Last updated on July 5th, 2025
A mixed number, or a mixed fraction, is a combination of a whole number with a proper fraction. Mixed numbers help us understand a quantity more simply. Let us learn more about mixed numbers in this article.
A mixed number consists of a whole number and a proper fraction combined. It represents a value greater than a whole, but it is not a whole number by itself. The parts of a mixed number include the whole number, the numerator, and the denominator. The numerator represents how many parts are taken, and the denominator shows the total number of equal parts in one whole.
The properties of mixed numbers are mentioned below:
To add mixed numbers, we have to follow the steps mentioned below:
Step 1: Convert Mixed Numbers to Improper Fractions (Optional, but Useful for Complex Problems)
For easier addition, you can convert mixed numbers into improper fractions.
Step 2: Find a Common Denominator (If Necessary)
If the fractions have different denominators, find the Least Common Denominator (LCD) and convert both fractions.
Step 3: Add Whole Numbers and Fractions Separately
Separately add the whole numbers and the fractions
Step 4: Simplify (If Necessary)
If the fraction part is improper, convert it to a mixed number and adjust the final answer. If possible, simplify the fraction.
To subtract mixed numbers, the steps are mentioned below:
Step 1: Convert Mixed Numbers to Improper Fractions (Optional, but Useful for Complex Problems)
If the mixed numbers have different denominators or borrowing is needed, converting them into improper fractions makes subtraction easier.
However, if the whole numbers and fractions can be subtracted directly, you may skip this step.
Step 2: Find a Common Denominator (If Necessary)
If the fractions have different denominators, find the Least Common Denominator (LCD) and convert both fractions.
Step 3: Subtract Whole Numbers and Fractions Separately
As it is mentioned above, subtract the whole numbers and the fractions separately
Step 4: Borrowing (If the First Fraction is Smaller than the Second)
If the fraction in the first number is smaller than that in the second, borrow 1 from the whole number and convert it into an equivalent fraction.
For converting improper fractions to mixed numbers, the following steps are used:
Step 1: Divide the Numerator by the Denominator
Perform long division to divide the numerator by the denominator.
Step 2: Write the Whole Number
The quotient from Step 1 becomes the whole number of the mixed number.
Step 3: Use the Remainder as the New Numerator
The remainder from Step 1 becomes the numerator of the fraction.
The denominator remains the same.
Step 4: Write the Mixed Number
Combine the whole number and fraction to form the mixed number.
To convert mixed numbers to improper fractions, follow the steps mentioned below:
Step 1: Identify the Whole Number and Fraction
A mixed number consists of a whole number and a fraction (numerator/denominator)
Step 2: Multiply the Whole Number by the Denominator
Multiply the whole number by the denominator of the fraction.
Whole Number×Denominator
Step 3: Add the Numerator to the Result
Take the result from Step 2 and add the numerator of the fraction.
Step 4: Place the Sum Over the Original Denominator
Write the result from Step 3 as the numerator, keeping the denominator the same.
To convert mixed numbers to decimals, follow the steps mentioned below:
Step 1: Identify the Whole Number and Fraction
A mixed number consists of a whole number and a fraction.
Example: Convert 3 ½ to a decimal.
Whole number = 3
Fraction = ½
Step 2: Convert the Fraction to a Decimal
To convert the fraction to a decimal, divide the numerator by the denominator.
1/2 = 1 ÷ 2 = 0.5
So, ½ = 0.5
Step 3: Add the Decimal to the Whole Number
Now, add the decimal from Step 2 to the whole number.
3+0.5=3.5
Therefore, 3 ½ = 3.5 in decimal form.
The mixed numbers have numerous applications across various fields. Let us explore how mixed numbers are used in different areas:
Cooking and Baking: Mixed numbers are essential in cooking and baking, where ingredients are measured precisely, such as 2 ½ cups of flour or 3 ¾ teaspoons of sugar. These measurements ensure that flavors and textures are balanced and that recipes turn out as expected.
Construction and Carpentry: Mixed numbers are used in measuring materials for construction. For measuring the dimensions like 4 ⅜ inches or 6 ½ feet for door frame, such mixed numbers are used for accuracy.
6 ½ feet for a door frame. These precise measurements ensure that parts fit together correctly, preventing structural issues.
Time Management and Scheduling: Mixed numbers are commonly used when planning and managing time. Appointments, travel durations, and schedules often involve expressions like 1 ½ hours or 2 ¾ hours. For example, if a movie starts at 6:30 PM and lasts 1 ¾ hours, knowing how to work with mixed numbers helps determine when it will end. It will end at 8:15 PM
Students tend to make mistakes while understanding the concept of mixed numbers. Let us see some common mistakes and how to avoid them in mixed numbers:
Convert 312 to an improper fraction.
72
Multiply the whole number by the denominator:
3×2=6
Add the numerator:
6+1=7
Write over the original denominator:
72
Convert 114 to a mixed number.
234
Divide the numerator by the denominator:
11÷4=2 with a remainder of 3
The quotient is the whole number, and the remainder over the denominator is the fraction:
234
Add 214 and 323
51112
Convert each into an improper fraction:
214 = 2 * 4 + 1 4 = 94
323 = 3 * 3 + 23 = 113
Find the Common denominator:
94 = 9 * 34 * 3 = 2712
113 = 11 * 43 * 4 = 4412
Add fractions:
2712 + 4412 = 7112
Convert back to a mixed number:
71/12 = 5 remainder 11, so 51112
Simplify the mixed number 5812
523
Simplify the fraction:
8/12
Divide the numerator and denominator by 4:
8 / 412 / 4 = 23
Write the simplified number:
523
Add 338 and 258
6
Add the whole numbers:
3 + 2 = 5
Add the fractional parts:
38 + 58 = 88 = 1
Combine the sums:
5 + 1 = 6
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.