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Last updated on July 5th, 2025

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Mixed Numbers

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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.

Mixed Numbers for UAE Students
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What are Mixed Numbers

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.
 

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What are the Properties of Mixed Numbers?

 The properties of mixed numbers are mentioned below:

  • A combination of whole numbers and fractions
  • Can be converted to an improper fraction
  • Can be converted to a decimal
  • Can be used in basic arithmetic operations
  • Obeys the commutative property (for addition and multiplication)
  • Does not follow the commutative property for subtraction and division
  • Follows the associative property (for addition and multiplication)
  • Follows the identity property
     
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How to Add Mixed Numbers?

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.
 

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How to Subtract Mixed Numbers?

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.
 

Professor Greenline from BrightChamps

How to Convert Improper Fractions to Mixed Numbers?

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.
 

Professor Greenline from BrightChamps

How to Convert Mixed Numbers to Improper Fractions?

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.
 

Professor Greenline from BrightChamps

How to Convert Mixed Numbers to Decimals?

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.
 

Professor Greenline from BrightChamps

Real Life Applications of Mixed Numbers

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 
 

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Common Mistakes and How to Avoid Them in Mixed Numbers

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:

Mistake 1

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Misplacing the Whole Number and Fraction
 

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Remember that a mixed number consists of a whole number and a proper fraction (e.g., 4 ½ means 4 + ½). Always separate the whole number from the fraction properly when writing or reading a mixed number.
 

Mistake 2

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Incorrectly Converting Mixed Numbers to Improper Fractions
 

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Use the correct formula:
Improper Fraction = (Whole Number × Denominator) + Numerator over the denominator
 

Mistake 3

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Incorrectly Converting Improper Fractions to Mixed Numbers
 

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 Divide the numerator by the denominator. The quotient is the whole number. The remainder becomes the new numerator over the original denominator.
 

Mistake 4

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Forgetting to Simplify the Fraction in a Mixed Number
 

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Always check if the fraction part can be simplified. Find the greatest common divisor (GCD) and divide the numerator and denominator by it.
 

Mistake 5

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Adding Mixed Numbers Incorrectly
 

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 First convert mixed numbers to improper fractions., then find a common denominator and add. Convert back to a mixed number if needed.
 

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Solved Examples on Mixed Numbers

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Problem 1

Convert 312 to an improper fraction.

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72

Explanation

 Multiply the whole number by the denominator:
3×2=6
Add the numerator:
6+1=7
Write over the original denominator:
72
 

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Problem 2

Convert 114 to a mixed number.

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 234
 

Explanation

 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
 

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Problem 3

Add 214 and 323

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51112
 

Explanation

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
 

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Problem 4

Simplify the mixed number 5812

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 523
 

Explanation

 Simplify the fraction:
8/12
Divide the numerator and denominator by 4:
8 / 412 / 4 = 23
Write the simplified number:
523
 

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Max, the Girl Character from BrightChamps

Problem 5

Add 338 and 258

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 6

Explanation

 Add the whole numbers:
3 + 2 = 5
Add the fractional parts:
38 + 58 = 88 = 1
Combine the sums:
5 + 1 = 6
 

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FAQs on Mixed Numbers

1.How do you convert an improper fraction to a mixed number?

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2.Why do we use mixed numbers?

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3.How do you add mixed numbers?

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4.How do you subtract mixed numbers?

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5.How do you multiply mixed numbers?

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6.How can children in United Arab Emirates use numbers in everyday life to understand Mixed Numbers?

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7.What are some fun ways kids in United Arab Emirates can practice Mixed Numbers with numbers?

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8.What role do numbers and Mixed Numbers play in helping children in United Arab Emirates develop problem-solving skills?

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9.How can families in United Arab Emirates create number-rich environments to improve Mixed Numbers skills?

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Hiralee Lalitkumar Makwana

About the Author

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.

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Fun Fact

: She loves to read number jokes and games.

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