reliable.
How to Use the Online Fraction Calculator?
1. Adding a Fraction: Click the “Add Fraction” button to insert a new fraction input field. A new whole numbers, numerator and denominator box will appear, along with an operator (+, -, ×, ÷). You can add multiple fractions by repeating this step.
2. Removing a Fraction: Click the “Remove Fraction” button to delete the last added fraction along with its operator.
3. Entering Fractions: Adjust the input boxes as needed and entering whole numbers, numerators, and denominators. Decimal values are not allowed—only whole numbers can be used. The whole number part is optional, but the numerator and denominator fields must not be left empty or set to zero.
4. Performing Calculations: After entering all fractions, click the “Calculate” button. The calculator will display the result along with detailed step-by-step calculations. The result will be shown as:
- A proper or improper fraction
- A mixed fraction (if applicable)
- A decimal equivalent
5. Hiding Calculation Steps: Click the “Hide Steps” button to conceal the detailed solution steps.
6. Resetting the Calculator: Click the “Reset” button to clear all input fields and restart the calculation process.
This tool ensures accurate fraction operations with a user-friendly interface, making it ideal for students, professionals, and anyone working with fractions.
What is a Mixed Fraction?
A mixed fraction, also known as a mixed number, is a way to represent a value that consists of both a whole number and a proper fraction. It is used when a number is greater than one but not a whole number.
For example, in the mixed fraction 2$\frac{3}{4}$, the whole number (2) represents the complete units, while the fraction ($\frac{3}{4}$) represents the additional part of a whole. This means the total value is two whole parts plus three-fourths of another whole part.
In a fraction, there are three key components:
- Whole Number: The integer part of the fraction that represents full units.
- Numerator: The top number of the fraction, representing how many parts of the whole are considered.
- Denominator: The bottom number of the fraction, representing the total number of equal parts the whole is divided into.
Why Can’t the Numerator or Denominator Be Zero?
When working with fractions, it is important to understand the restrictions on numerators and denominators:
- Numerator must be nonzero (except for zero fractions): A fraction with a zero numerator (e.g., $\frac{0}{4}$) always results in zero, regardless of the denominator. While such fractions are valid, they are often unnecessary in calculations.
- Denominator cannot be zero: A fraction with a denominator of zero (e.g., $\frac{3}{0}$) is undefined in mathematics because division by zero is impossible. Since division is the process of splitting into equal parts, having zero parts to divide by makes no logical sense.
In short, while a numerator of zero makes the entire fraction zero, a denominator of zero makes the fraction undefined, which is why it is not allowed.
To manually calculate mixed fractions, follow these steps for each operation (Mixed Fraction Calculator):
1. Addition of Fractions:
$2\frac{2}{3} + 1\frac{4}{5}$
Step 1: Convert Mixed Fractions to Improper Fractions
Convert the mixed fractions into improper fractions:
$2\frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}$
$1\frac{4}{5} = \frac{(1 \times 5) + 4}{5} = \frac{5 + 4}{5} = \frac{9}{5}$
Now, the addition problem is:
$\frac{8}{3} + \frac{9}{5}$
Step 2: Find the Least Common Denominator (LCD)
The denominators are 3 and 5. The Least Common Multiple (LCM) of 3 and 5 is **15**.
Step 3: Convert to Equivalent Fractions
Convert both fractions so they have a denominator of 15:
$\frac{8}{3} = \frac{8 \times 5}{3 \times 5} = \frac{40}{15}$
$\frac{9}{5} = \frac{9 \times 3}{5 \times 3} = \frac{27}{15}$
Now, the equation is:
$\frac{40}{15} + \frac{27}{15}$
Step 4: Add the Numerators
Since the denominators are the same, add the numerators:
$\frac{40 + 27}{15} = \frac{67}{15}$
Step 5: Convert to a Mixed Fraction (If Necessary)
Since $\frac{67}{15}$ is an improper fraction, convert it into a mixed fraction:
$67 \div 15 = 4$ remainder $7$
So,
$\frac{67}{15} = 4\frac{7}{15}$
Final Answer:
$4\frac{7}{15}$ (Mixed Fraction) or $\frac{67}{15}$ (Improper Fraction)
Effortlessly calculate above fractions with our Mixed Fraction Calculator.
