$\frac{12}{5}+\frac{4}{3}=$
Answer (1)
Find the least common denominator (LCD) of 5 and 3, which is 15.
Convert both fractions to equivalent fractions with the LCD: 5 12 = 15 36 and 3 4 = 15 20 .
Add the equivalent fractions: 15 36 + 15 20 = 15 56 .
The final answer is 15 56 .
Explanation
Understanding the Problem We are asked to add two fractions: 5 12 and 3 4 . To add fractions, we need to find a common denominator.
Finding the Common Denominator The least common denominator (LCD) of 5 and 3 is 15. We need to convert both fractions to equivalent fractions with a denominator of 15.
Converting the First Fraction To convert 5 12 to a fraction with a denominator of 15, we multiply both the numerator and denominator by 3: 5 12 = 5 × 3 12 × 3 = 15 36 .
Converting the Second Fraction To convert 3 4 to a fraction with a denominator of 15, we multiply both the numerator and denominator by 5: 3 4 = 3 × 5 4 × 5 = 15 20 .
Adding the Fractions Now that both fractions have the same denominator, we can add them: 15 36 + 15 20 = 15 36 + 20 = 15 56 .
Simplifying the Result The fraction 15 56 is an improper fraction. We can convert it to a mixed number by dividing 56 by 15. 56 divided by 15 is 3 with a remainder of 11. So, 15 56 = 3 15 11 . However, the question asks for the result of the addition, so we can leave the answer as an improper fraction.
Final Answer Therefore, the sum of the two fractions is 15 56 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you are baking a cake and the recipe calls for 2 1 cup of flour and 4 1 cup of sugar, you need to be able to add these fractions to know the total amount of dry ingredients. Understanding how to add fractions is a fundamental skill that helps in many practical situations.
