Add these two fractions: [tex]$\frac{1}{2}+\frac{3}{8}=?$[/tex]
Answer (1)
Find a common denominator for the fractions, which is 8.
Convert 2 1 to 8 4 .
Add the fractions: 8 4 + 8 3 = 8 7 .
The final answer is 8 7 .
Explanation
Finding the Common Denominator We are asked to add two fractions, 2 1 and 8 3 . To add fractions, they must have the same denominator. The least common denominator (LCD) of 2 and 8 is 8.
Rewriting the Fractions We need to rewrite 2 1 with a denominator of 8. To do this, we multiply both the numerator and the denominator by 4: 2 1 = 2 × 4 1 × 4 = 8 4 Now we have both fractions with the same denominator: 8 4 and 8 3 .
Adding the Fractions Now we can add the fractions by adding their numerators: 8 4 + 8 3 = 8 4 + 3 = 8 7
Simplifying the Result The fraction 8 7 is already in its simplest form, as 7 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 cut into 8 slices and you eat 1 slice, you have eaten 8 1 of the pizza. If a friend eats 3 slices, they have eaten 8 3 of the pizza. Together, you and your friend have eaten 8 1 + 8 3 = 8 4 = 2 1 of the pizza.
