((2)/(3)+(4)/(9)) Of (3)/(5)- 1(2)/(3)times1(1)/(4)-(1)/(3)

3 min read Jun 16, 2024

Solving the Mathematical Expression: ((2)/(3)+(4)/(9)) of (3)/(5)- 1(2)/(3)times1(1)/(4)-(1)/(3)

This expression involves fractions, mixed numbers, and operations like addition, subtraction, multiplication, and "of". Let's break it down step by step to find the solution.

Step 1: Simplifying the Parenthesis

First, we simplify the expression within the parenthesis:

(2/3) + (4/9) = (6/9) + (4/9) = 10/9

Step 2: "Of" Operation

The word "of" signifies multiplication. So, we multiply the simplified parenthesis by (3/5):

(10/9) of (3/5) = (10/9) * (3/5) = 2/3

Step 3: Converting Mixed Numbers to Fractions

Let's convert the mixed numbers to fractions:

1(2/3) = (3*1 + 2)/3 = 5/3
1(1/4) = (4*1 + 1)/4 = 5/4

Step 4: Multiplication and Division

Next, we perform the multiplication and division operations:

(5/3) * (5/4) = 25/12

Step 5: Combining All Terms

Now, we combine all the simplified terms:

2/3 - 25/12 - 1/3

Step 6: Finding a Common Denominator

To add and subtract fractions, we need a common denominator. The least common denominator for 3 and 12 is 12:

(2/3) * (4/4) = 8/12
(25/12)
(1/3) * (4/4) = 4/12

Step 7: Final Calculation

Finally, we perform the addition and subtraction:

(8/12) - (25/12) - (4/12) = -21/12

Simplifying the Result

The final answer can be simplified by dividing both numerator and denominator by their greatest common factor (3):

-21/12 = -7/4

Therefore, the solution to the given expression is -7/4.