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Last updated on September 16, 2025

Mixed Fraction

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A whole number and a proper fraction are combined to form a mixed fraction. It is important to know about mixed fractions because they have varied applications. They are especially useful while measuring cooking ingredients and reading a clock. In this topic, we will learn more about mixed fractions.

Mixed Fraction for Vietnamese Students
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What are Mixed Fractions?

A mixed fraction is a combination of a whole number and a proper fraction. Take a look at this mixed fraction, 3 3/4 (or three and three-fourths), which is a numerical expression. Mixed fractions represent numbers greater than a whole number but less than the next whole number.  A mixed fraction can be denoted as:    

 

Whole Number + Numerator/Denominator

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Are Mixed Numbers Rational Numbers?

Any number that can be expressed as a fraction a/b is a rational number, where b is not zero and both a and b are whole numbers. Now, any mixed number can be converted to a fraction. Therefore, all mixed numbers are rational numbers. For example, take the mixed fraction 5 3/4:

 

We can then convert the mixed fraction into an improper fraction. (5 × 4) + 3 = 20 + 3 = 23/4

 

This is a rational number, in which the numerator and the denominator are whole numbers. When we divide,

23 ÷ 4 = 5.75 

 

The result is a terminating decimal, which means it stops after a certain number of digits. Therefore, 23/4 is a rational number.

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How to Represent Improper Fractions as Mixed Fractions?

In an improper fraction, the numerator is always greater than the denominator. 14/10, 3/1, and 16/13 are a few examples of improper fractions. Here, the top number is greater than the bottom number. To convert an improper fraction into a mixed fraction, follow the given steps:  

 

 

Step 1: Divide the numerator by the denominator.

 

Step 2: Identify the quotient and remainder. 

 

Step 3: Write them in the given form as Q(R/D).



Here, Q is the quotient, R is the remainder, and D is the denominator of the improper fraction. 

 

 

Let us take an example to better understand how to convert improper fractions into mixed fractions. 

Convert the improper fraction 14/5 into a mixed fraction. 

 

Step 1: We can divide the numerator by the denominator. 

14 ÷ 5

 

 

Step 2: Quotient = 2

Remainder = 4

 

 

Step 3: 2 4/5

14/5 = 2 4/5

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What are the Operations on Mixed Fractions?

Any arithmetic operations such as addition, subtraction, multiplication, and division are applicable on mixed fractions. 

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Addition of mixed fractions

We must follow certain steps while adding mixed fractions. 

 

 

Step 1: In the first step, we should convert mixed numbers to improper fractions. 

 

 

Step 2: Verify whether the denominators are equal. 

 

 

Step 3: If the denominators are the same, add the numerators and write down the answer. 

 

 

Step 4: If the denominators are different, find the LCD and convert them to like fractions. 

 

 

Step 5: Add all the numerators and find the answer. 

 

 

For example, add 1 3/5 and 2 4/5

 

Step 1: 135 =  (1×5 +3)/5 = 8/5

2 4/5 =  (2×5 +4)/5 = 14/5

 

 

Step 2: The denominators of both the fractions are 5. 

 

 

Step 3: 8/5 + 14/5 = 8 + 14/5 = 22/5

 

 

Step 4: 22 ÷ 5 → Quotient = 4, Remainder = 2;

Mixed fraction = 4 2/5

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Subtraction of mixed fractions

The given steps should be followed while subtracting mixed fractions: 

 

Step 1: Convert mixed fractions to improper fractions. 

 

Step 2: Check if the denominators are equal. 

 

Step 3: If the denominators are equal, then simply subtract the numerators. 

 

Step 4: If the denominators are different, find the LCD and adjust the fractions. 

 

Step 5: Subtract only the numerators and retain the denominator. 

 

For example, subtract 3 2/4 and 4 3/4

 

Step 1: 3 2/4 = (3×4 +2)/4 = 14/4
 4 3/4 = (4×4 +3)/4 = 19/4

 

Step 2: The denominators of both the fractions are 4.

 

Step 3: 14/4 - 19/4 = 1/4 - 19/4 = -5/4
-5/4 = -1 1/4 (Remainder positive: 1)

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Multiplying mixed fractions

The following steps are used to multiply mixed fractions:

 

Step 1: Convert the mixed fractions to improper fractions. 

 

 

Step 2: Multiply the numerators together and the denominators together. 

 

 

Step 3: The fraction can be simplified into its lowest form, or convert the product into a mixed fraction or an improper form. 

 

 

For example, multiply 2 1/4 and 3 2/4

 

Step 1: 2 1/4 = 2 × 4 + 1/4 = 8 + 1/4 = 9/4 

3 2/4 = 3 × 4 + 2/4 = 12 + 2/4 = 14/4

 

 

Step 2: 9/4 × 14/4 = 9 × 14 /4 × 4 = 126/16

 

 

Step 3: Simplify 126 and 16 by finding the greatest common divisor (GCD) of 126 and 16. 



