112 LearnersLast updated on June 18th, 2025
Addition of Fractions
Unlike regular addition, where we simply add numbers together, adding fractions requires a slightly different method. The addition of fractions is simple and can be done easily if the denominators are equal. In this topic, we are going to talk about the addition of fractions.
How to Add Fractions?
Fractions are part of a whole and are made up of two parts: a numerator and a denominator, which is separated by a bar. We represent the fraction as a/b. Where ‘a’ is the numerator and ‘b’ is the denominator. The addition of fractions is finding the sum of two or more fractions. There are various types of fractions, and each type has a slightly different way of adding.
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How to Add Fractions?
Fractions are part of a whole and are made up of two parts: a numerator and a denominator, which is separated by a bar. We represent the fraction as a/b. Where ‘a’ is the numerator and ‘b’ is the denominator. The addition of fractions is finding the sum of two or more fractions. There are various types of fractions, and each type has a slightly different way of adding.
Adding Fractions with Like Denominators
Fractions can have the same denominators and different numerators. To add fractions with the same denominators, we simply need to add the numerators over the common denominator.
Example: Add the fractions: 39 + 49
We can see that the fractions have the same denominator and different numerators. These fractions are called fractions.
We add the fractions as: 3 + 49 = 79
Adding Fractions with Different Denominators
To add fractions with different or unlike denominators, there are a few steps that must be followed:
Step 1: Identify the denominators of the given fractions before adding them.
Step 2: Determine the lowest common denominator of the denominators of the fractions
Step 3: Multiply the numerator and denominator by the same number to make the denominators of all fractions equal.
Step 4: Add the numerators of all the fractions while maintaining the denominator.
How to Add Mixed Fractions?
Mixed fractions (or mixed numbers) are numbers that combine a whole number and a fraction. To add a mixed number, there are a few extra steps compared to regular addition of fractions.
Step 1: Convert the mixed fraction into improper fractions. We need to multiply the whole number by the denominator and then add the numerator. The result will become our numerator, and the denominator will be the same.
Step 2: Determine the least common denominator or the lowest integer that can be divided equally by each denominator.
Step 3: Add the fractions’ numerators, while maintaining the least common denominator as the denominator.
For example: 234 and 112
We convert the mixed fractions into improper fractions
So, 234 = 114 and 112 = 32
Now, we find the common denominator. The denominators are 4 and 2, so the least common denominator of 4 and 2 is 4.
To make the denominators equal, multiply both the numerator and denominator with the least common denominator. So since 4 is the least common denominator, we need to multiply 32 with 2.
114 will be the same and 3 × 22 × 2 = 64
Now, we add the fractions: 114 + 64 =174 .
How to Add Fractions with Whole Numbers?
When converting a whole number into a fraction, we give it a denominator of 1. This helps in adding it to other fractions.
Step 1: Convert the whole number into an improper fraction. We multiply the whole number by the denominator of the given fraction. The result becomes the new numerator, and the denominator remains the same.
Step 2: Add the improper fractions and the given fraction.
Step 3: Simplify the resulting fraction if it is possible.
Common Mistakes and How to Avoid Them in Addition of Fractions.
When learning about the addition of fractions, students may make mistakes during calculations. Here are a few mistakes that students make in addition of fractions and ways to avoid them:
Mistake 1
Adding denominators instead of keeping it the same
When adding fractions, students often mistakenly add the denominators instead of keeping them the same. Remember, only the numerators should be added, while the denominator remains unchanged. This is because the denominator represents the total number of equal parts, and changing it would alter the fraction’s value.
Mistake 2
Not finding the common denominator when adding.
When adding fractions, students might add the fractions without finding the denominators. Students must make sure to find the least common denominator. Find the LCD and then add only the numerators.
Mistake 3
Not simplifying the answer.
Fractions must always be reduced to their simplest form. Students should always simplify the result after adding fractions. This makes it easier to understand and work with.
Mistake 4
Confusing mixed numbers with improper fractions
Students might often treat mixed numbers as improper fractions. This results in incorrectly calculating problems that involve mixed numbers. Always convert mixed numbers into improper fractions before adding.
Mistake 5
Confusing addition of fractions with multiplication of fractions
Students might multiply fractions instead of adding fractions. For example, 12 + 12 = 14 (this is multiplication of fractions which is incorrect). Students must know that addition requires the same denominator, while multiplication does not.
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Real life applications on Addition of Fractions
The addition of fractions is used widely in various fields. Here are a few real-world applications that use the addition of fractions:
Cooking: Recipes often require fractional measurements of ingredients. Adding the fractions would ensure accurate measurements for a perfect dish.
Construction: Builders often use fractional measurements of inches and feet. Adding fractions would ensure precise cutting and fitting of materials.
Sports: Athletes track distances in fractions. Adding the fractions of their distances would help in monitoring training progress and performance.
Solved examples on Addition of Fractions
Problem 1
Add 3/8 + 2/8
5/8
Explanation
Since the denominators are the same, simply add the numerators.
3/8 + 2/8 = 5/8
Problem 2
Add 1/4 + 1/6
5/12
Explanation
First, we find the least common denominator of 4 and 6, which is 12.
Convert the fractions: 1 × 3/4 × 3 = 3/12,
1 × 2/6 × 2 = 2/12
Add the numerators: 3/12 + 2/12 = 5/12
Problem 3
Add 21/3 + 12/3
4
Explanation
Convert the mixed numbers into improper fractions:
21/3 = 7/3,
12/3 = 5/3
Add the fractions: 7/3 + 5/3 = 12/3 = 4
Problem 4
Add 9/4 + 5/4
31/2
Explanation
Since the denominators are the same, add the numerators: 9/4 + 5/4 = 14/4
Convert to mixed number: 31/2
Problem 5
Add 1/3 + 1/4 + 1/6
9/12 = 3/4
Explanation
The least common denominator of 3, 4, and 6 is 12
Convert the fractions:
1/3 = 4/12
1/4 = 3/12
1/6 = 2/12
Add the fractions: 4/12 + 3/12 + 2/12 = 9/12 = 3/4
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FAQs on Addition of Fractions
1. What does the addition of fractions mean?
2.How do we add numbers that have the same denominator?
3.Why should the resulting fraction be simplified?
4.Can mixed numbers be added directly?
5.Is there a way to visually understand the addition of fractions?
6.How can children in United Kingdom use numbers in everyday life to understand Addition of Fractions?
7.What are some fun ways kids in United Kingdom can practice Addition of Fractions with numbers?
8.What role do numbers and Addition of Fractions play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Addition of Fractions 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.
