(8)/(9)x(4)/(5) (5)/(6)-(9)/(5)x(8)/(9)'

3 min read Jun 16, 2024

(8)/(9)x(4)/(5) (5)/(6)-(9)/(5)x(8)/(9)'

Simplifying the Expression: (8/9) x (4/5) x (5/6) - (9/5) x (8/9)

This expression involves multiplication and subtraction of fractions. To solve it, we will follow the order of operations (PEMDAS/BODMAS) and simplify step-by-step.

Step 1: Multiplication

Let's start by performing the multiplications:

(8/9) x (4/5) x (5/6):
- Multiply the numerators: 8 x 4 x 5 = 160
- Multiply the denominators: 9 x 5 x 6 = 270
- The result: 160/270
(9/5) x (8/9):
- Multiply the numerators: 9 x 8 = 72
- Multiply the denominators: 5 x 9 = 45
- The result: 72/45

Now, our expression looks like this: (160/270) - (72/45)

Step 2: Simplification (Optional)

Before subtraction, we can simplify both fractions by finding their greatest common factors:

160/270: The greatest common factor is 10.
- 160 / 10 = 16
- 270 / 10 = 27
- Simplified fraction: 16/27
72/45: The greatest common factor is 9.
- 72 / 9 = 8
- 45 / 9 = 5
- Simplified fraction: 8/5

The expression now is: (16/27) - (8/5)

Step 3: Subtraction

To subtract fractions, they must have a common denominator. The least common multiple of 27 and 5 is 135.

(16/27): Multiply numerator and denominator by 5: (16 * 5) / (27 * 5) = 80/135
(8/5): Multiply numerator and denominator by 27: (8 * 27) / (5 * 27) = 216/135

Now, the expression is: (80/135) - (216/135)

Finally, subtract the numerators and keep the denominator: (80 - 216) / 135 = -136/135

Final Answer

The simplified result of the expression (8/9) x (4/5) x (5/6) - (9/5) x (8/9) is -136/135.