[tex]\frac{3}{4}+\frac{5}{9}=+\quad+\quad=[/tex]
Answer (1)
Find the least common multiple (LCM) of the denominators 4 and 9, which is 36.
Rewrite the fractions with the common denominator: 4 3 = 36 27 and 9 5 = 36 20 .
Add the numerators: 36 27 + 36 20 = 36 47 .
The final answer is 36 47 .
Explanation
Understanding the Problem We are given the expression 4 3 + 9 5 and we need to find the sum of these two fractions.
Finding the Common Denominator To add these fractions, we need to find a common denominator. The least common multiple (LCM) of the denominators 4 and 9 will be our common denominator. The LCM of 4 and 9 is 36.
Rewriting Fractions Now, we rewrite both fractions with the common denominator of 36. To do this, we multiply the numerator and denominator of the first fraction by 9, and the numerator and denominator of the second fraction by 4: 4 3 = 4 × 9 3 × 9 = 36 27 9 5 = 9 × 4 5 × 4 = 36 20
Adding the Fractions Now that both fractions have the same denominator, we can add their numerators: 36 27 + 36 20 = 36 27 + 20 = 36 47
Final Answer The resulting fraction is 36 47 . Since 47 is a prime number and does not divide 36, the fraction is already in its simplest form. Therefore, the sum of the two fractions is 36 47 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 4 3 cup of flour and you only have 9 5 cup, you need to calculate how much more flour you need. Adding fractions is also useful when calculating distances or time. For instance, if you walk 4 3 of a mile to the store and then 9 5 of a mile to a friend's house, you can add the fractions to find the total distance you walked.