To find the GCD, we must identify the prime factorization of 126. 
126 = 2 × 32 × 7 

The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.

Prime factorization of 16 = 24

The factors of 16 include 1, 2, 4, 8, and 16.

The greatest common divisor of 126 and 16 is 2. 

Now, we can divide the numerator and denominator by 2. 


126 ÷ 2 / 16 ÷ 2 = 63/8

 

 

Step 4: Next, we can convert the fraction into a mixed fraction. 

63 ÷ 8

Quotient = 7

Remainder = 7

63/8 = 7 7/8

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Division of mixed fractions

The given steps are followed to divide mixed fractions: 

 

Step 1: Convert the given mixed fractions to improper fractions. 

 

 

Step 2: Multiply the reciprocal of the second fraction by the first fraction. 

 

 

Step 3: The result can be simplified to its lowest form if possible, or convert the result to a mixed or improper fraction. 

 

 

For example, divide 1 1/3 and 2 2/3

Step 1:  1 1/3 = 1 × 3 + 1/3 = 4/3

2 2/3 = 2 × 3 + 2/3 = 8/3

 

 

Step 2: Now we can multiply the reciprocal of the second fraction by the first fraction.

The reciprocal of 8/3 is 3/8


4/3 × 3/8 = 12/24

 

 

Step 3: 12/24 can be simplified to 1/2

 

Therefore, 1 1/3 ÷ 2 2/3 = 1/2

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Real-Life Applications of Mixed Fractions

A mixed fraction is a number that consists of two parts: a whole and a proper fraction. In our daily lives, from cooking to construction and engineering, we use mixed fractions to represent various measurements or calculations. Here are some real-life applications of mixed fractions:

 

  • When we cook, we usually measure ingredients in mixed fractions. This helps us to easily understand the needed measurements and quantities without getting too many ingredients. For example, 2 1/2 tablespoons of coconut oil are added to 4 1/2 cups of flour.

 

  • In construction and engineering, accurate measurements are vital to work and complete projects effectively. For example, engineers use mixed fractions such as 312 to cut a piece of iron rod for a room.

 

  • We use mixed fractions for time management, which helps to estimate the time required for a task or project. It is especially useful while reading clocks.

 

  • Mixed fractions are used to denote precise numbers. Therefore, they are widely used in finance, economics, and budgeting, where accurate numbers are displayed.
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Common Mistakes and How to Avoid Them in Mixed Fractions

Students often make mistakes when performing arithmetic operations such as addition, subtraction, multiplication, and division using mixed fractions. Here are some common errors and their helpful solutions to avoid them. 

Mistake 1

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Converting Mixed Fractions to Improper Fractions Incorrectly

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Students tend to make mistakes while converting mixed fractions to improper fractions. This can be avoided by using the correct formula:

(whole number × denominator) + numerator/denominator 

 

Not using the correct formula will lead to errors. Now, let us try to convert 436 to an improper fraction.

4 3/6  = (4 × 6) + 3/6 = 27/6 

Mistake 2

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Forgetting to Convert Mixed Fractions

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Sometimes, students forget to convert the given mixed fractions into improper fractions. Therefore, keep in mind that before performing any arithmetic process, such as addition, subtraction, multiplication, or division, first convert the mixed fraction to an improper fraction. Otherwise, that leads to wrong results. 

Mistake 3

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Using the Wrong Reciprocal for Division

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For dividing the mixed fraction, it involves the reciprocal of the second fraction. Students make mistakes in finding out the reciprocal of the number. If the reciprocal of the first fraction is used instead of the second fraction, it will lead to errors.

Mistake 4

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Not Simplifying Fractions

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Students should always reduce the fractions to their simplest forms. Not simplifying the fractions can cause unnecessary confusion and incorrect answers. 

Mistake 5

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Incorrect Conversion to a Mixed Number

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Divide the numerator by the denominator after performing the arithmetic. Then write the answer as quotient (remainder/denominator) or Q(R/D).

 

E.g., when 14 is divided by 5, 

Quotient = 2

Remainder = 4

Hence, 14/5 = 2 4/5

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Solved Examples of Mixed Fractions

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Problem 1

Convert the following mixed fraction to an improper fraction. 4 5/6

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29/6

Explanation

To convert a mixed fraction to an improper fraction, we can use the formula:

Improper fraction = (Whole number × Denominator) + Numerator/Denominator 

Now, we can substitute the values.

Improper fraction = (4 × 6) + 5 = 24 + 5 = 29/6 

29/6 It is already in its lowest form. 

