x(1%2B1%2F8)x(1%2B1%2F15).jpeg "(1+1/3)x(1+1/8)x(1+1/15)")
Simplifying the Expression: (1+1/3)x(1+1/8)x(1+1/15)
This expression involves a series of multiplications of fractions. To simplify it, we can break down each individual fraction and then multiply them together.
Step 1: Simplifying Individual Fractions
- (1+1/3) : This can be simplified by finding a common denominator for 1 and 1/3. The common denominator is 3, so we get: (3/3 + 1/3) = 4/3
- (1+1/8) : Similarly, we find a common denominator for 1 and 1/8: (8/8 + 1/8) = 9/8
- (1+1/15) : Again, finding a common denominator for 1 and 1/15: (15/15 + 1/15) = 16/15
Step 2: Multiplying the Simplified Fractions
Now we have: (4/3) x (9/8) x (16/15)
To multiply fractions, we simply multiply the numerators together and the denominators together:
- Numerator: 4 x 9 x 16 = 576
- Denominator: 3 x 8 x 15 = 360
This gives us 576/360.
Step 3: Simplifying the Result
The fraction 576/360 can be simplified by finding the greatest common factor (GCD) of 576 and 360, which is 72. Dividing both numerator and denominator by 72, we get:
- 576/72 = 8
- 360/72 = 5
Therefore, the simplified form of the expression (1+1/3)x(1+1/8)x(1+1/15) is 8/5.