Add these two fractions:
$\frac{1}{3}+\frac{1}{6}=?$
Answer (1)
Find the least common denominator (LCD) of 3 and 6, which is 6.
Rewrite 3 1 as 6 2 .
Add the fractions: 6 2 + 6 1 = 6 3 .
Simplify the result: 6 3 = 2 1 .
2 1
Explanation
Finding a Common Denominator We need to add two fractions, 3 1 and 6 1 . To do this, we need to find a common denominator. The least common denominator (LCD) is the smallest multiple that both denominators (3 and 6) share.
Determining the LCD The least common multiple of 3 and 6 is 6. So, we will use 6 as our common denominator.
Rewriting Fractions with the LCD Now, we need to rewrite each fraction with the common denominator of 6. The fraction 6 1 already has the correct denominator. For the fraction 3 1 , we need to multiply both the numerator and the denominator by 2 to get an equivalent fraction with a denominator of 6: 3 1 = 3 × 2 1 × 2 = 6 2
Adding the Fractions Now that both fractions have the same denominator, we can add them: 6 2 + 6 1 = 6 2 + 1 = 6 3
Simplifying the Result Finally, we simplify the resulting fraction. Both the numerator and the denominator are divisible by 3: 6 3 = 6 ÷ 3 3 ÷ 3 = 2 1
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 1 cup of flour and you only have a 6 1 cup measuring spoon, you need to know how many times to fill the 6 1 cup to get 3 1 cup. By adding 6 1 + 6 1 = 6 2 = 3 1 , you know that you need to fill the 6 1 cup measuring spoon twice.
