1068 LearnersLast updated on June 5th, 2025
Proper Fraction
When the numerator is less than the denominator in a fraction, we call it a proper fraction.A proper fraction always has a value less than 1. In this topic, we will discuss proper fractions and how they differ from improper fractions.
What is Proper Fraction in Math?
A fraction contains two parts: a numerator and a denominator separated by a bar. There are various types of fractions based on the values of the numerator and denominator. A proper fraction is a type of fraction where the numerator is less than the denominator.
For example, 15/24 and 23/40 are some examples of proper fractions.
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How to find Proper Fraction?
To find whether a fraction is a proper fraction, we follow these steps:
Step 1: Identify whether the numerator is smaller than the denominator.
Step 2: Check the denominator and identify if it is greater than the numerator.
Step 3: Make sure that both numbers are positive or negative.
If the numerator < denominator, it is a proper fraction.
If the numerator ≥ denominator, it is an improper fraction.
Difference between Proper and Improper Fractions
Here are some of the main differences between improper and proper fractions:
| Proper Fraction | Improper Fraction |
| The numerator is smaller than the denominator | Greater than or equal to denominator |
| The denominator is larger than the numerator | Smaller than or equal to the numerator |
| The value of the fraction is less than 1. | The value of the fraction is 1 or more. |
| Example: 3/4, 4/6, 7/8. | Example: 5/3, 10/7. |
How to convert improper fraction to proper fraction
By converting an improper fraction into a mixed number, we will get a whole number and a proper fraction. Let us convert 17/7 to a mixed fraction using the following steps:
Step 1: We first divide the numerator by the denominator. We divide 17/7, we get the quotient which is 2, and the remainder is 3.
Step 2: The quotient is 2, which will be the whole number in the mixed fraction.
Step 3: The numerator will be the remainder, in this example the numerator is 3.
Step 4: The denominator will remain the same. So the final answer will be 2 37.
How to Add Mixed Fraction to Proper Fraction?
To add a mixed fraction and a proper fraction, we first need to convert the mixed fraction into an improper fraction. Once the mixed number is converted, we will then add both fractions in the usual way of the addition of fractions. Let us take the earlier mixed number 2 37 and add it to 4/7 .
- Convert 2 37 into an improper fraction that is 177
- Add 177 + 47 using the usual method. If the fractions have similar denominators, add the numerators directly and keep the same denominator. If the denominators are different, find the least common multiple of the denominators and adjust the fractions before adding.
- 177 + 47 = 217 = 3.
Operations on Proper Fractions
Similar to most fractions, proper fractions can be added, subtracted, multiplied, or divided with other. To add two fractions a/b and c/d, the formulas of each operation are as follows:
| Operation | Formula | Example |
| Addition |
a/b + c/d = ad + bc/bd |
1/3 + 1/6 = 2 + 1/6 = 3/6 = 1/2 |
| Subtraction | a/b - c/d = ad - bc/bd | 3/4 + 1/4 = 3 - 1/4 = 2/4 = 1/2 |
| Multiplication | a/b × c/d = ac/bd | 2/3 × 3/4 = 6/12 = 1/2 |
| Division | a/b ÷ c/d = a/b × d/c = ad/bc | 2/5 ÷ 1/2 = 2/5 × 2/1 = 4/5 |
Real-life Applications on Proper Fractions
Proper fractions are commonly used across different fields and industries. Here are a few real-world applications:
- Cooking: Proper fractions are used in recipes to measure ingredients like flour, milk, and sugar.
- Construction: During construction work, measurements like 58 inches or feet are used to cut materials efficiently and accurately.
- Finance and budgeting: Proper fractions are used in dividing money when allocating a budget or trying to divide your salary for rent and groceries.
Common Mistakes and How to Avoid Them in Proper Fractions
Students tend to get confused between proper fractions with other types of fractions. Here are a few common mistakes that students make and ways to avoid them:
Mistake 1
Confusing proper and improper fractions
Students may assume that a proper fraction is when there is both a numerator and denominator. But remember that a fraction is called a proper fraction only when the numerator is less than the denominator.
Mistake 2
Incorrectly adding proper fractions with different denominators
When adding proper fractions, students may ignore the fact that there are different denominators. Remember to find the least common denominator first and once all denominators are equal, then the numerators can be added together.
Mistake 3
Ignoring the negative sign in proper fractions
A fraction that has a negative sign is different from a positive fraction. -34 is not the same as 34. Students must always pay attention to negative signs when solving problems.
Mistake 4
Assuming larger denominators means a larger fraction
Students may assume that 17 is larger than 14 because 7 is larger than 4. This is incorrect because a larger denominator means that the fraction is smaller than the fraction with the smaller denominator.
Mistake 5
Assuming a proper fraction can be greater than 1
Students may think that a proper fraction can be greater than 1. Remember that a proper fraction is always less than 1 because the numerator is smaller than the denominator.
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Solved Examples on Proper Fractions
Problem 1
Solve 2/5 + 1/5
3/5
Explanation
The denominators are the same, so we add the numerators: 2 + 1 = 3
The denominator remains 5, so the sum is 3/5.
Problem 2
Solve 5/9 - 2/9
3/9 = 1/3
Explanation
The denominators are the same, so subtract the numerators: 5 - 2 =3
The denominators remain 9, so the result is 3/9 = 1/3
Problem 3
Solve 3/4 × 2/5
6/20 = 3/10
Explanation
Multiply the numerators: 3 × 2 = 6
Then, we multiply the denominators: 4 × 5 = 20.
We get the result 6/20 = 3/10
Problem 4
4/7 / 2/3
12/14 = 6/7
Explanation
Convert division into multiplication by flipping the second fraction (reciprocal).
4/7 × 3/2
Multiply the numerators: 4 × 3 = 12
Multiply the denominators: 7 × 2 = 14
The result we will get is: 12/14 = 6/7
Problem 5
Convert 5/8 into a decimal.
0.625
Explanation
Divide 5 by 8, and we will get 0.625.
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FAQs on Proper Fractions
1.How can we determine whether a fraction is a proper fraction?
2.Can a proper fraction be greater than 1?
3.Can a proper fraction be negative?
4.How do you convert a proper fraction to a decimal number?
5.Can 0 be in a proper fraction?
6.How can children in Vietnam use numbers in everyday life to understand Proper Fraction?
7.What are some fun ways kids in Vietnam can practice Proper Fraction with numbers?
8.What role do numbers and Proper Fraction play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Proper Fraction 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.
Fun Fact
: She loves to read number jokes and games.
