Add these two fractions: [tex]$\frac{1}{3}+\frac{1}{2}=?$[/tex]
Answer (1)
Find a common denominator for the fractions, which is 6.
Rewrite the fractions with the common denominator: 3 1 = 6 2 and 2 1 = 6 3 .
Add the fractions: 6 2 + 6 3 = 6 5 .
The sum of the fractions is 6 5 .
Explanation
Problem Analysis We are asked to add two fractions: 3 1 and 2 1 . To add fractions, we need to find a common denominator.
Finding the Common Denominator The denominators of the two fractions are 3 and 2. The least common multiple (LCM) of 3 and 2 is 6. So, we will use 6 as the common denominator.
Rewriting the Fractions Now, we rewrite each fraction with the common denominator of 6. 3 1 = 3 × 2 1 × 2 = 6 2 2 1 = 2 × 3 1 × 3 = 6 3
Adding the Fractions Now that the fractions have the same denominator, we can add them: 6 2 + 6 3 = 6 2 + 3 = 6 5
Simplifying the Result The resulting fraction is 6 5 . This fraction is already in its simplest form, as 5 and 6 have no common factors other than 1.
Final Answer Therefore, the sum of the two fractions is 6 5 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 3 1 cup of flour and 2 1 cup of sugar, you need to add these fractions to determine the total amount of dry ingredients. Understanding how to add fractions helps in accurately following recipes and achieving the desired results in the kitchen. This skill is also useful in various other real-life situations where proportional quantities need to be combined.
