Addition of Fractions: Definition, Methods & Real-World Applications

Imagine you and your friends are eating pizza together. Your friend eats two-fourths of the pizza while you take one-fourth. In total, how much of the pizza has been consumed? You must add fractions to find out! Everyday chores like budgeting, cooking, and even engineering computations require an understanding of fraction addition.

In this article, we will examine:

• What is mean by fraction addition?
• How do we add fractions of different cases?
• How does fraction addition is related to real-life?

What are fractions?

A whole is made up of fractions. The numerator and the denominator are the two components that make up a fraction. When a is the numerator and b is the denominator, and b cannot be 0, a fraction is generally represented as a/b.

Determining the sum of two or more fractions is known as fraction addition. With the aid of the following example, let's now examine the fundamental procedures for adding fractions.

Addition of fractions

Combining two or more fractional values to find their sum is known as adding fractions. There are different cases in addition of fractions such as addition of like fractions, unlike fractions, mixed fractions, and fractions with a whole number.

Case 1: Adding Fractions with the Same Denominator (Like fractions)

When two like fractions are added, numerators must be added and the denominator must be retained.
a/b + c/b = (a + c)/b

Example:

2/7 + 3/7 = 5/7
Here, we add the numerators while maintaining the denominator at 7.
2/7 + 3/7 = (2+3)/7 = 5/7 is one way to describe this. This results in a 5/7 total.

Case 2: Adding Fractions with Different Denominators (unlike fractions)

The fractions are referred to be unlike fractions when the denominators differ. Converting an unlike fraction into a like fraction is the first step is to add two unlike fractions. An unlike fraction can be converted into a like fraction by determining the Least Common Multiple (LCM) of the denominators. When the like fractions are obtained, use the same procedure discussed in the previous case to perform the addition.

Example:

1/4 + 1/6
Step 1: We determine the LCM of 4 and 6 to make them equal because the given fraction is an unlike fraction. 12 is the LCM of 4 and 6.
Step 2: To convert the given fraction to like fractions, multiply 1/4 by 3/3 and 1/6 by 2/2.
1/4 = (1×3)/(4×3) = 3/12
1/6 = (1×2)/(6×2) = 2/12
Step 3: Since the given fractions are converted into like fractions, we add the numerators while maintaining the denominator at 12.
3/12 + 2/12 = (2+3)/12 = 5/12 is one way to describe this. This results in a 5/12 total.

Case 3: Adding Fractions with Whole Numbers

Combining and expressing them as a mixed fraction is a simple method of adding a whole integer and a proper fraction. For example, 3 + 1/4 can be summed up to 3 + 1/4 = 3 1/4. To add fractions with whole numbers, there is an alternative technique as well. Let's use the following example to understand that better.

Example

4 + 1/2
Step 1: Using this strategy, we write 1 as the denominator to convert the entire integer to its fractional form. Since 4 is a whole number in this case, it can be expressed as 4/1.
Step 2: Now add 4/1 + 1/2 using the procedures followed in the previous cases.
4/1 = (2×4)/(2×1) = 8/2
1/2 = (1×1)/(2×1) = 1/2
8/2 + 1/2 = 9/2

Case 4: Adding two mixed fractions

The same rules that apply to adding fractions also apply when adding mixed numbers. Converting the mixed fractions to improper fractions is the only additional step. Let's look at an example to understand this better.

Example

4 1/2 + 3 1/5
Step 1: Convert the given fractions into improper fractions.
4 1/2 = 9/2 and 3 1/5 = 16/5.
Step 2: Convert the obtained unlike fractions into like fractions using steps discussed in the previous cases.
9/2 = (9×5)/(2×5) = 45/10
16/5 = (16×2)/(5×2) = 32/10
Step 3: Add the numerators of the obtained like fractions and retain the denominator.
45/10 + 32/10 = 77/10

Practice Questions

Test yourself with these problems:

1. Add 3/5 + 2/5.
2. Add 4/5 + 6/7.
3. Add 3 + 1/7.
4. Add 3 1/2 + 4 1/3.

Real-World Applications of Adding Fractions

• Cooking & Baking: Adjusting the ingredients of a recipe (e.g., adding 1/3 cup of flour to 1/4 cup).
• Finance: Summing tax rates, discounts, or interests.
• Construction & Engineering: Measuring materials in fractional inches or meters.
• Sports & Fitness: Tracking scores that involve fractions.

A basic idea that makes arithmetic easier in daily life is the addition of fractions. Knowing how to add fractions makes problem-solving simpler and more effective, whether you're working on engineering projects, managing finances, or double a recipe!