Mixed Number Calculator

Mixed Number Calculator

This online mixed fractions calculator is the best tool that allows you to add, subtract, multiply, and divide mixed fractions. For more clarity, this whole number and fraction calculator helps you solve problems involving whole numbers and proper fractions. One thing makes this mixed number calculator stand out from other mixed fraction calculators. It gives its users a step-by-step illustration of how to do the calculations.

Rules for Using the Mixed Number Calculator

1. The first thing to do is input the mixed numbers you want to perform the mathematical operation on into the fields. The mixed numbers should be in this format: \$3 \frac{2}{5}\$ (where 3 is the whole number and \$\frac{2}{5}\$ is the proper fraction) and \$7 \frac{1}{2}\$ (where 7 is the whole number and \$\frac{1}{2}\$ is the proper fraction). You can input in this fraction calculator up to 3 digits for each whole number, numerator, or denominator. For example, 112 for the whole number, 324 for the numerator, and 733 for the denominator. Ensure you maintain a single space between the whole number and the fraction, and utilize a forward slash to separate each fraction's numerator and denominator.

2. The mixed numbers calculator has multiple operators you can choose from, depending on the operation you intend to perform. The operators available on this calculator are the addition operator (+), subtraction operator (-), multiplication operator (×), division operator (÷), and the "of" operator.

3. When you have entered mixed fractions and selected the desired operator, you can get the answer by clicking the "Сalculate" button below the input fields.

Practical Examples

This section will provide a practical illustration of effectively utilizing this online mixed number calculator.

Adding Mixed Fractions

Let's assume you are faced with the problem of adding mixed fractions, for instance, \$3 \frac{1}{3}\$ and \$7 \frac{4}{9}\$.

Start with the mixed number to the left of the addition operator (+): \$3 \frac{1}{3}\$ (where 3 is the whole number, 1 is the numerator, and 3 is the denominator). First, enter 3 (the whole number), then enter one space, then enter 1 (the numerator), then a forward slash, and finally enter 3 (the denominator).

For a mixed number to the right of the addition operator (+): \$7 \frac{4}{9}\$ (where 7 is the whole number, 4 is the numerator, and 9 is the denominator). First, enter 7 (the whole number), then enter one space, then enter 4 (the numerator), followed by a straight slash, and finally enter 9 (the denominator).

After successfully inputting the mixed numbers into the appropriate fields and choosing the required mathematical operator (in this case, addition), click the "Сalculate" button. And the calculator will show the result in the answer field.

Subtracting Mixed Fractions

Subtracting mixed fractions has similar steps. We will illustrate it with an example to help you understand how to subtract mixed numbers correctly. Let’s say we want to subtract \$4 \frac{1}{2}\$ from \$12 \frac{3}{5}\$.

Let's begin with the mixed numbers on the left side of the subtraction operator (-): \$12 \frac{3}{5}\$ (where 12 is the whole number, 3 is the numerator, and 5 is the denominator). Start by entering 12 (whole number), followed by a single space, then 3 (numerator), next is a forward slash, and lastly, 5 (denominator).

Moving on to the mixed numbers found on the right side of the subtraction operator (-): \$4 \frac{1}{2}\$ (where 4 is the whole number, 1 is the numerator, and 2 is the denominator). Start by entering 4 (the whole number), then a space, then 1 (the numerator), then a forward slash, and finally 2 (the denominator).

After you have completed the steps above, select the subtraction operator (-) and click the button with the "Calculate" label. The result will appear in the answer box below the "Calculate" button.

Based on the practical examples we have shown for adding and subtracting mixed numbers, you should be able to perform other mathematical operations. These include multiplying and dividing mixed numbers, finding fractions from a mixed number, etc. You should input the mixed fractions in the boxes and choose the operator that will solve the mathematical problem.

