[tex]\frac{2}{3}+\frac{4}{5}[/tex]
Answer (2)
Find a common denominator for the fractions, which is 15.
Rewrite the fractions with the common denominator: 3 2 = 15 10 and 5 4 = 15 12 .
Add the fractions: 15 10 + 15 12 = 15 22 .
The final answer is 15 22 .
Explanation
Finding a Common Denominator We are asked to add two fractions: 3 2 and 5 4 . To add fractions, we need to find a common denominator. The least common multiple (LCM) of 3 and 5 is 15.
Rewriting Fractions Now, we rewrite each fraction with the common denominator of 15: 3 2 = 3 × 5 2 × 5 = 15 10 5 4 = 5 × 3 4 × 3 = 15 12
Adding the Fractions Now that both fractions have the same denominator, we can add them: 15 10 + 15 12 = 15 10 + 12 = 15 22
Simplifying the Result The fraction 15 22 is already in its simplest form, as 22 and 15 have no common factors other than 1. We can also express this as a mixed number: 1 15 7 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to add fractions is essential for accurate calculations in these situations. For example, if you need 3 2 cup of flour and 5 4 cup of sugar for a recipe, you need to add these fractions to know the total amount of dry ingredients.
To add 3 2 and 5 4 , find a common denominator of 15, rewrite the fractions as 15 10 and 15 12 , and add them to get 15 22 or 1 15 7 . The final answer is 15 22 .
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