 

Hence, the improper fraction of the mixed fraction 4 5/6 is 29/6

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Problem 2

Add 2 3/4 and 1 2/4

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4 1/4

Explanation

We should first convert the given mixed fractions to improper fractions before adding them. 
Converting 2 3/4 we get, (2 × 4 + 3)/4 = 11/4
Converting 1 2/4 we get (1 × 4 + 2)/ 4= 6/4 
Now we can add the converted fractions.
11/4 +6/4 = 17/4
Now convert 17/4 into a mixed fraction.
Divide 17 by 4:
17 ÷ 4 
Quotient: 4
Remainder: 1
We can write the fraction in the Q(R/D) form
Therefore, 17/4 = 4 1/4

Thus, 2 3/4 + 1 2/4 = 4 1/4

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Problem 3

Subtract 4 3/6 and 3 1/6

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1 1/3

Explanation

First, we must convert the given mixed fractions to improper fractions.
Convert 4 3/6 = (4 × 6 + 3) /6= 27/6
Convert 3 1/6 = (3 × 6 +1)/6 = 19/6
Now, we can subtract 27/6 and 19/6
27/6 - 19/6 = 8/6
Next, we can simplify the obtained fraction. We can divide both the numerator and denominator by 2: 
  (8 ÷ 2) / (6  ÷ 2) = 4/3
4/3 It is an improper fraction, so we can convert it to a mixed number. 
4 ÷ 3 
Quotient = 1
Remainder = 1
So, the mixed fraction will be 1 /13
Thus, 4 3/6 - 3 1/6 = 1 1/3

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Problem 4

Multiply 3 2/5 and 1 2/3

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5 2/3

Explanation

To convert a mixed fraction into an improper fraction, use the formula: 
Improper fraction = (Whole number × Denominator) + Numerator / Denominator
Convert 3 2/5 = (3 × 5 + 2)/5 = 17/5 
Convert 1 2/3 = (1 × 3 + 2)= 5/3
Now, we can multiply the fractions.
17/5 × 5/3 = (17 ×  5) / (5 × 3) = 85/15
Next, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD). 
For that, we must find the prime factorization of both numbers. 
85 = 5 × 17
15 = 3 × 5 
The only common factor of 85 and 15 is 5. Therefore, 5 is the GCD of 85 and 15. 
Now we can divide both the numerator and the denominator by 5. 
85/15 = 85 ÷ 5 / 15 ÷ 5 = 17/3
To convert 17/3, divide 17 by 3. 
17 ÷ 3
Quotient = 5 
Remainder = 2 
Thus, 17/3 = 5 2/3
Hence, 3 2/5 × 1 2/3 = 5 2/3

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Problem 5

Divide 5 4/7 and 3 2/5

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1 76/119

Explanation

First, convert the mixed fraction to an improper fraction. 
Convert 5 4/7  = (5 × 7 + 4)/7 = 39/7
Convert 3 2/5 = (3 × 5 + 2)/5 = 17/5
Next, multiply the reciprocal of the second fraction by the first fraction.
Reciprocal of 17/5 = 5/17
Thus, 39/7 × 5/17
39 × 5 / 7 × 17 = 195/119
Now, we can convert it to a mixed fraction. 
195 ÷ 119 
Quotient = 1
Remainder = 76
So, 195/119 = 1 76/119
Therefore, 5 4/7 ÷ 3 2/5 = 1 76/119

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FAQs on Mixed Fractions

1.Define mixed fractions.

A combination of a whole number and a proper fraction is called a mixed fraction or mixed number. For example, 5 4/7, 3 2/5, and 1 1/3 are some examples of mixed fractions and have a value greater than 1.

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2.How can you convert a mixed fraction into an improper fraction?

To convert a mixed fraction to an improper fraction, we can use a formula: 

Improper fraction = (Whole number × Denominator) + Numerator / Denominator
For instance, to convert 5 4/7 = (5 × 7) + 4 = 39/7

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3.How can you convert an improper fraction into a mixed fraction?

The first step is to divide the numerator by the denominator. Then, we can use the formula, Q(R/D)

For example, to convert 17/3
Divide 17 by 3

We get a quotient of 5 and remainder is 2 
Thus, 17/3 = 5 2/3

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4.How to add mixed fractions?

Step 1: Convert the mixed fraction into an improper fraction.

 

Step 2: If the denominators are different, find a common denominator. 

 

Step 3: Add the fractions.

 

Step 4: Change the improper fraction to a mixed fraction if needed or simplify the obtained fraction.

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5.How can children in Vietnam use numbers in everyday life to understand Mixed Fraction?

Numbers appear everywhere—from counting money to measuring ingredients. Kids in Vietnam see how Mixed Fraction helps solve real problems, making numbers meaningful beyond the classroom.

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6.What are some fun ways kids in Vietnam can practice Mixed Fraction with numbers?

Games like board games, sports scoring, or even cooking help children in Vietnam use numbers naturally. These activities make practicing Mixed Fraction enjoyable and connected to their world.

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7.What role do numbers and Mixed Fraction play in helping children in Vietnam develop problem-solving skills?

Working with numbers through Mixed Fraction sharpens reasoning and critical thinking, preparing kids in Vietnam for challenges inside and outside the classroom.

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8.How can families in Vietnam create number-rich environments to improve Mixed Fraction skills?

Families can include counting chores, measuring recipes, or budgeting allowances, helping children connect numbers and Mixed Fraction with everyday activities.

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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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