Question

3 1/4 (1 1/2+1/8)²- 2 2/3​

Answer 1

$3\frac{1}{4} *(\frac{11}{2}+\frac{1}{8})^{2}-2\frac{2}{3}=3\frac{1}{4}*31\frac{41}{64}-2\frac{2}{3}=102\frac{213}{256}-2\frac{2}{3}=100\frac{127}{768}$

Answer 2

To simplify the expression, let's break it down step by step:

1. Start with the expression inside the parentheses: (1 1/2 + 1/8).

   First, convert 1 1/2 to an improper fraction: 1 1/2 = 3/2

   Now, add 3/2 to 1/8: 3/2 + 1/8 = 12/8 + 1/8 = 13/8

2. Square the result from step 1: (13/8)²

   To square a fraction, square both the numerator and the denominator: (13/8)² = (13²)/(8²) = 169/64

3. Now, let's go back to the original expression with the simplified parentheses: 3 1/4 * (169/64) - 2 2/3

4. Convert the mixed numbers to improper fractions: 3 1/4 = 13/4 2 2/3 = 8/3

5. Now, we have the expression as: (13/4) * (169/64) - (8/3)

6. Multiply the fractions: (13/4) * (169/64) = (13 * 169) / (4 * 64) = 2197/256

7. Subtract the result from step 6 from 8/3: (8/3) - (2197/256)

8. To subtract fractions, they need a common denominator. In this case, the common denominator is 256. Convert 8/3 to have a denominator of 256: (8/3) * (256/256) = (8 * 256) / (3 * 256) = 2048/768

9. Now, subtract the fractions: (2048/768) - (2197/256)

10. To subtract fractions, they need a common denominator. In this case, the common denominator is 768. Convert 2197/256 to have a denominator of 768: (2197/256) * (3/3) = (2197 * 3) / (256 * 3) = 6591/768

11. Now, subtract the fractions with a common denominator of 768: (2048/768) - (6591/768)

12. Subtract the numerators while keeping the common denominator: (2048 - 6591) / 768 = (-4543) / 768

So, the simplified expression is: -4543/768

You can further simplify this fraction by finding the greatest common divisor (GCD) of the numerator and denominator, but it's unlikely that it simplifies further.