2. Subtraction of Fractions
$2\frac{2}{3} – 1\frac{4}{5}$
Step 1: Convert Mixed Fractions to Improper Fractions
Convert the mixed fractions into improper fractions:
$2\frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}$
$1\frac{4}{5} = \frac{(1 \times 5) + 4}{5} = \frac{5 + 4}{5} = \frac{9}{5}$
Now, the subtraction problem is:
$\frac{8}{3} – \frac{9}{5}$
Step 2: Find the Least Common Denominator (LCD)
The denominators are 3 and 5. The Least Common Multiple (LCM) of 3 and 5 is **15**.
Step 3: Convert to Equivalent Fractions
Convert both fractions so they have a denominator of 15:
$\frac{8}{3} = \frac{8 \times 5}{3 \times 5} = \frac{40}{15}$
$\frac{9}{5} = \frac{9 \times 3}{5 \times 3} = \frac{27}{15}$
Now, the equation is:
$\frac{40}{15} – \frac{27}{15}$
Step 4: Subtract the Numerators
Since the denominators are the same, subtract the numerators:
$\frac{40 – 27}{15} = \frac{13}{15}$
Final Answer:
$\frac{13}{15}$ (Simplified Fraction)
3. Multiplication of Fractions
$\frac{2}{3} \times \frac{4}{5}$
Step 1: Multiply the Numerators and Denominators
2$\frac{2}{3} \times \frac{4}{5}$ = $\frac{2 \times 4}{3 \times 5}$ = $\frac{8}{15}$
Final Answer:
$\frac{8}{15}$
This fraction is already in its simplest form. Effortlessly calculate above fractions with our Mixed Fraction Calculator.
4. Division of Fractions
$2\frac{2}{3} \div 1\frac{4}{5}$
Step 1: Convert Mixed Fractions to Improper Fractions
Convert the mixed fractions into improper fractions:
$2\frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}$
$1\frac{4}{5} = \frac{(1 \times 5) + 4}{5} = \frac{5 + 4}{5} = \frac{9}{5}$
Now, the division problem is:
$\frac{8}{3} \div \frac{9}{5}$
Step 2: Convert Division into Multiplication
Dividing by a fraction is the same as multiplying by its reciprocal:
$\frac{8}{3} \times \frac{5}{9}$
Step 3: Multiply the Numerators and Denominators
$\frac{8 \times 5}{3 \times 9} = \frac{40}{27}$
Step 4: Convert to a Mixed Fraction
Divide 40 by 27:
$40 \div 27 = 1$ remainder $13$
So,
$\frac{40}{27} = 1\frac{13}{27}$
Final Answer:
$1\frac{13}{27}$ (Mixed Fraction) or $\frac{40}{27}$ (Improper Fraction)
Effortlessly calculate above fractions with our Mixed Fraction Calculator.
Initial Expression:
$2\frac{2}{3} + 1\frac{4}{5} – \frac{3}{7} \times \frac{5}{9} \div \frac{2}{3}$
Step 1: Convert Mixed Fractions to Improper Fractions
Convert the mixed fractions into improper fractions:
$2\frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}$
$1\frac{4}{5} = \frac{(1 \times 5) + 4}{5} = \frac{5 + 4}{5} = \frac{9}{5}$
Now, the expression becomes:
$\frac{8}{3} + \frac{9}{5} – \frac{3}{7} \times \frac{5}{9} \div \frac{2}{3}$
Step 2: Solve Multiplication and Division First (Order of Operations – BODMAS)
Multiplication:
$\frac{3}{7} \times \frac{5}{9} = \frac{3 \times 5}{7 \times 9} = \frac{15}{63}$
Simplify:
$\frac{15}{63} = \frac{5}{21}$ (Divide numerator and denominator by 3)
Division:
$\frac{5}{21} \div \frac{2}{3}$
Convert division into multiplication by taking the reciprocal:
$\frac{5}{21} \times \frac{3}{2} = \frac{5 \times 3}{21 \times 2} = \frac{15}{42}$
Simplify:
$\frac{15}{42} = \frac{5}{14}$ (Divide numerator and denominator by 3)
Now, the expression simplifies to:
$\frac{8}{3} + \frac{9}{5} – \frac{5}{14}$
Step 3: Find the Least Common Denominator (LCD)
The denominators are 3, 5, and 14.
