\frac{3}{4}+\frac{5}{9}=\frac{}{36}=
Answer (2)
Find a common denominator for 4 3 and 9 5 , which is 36.
Convert the fractions: 4 3 = 36 27 and 9 5 = 36 20 .
Add the fractions: 36 27 + 36 20 = 36 47 .
Solve for x in 36 47 = 27 x , which gives x = 4 141 .
The final answer is 4 141 .
Explanation
Understanding the Problem We are given the equation 4 3 + 9 5 = 27 ? and we need to find the missing number in the numerator on the right side of the equation.
Finding a Common Denominator First, we need to add the two fractions on the left side of the equation. To do this, we need to find a common denominator for the fractions 4 3 and 9 5 . The least common multiple of 4 and 9 is 36.
Converting Fractions Now we convert both fractions to have the denominator 36: 4 3 = 4 × 9 3 × 9 = 36 27 9 5 = 9 × 4 5 × 4 = 36 20
Adding the Fractions Now we can add the two fractions: 36 27 + 36 20 = 36 27 + 20 = 36 47
Setting up the Equation So we have 36 47 = 27 ? . Let the missing number be x . Then we have 36 47 = 27 x .
Solving for x To solve for x , we multiply both sides of the equation by 27: x = 36 47 × 27 = 36 47 × 27 = 4 47 × 3 = 4 141 = 35.25
Final Answer Since the original problem asks for a number to fill in the numerator, we can express the answer as a fraction. Therefore, the missing number is 4 141 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to add and equate fractions is essential for accurate calculations in these situations. For example, if you are baking a cake and need to combine 4 3 cup of flour and 9 5 cup of sugar, you need to find a common denominator to determine the total amount of dry ingredients. This problem demonstrates the importance of mastering fraction operations for practical applications.
To solve 4 3 + 9 5 = 27 ? , we convert the fractions to a common denominator of 36 and find that 36 47 = 4 141 . Therefore, the missing numerator is 4 141 .
;
