Add these two fractions: [tex]$\frac{1}{4}+\frac{3}{8}=?$[/tex]
Answer (1)
Find a common denominator for the fractions, which is 8.
Convert 4 1 to 8 2 by multiplying the numerator and denominator by 2.
Add the fractions: 8 2 + 8 3 = 8 5 .
The final answer is 8 5 .
Explanation
Finding a Common Denominator We are asked to add two fractions: 4 1 and 8 3 . To add fractions, they must have the same denominator.
Converting Fractions The least common multiple of 4 and 8 is 8. So, we need to convert 4 1 to an equivalent fraction with a denominator of 8. To do this, we multiply both the numerator and the denominator of 4 1 by 2: 4 1 = 4 × 2 1 × 2 = 8 2
Adding the Fractions Now that both fractions have the same denominator, we can add them: 8 2 + 8 3 = 8 2 + 3 = 8 5
Simplifying the Result The resulting fraction, 8 5 , is already in its simplest form, as 5 and 8 have no common factors other than 1.
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you have a pizza that is cut into 8 slices and you eat 3 slices, you have eaten 8 3 of the pizza. If a friend eats 2 slices, together you have eaten 8 3 + 8 2 = 8 5 of the pizza. Understanding how to add fractions is essential for many practical applications.