Find the LCM(3, 5, 14) = 210.
Step 4: Convert Fractions to Equivalent Fractions
$\frac{8}{3} = \frac{8 \times 70}{3 \times 70} = \frac{560}{210}$
$\frac{9}{5} = \frac{9 \times 42}{5 \times 42} = \frac{378}{210}$
$\frac{5}{14} = \frac{5 \times 15}{14 \times 15} = \frac{75}{210}$
Now, the expression is:
$\frac{560}{210} + \frac{378}{210} – \frac{75}{210}$
Step 5: Perform Addition and Subtraction
Add the first two fractions:
$\frac{560}{210} + \frac{378}{210} = \frac{560 + 378}{210} = \frac{938}{210}$
Subtract the last fraction:
$\frac{938}{210} – \frac{75}{210} = \frac{938 – 75}{210} = \frac{863}{210}$
Step 6: Convert to a Mixed Fraction
Divide 863 by 210:
$863 \div 210 = 4$ remainder $23$
So,
$\frac{863}{210} = 4\frac{23}{210}$
Final Answer:
$4\frac{23}{210}$ (Mixed Fraction) or $\frac{863}{210}$ (Improper Fraction)
Effortlessly calculate above fractions with our Mixed Fraction Calculator.
FAQs on Mixed Fraction Calculator
1. How to calculate mixed fractions?
To calculate mixed fractions, follow these steps:
- Convert mixed fractions into improper fractions.
- Perform the required arithmetic operation (addition, subtraction, multiplication, or division).
- If needed, convert the result back into a mixed fraction.
2. How do I convert to a mixed fraction?
To convert an improper fraction into a mixed fraction:
- Divide the numerator by the denominator.
- The quotient becomes the whole number, and the remainder is the new numerator.
- Write the remainder over the original denominator.
Example:
$\frac{22}{7}$ → $3\frac{1}{7}$ (since $22 \div 7 = 3$ remainder 1)
3. What is 117.755 as a mixed number?
To convert 117.755 into a mixed fraction:
- Separate the whole number 117.
- Convert 0.755 into a fraction:
- 0.755 ≈ $\frac{755}{1000}$ (Simplify to $\frac{151}{200}$)
- Final mixed fraction: $117\frac{151}{200}$
4. What are 5 examples of mixed fractions?
Here are five examples of mixed fractions:
- $2\frac{3}{5}$
- $5\frac{1}{4}$
- $7\frac{2}{9}$
- $10\frac{5}{6}$
- $12\frac{7}{8}$
5. What is 8 3 as a mixed number?
If you mean $\frac{8}{3}$ as a mixed number:
- $8 \div 3 = 2$ remainder 2
- $\frac{8}{3} = 2\frac{2}{3}$
6. How to write a mixed number?
To write a mixed number:
- Write the whole number part.
- Write the fraction part beside it.
Example: $4\frac{1}{2}$ (which means 4 whole parts and 1/2 of another part).
Conclusion: Our Mixed Fraction Calculator simplifies the process of performing operations on mixed fractions with clear and accurate calculations. It provides a step-by-step breakdown for addition, subtraction, multiplication, and division, ensuring an easy understanding of each operation. By using this tool, you can quickly compute mixed fraction problems, view detailed solution steps, and obtain precise results in seconds. Mastering mixed fraction operations enhances your math skills, aids in practical calculations, and helps solve problems efficiently—whether for everyday use, academic purposes, or advanced applications.
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