Multiplying Mixed Numbers

Multiplication of mixed numbers is a fundamental mathematical operation that's crucial in various fields of study and everyday calculations. The Mixed Number Calculator simplifies this process, making it accessible for everyone from students to professionals. To understand how to multiply mixed numbers, let's delve into the process and see how our calculator simplifies these computations.

The Process of Multiplying Mixed Numbers

When you multiply mixed numbers, the first step is to convert them into improper fractions. An improper fraction is where the numerator is greater than or equal to the denominator. For instance, to multiply \$3 \frac{1}{4}\$ by \$2 \frac{2}{3}\$, you would first convert these mixed numbers into improper fractions.

1. Convert the Mixed Numbers: For \$3 \frac{1}{4}\$, multiply the whole number (3) by the denominator (4) and add the numerator (1), giving you \$\frac{13}{4}\$. Similarly, for \$2 \frac{2}{3}\$, you get \$\frac{8}{3}\$.
2. Multiply the Fractions: Now, multiply the two improper fractions: \$\frac{13}{4} \times \frac{8}{3}\$.
3. Multiply the Numerators: Multiply the numerators of the fractions (13 and 8), which equals 104.
4. Multiply the Denominators: Similarly, multiply the denominators (4 and 3), which equals 12.
5. Simplify the Fraction: You now have \$\frac{104}{12}\$. Simplify this fraction to its lowest terms to get the final answer.

Simplifying the Result

The Mixed Number Calculator also helps in simplifying the result. For the above example, \$\frac{104}{12}\$ simplifies to \$\frac{26}{3}\$, or in mixed number form, \$8 \frac{2}{3}\$. Simplification involves finding the greatest common divisor of the numerator and the denominator and dividing both by this number.

Dividing Mixed Numbers

Dividing mixed numbers is another critical operation in mathematics, often encountered in various real-world applications, from academic problems to everyday scenarios. The Mixed Number Calculator streamlines the division of mixed numbers, offering an easy-to-follow method. Let's explore the steps involved in dividing mixed numbers and how the calculator aids in this process.

The Procedure for Dividing Mixed Numbers

Dividing mixed numbers involves a few straightforward steps. To illustrate, consider dividing \$5 \frac{1}{2}\$ by \$2 \frac{3}{4}\$.

1. Convert to Improper Fractions: The first step is converting each mixed number into an improper fraction. For \$5 \frac{1}{2}\$, the improper fraction is \$\frac{11}{2}\$. For \$2 \frac{3}{4}\$, it's \$\frac{11}{4}\$.

2. Reciprocal of the Divisor: Take the reciprocal (inverse) of the divisor. The reciprocal of \$\frac{11}{4}\$ is \$\frac{4}{11}\$.

3. Multiply the Fractions: Multiply the improper fraction of the dividend (the number being divided) by the reciprocal of the divisor. So, multiply \$\frac{11}{2}\$ by \$\frac{4}{11}\$.

4. Multiply the Numerators and Denominators: Multiply the numerators together and the denominators together. You get \$\frac{11 \times 4}{2 \times 11} = \frac{44}{22}\$.

5. Simplify the Result: Simplify the resulting fraction to the lowest terms. \$\frac{44}{22}\$ simplifies to 2.

Basic Knowledge of Mixed Numbers

In mathematics, a fraction is a number representing part or more of a unit. A fraction is written as two numbers, usually separated by a horizontal line indicating a division sign. The number above the line is the numerator. The number below the line is called the denominator. The denominator of a fraction is the number of equal parts of the whole divided into. And the numerator is the number of those parts of the whole taken.

Fractions can be proper or improper. A proper fraction is a fraction with a numerator smaller than the denominator. If the numerator is larger than the denominator, it is an improper fraction.

A mixed number is a fraction written as a whole number and a proper fraction. It is understood as the sum of the number and the fractional part. A fraction that does not have an integer part is called a simple fraction.

You can convert mixed numbers into improper fractions by multiplying the whole number with the denominator of the proper fraction and adding the product to the numerator of the proper fraction. The denominator remains unchanged.