Mixed Number Calculator
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Mixed Number Calculator
Quickly add, subtract, multiply, and divide mixed numbers or fractions using the mixed number calculator. This tool provides an accurate answer, accompanied by a step-by-step solution that explains the calculation process.
How to Use this Mixed Fraction Calculator?
Follow the given steps to use the calculator with fractions and mixed numbers.
- Enter the first mixed number by adding the whole number, numerator, and denominator.
- Select the operator you want to use, such as addition, subtraction, multiplication, or division.
- Enter the second mixed number in the same way.
- Click the “Calculate” button to get your answer.
- View the result, which includes the mixed number, improper fraction, and decimal value.
- Scroll down if you want to see the step-by-step calculation.
What is a Mixed Number?
A mixed number is made up of a whole number and a fraction. You can use ordering pizza as an example. If you order three pizzas and eat half a pizza, you still have two and a half pizzas. You can say you have 2 1/2 pizzas. Here, "2" is the whole number, and "1/2" is the proper fraction.
Knowing how to deal with mixed numbers helps you in a variety of tasks, like measuring ingredients, chopping wood to the right size, and even more difficult tasks in math.
Standard Calculations for Solving Mixed Numbers
There are a few steps that must be followed to get the right answer.
Adding Mixed Fractions
To add mixed numbers, check the denominators. If they’re the same, add the whole numbers and numerators. If not, find a common denominator first.
Example
For example, if you want to add 1 1/2 and 2 1/4,
\text{Given: } 1\frac{1}{2} + 2\frac{1}{4}
\text{Step 1: Make denominators the same by multiplying 2} \\
\frac{1}{2} = \frac{2}{4}
\text{Step 2: Add whole numbers} \\
1 + 2 = 3
\text{Step 3: Add fractions} \\
\frac{2}{4} + \frac{1}{4} = \frac{3}{4}
\text{Step 4: Combine results} \\
\text{Final Answer} = 3\frac{3}{4}
So, 1\frac{1}{2} + 2\frac{1}{4} = 3\frac{3}{4}
Subtracting Mixed Fractions
The process is similar. However, you must find a common denominator. If the numerator becomes greater than the denominator, borrow from the whole number.
Example
For instance, if you subtract 1 3/4 from 3 1/4:
\text{Given: } 3\frac{1}{4} - 1\frac{3}{4}
\text{Step 1: Borrow from the whole number} \\
3\frac{1}{4} = 2 + \left(1 + \frac{1}{4}\right) = 2\frac{5}{4}
\text{Step 2: Subtract whole numbers} \\
2 - 1 = 1
\text{Step 3: Subtract fractions} \\
\frac{5}{4} - \frac{3}{4} = \frac{2}{4}
\text{Step 4: Simplify} \\
\frac{2}{4} = \frac{1}{2}
\text{Final Answer: } 1\frac{1}{2}
Therefore, 3\frac{1}{4} - 1\frac{3}{4} = 1\frac{1}{2}
Multiply Mixed Numbers
Multiplying mixed fractions may seem difficult. However, it’s simple. First, convert them into improper fractions, where the numerator is greater than the denominator.
Example
\text{Given: } 1\frac{1}{2} \times 2\frac{1}{3}
\text{Step 1: Convert to improper fractions} \\
1\frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2} \\
2\frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}
\text{Step 2: Multiply numerators and denominators} \\
\frac{3}{2} \times \frac{7}{3} = \frac{3 \times 7}{2 \times 3} = \frac{21}{6}
\text{Step 3: Convert to mixed number} \\
\frac{21}{6} = 3\frac{3}{6}
\text{Step 4: Simplify} \\
3\frac{3}{6} = 3\frac{1}{2}
\text{Final Answer: } 3\frac{1}{2}
Hence, 1\frac{1}{2} \times 2\frac{1}{3} = 3\frac{1}{2}
Dividing Fractions With Whole Numbers
Dividing mixed numbers also requires you to convert them into improper fractions first. Once you have your improper fractions, you use a method called "keep, change, flip."
Example
- Keep the first fraction exactly as it is.
- Change the division sign to a multiplication sign.
- Flip the second fraction upside down (this is called finding the reciprocal).
- Multiply straight across just like you did in the previous section.
This rule also applies to dividing whole numbers by fractions. Let's look at equation 3 divided by 1/4.
\text{Given: } 3 \div \frac{1}{4}
\text{Step 1: Write as a fraction} \\
3 = \frac{3}{1}
\text{Step 2: Change division to multiplication and flip the fraction} \\
\frac{3}{1} \div \frac{1}{4} = \frac{3}{1} \times \frac{4}{1}
\text{Step 3: Multiply} \\
\frac{3}{1} \times \frac{4}{1} = \frac{12}{1}
\text{Final Answer: } 12
You can use this exact method for other common problems, like 2 divided by 1/3 (which equals 6), 2 divided by 1/4 (which equals 8), or 2 divided by 1/5 (which equals 10).
Frequently Asked Questions
What is 8/5 as a mixed number?
To convert 8/5, divide 8 by 5. Five goes into eight one time, with a remainder of three. Therefore, 8/5 is 1 3/5.
What is 5/4 as a mixed number?
Divide 5 by 4. You get one with a remainder of one. The mixed number is 1 1/4.
What is 9/2 as a mixed number?
Divide 9 by 2. Two goes into nine four times with a remainder of one. The answer is 4 1/2.
How do I calculate 1/3 divided by 2?
Turn 2 into a fraction (2/1). Keep 1/3, change division to multiplication, and flip 2/1 to 1/2. Multiply 1/3 by 1/2 to get 1/6.
What is 8/3 as a mixed number?
Divide 8 by 3. Three goes into eight two times with a remainder of two. The answer is 2 2/3.
Can this tool act as a whole number fraction calculator?
Yes, you can easily use this tool to calculate operations involving only proper fractions, only whole numbers, or a mixture of both.
What is 11/4 as a mixed number?
Divide 11 by 4. Four goes into eleven two times with a remainder of three. Your result is 2 3/4.
How do you solve 2 divided by 5/12?
Write 2 as 2/1. Keep 2/1, change to multiplication, and flip 5/12 to 12/5. Multiply across to get 24/5. Convert this improper fraction to get 4 4/5.
What is 7/4 as a mixed number?
Divide 7 by 4. Four goes into seven one time with a remainder of three. This gives you 1 3/4.