Add these two fractions:
[tex]\frac{3}{4}+\frac{2}{3}=?[/tex]
Answer (1)
Find a common denominator for the fractions 4 3 and 3 2 , which is 12.
Convert the fractions to equivalent fractions with the common denominator: 4 3 = 12 9 and 3 2 = 12 8 .
Add the equivalent fractions: 12 9 + 12 8 = 12 17 .
Express the result as a mixed number: 12 17 = 1 12 5 . The final answer is 12 17 .
Explanation
Finding a Common Denominator We need to add two fractions, 4 3 and 3 2 . To do this, we need to find a common denominator.
Determining the LCD The least common denominator (LCD) is the least common multiple (LCM) of the denominators 4 and 3. The LCM of 4 and 3 is 12.
Converting the First Fraction Now, we convert both fractions to equivalent fractions with a denominator of 12. To convert 4 3 to a fraction with a denominator of 12, we multiply both the numerator and denominator by 3: 4 3 = 4 × 3 3 × 3 = 12 9 .
Converting the Second Fraction To convert 3 2 to a fraction with a denominator of 12, we multiply both the numerator and denominator by 4: 3 2 = 3 × 4 2 × 4 = 12 8 .
Adding the Fractions Now that both fractions have the same denominator, we can add them: 12 9 + 12 8 = 12 9 + 8 = 12 17 .
Converting to a Mixed Number The result is 12 17 . This is an improper fraction, which means the numerator is greater than the denominator. We can express this as a mixed number. Divide 17 by 12 to get 1 with a remainder of 5. Therefore, 12 17 = 1 12 5 .
Final Answer Therefore, the sum of the two fractions is 12 17 or 1 12 5 .
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 4 3 cup of flour and 3 2 cup of sugar, you need to add these fractions to know the total amount of dry ingredients. Understanding how to add fractions is essential for accurate measurements and successful baking.
