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Last updated on September 16, 2025
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.
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
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.
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
Any arithmetic operations such as addition, subtraction, multiplication, and division are applicable on 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
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)
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
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
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:
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.
Convert the following mixed fraction to an improper fraction. 4 5/6
29/6
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
Add 2 3/4 and 1 2/4
4 1/4
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
Subtract 4 3/6 and 3 1/6
1 1/3
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
Multiply 3 2/5 and 1 2/3
5 2/3
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
Divide 5 4/7 and 3 2/5
1 76/119
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
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.