Answer:
1/8
Step-by-step explanation:
Simplify the following:
(1 + 3/4)/(1/2) - (1/2 + 1)^3
Hint: | Write (1 + 3/4)/(1/2) as a single fraction.
Multiply the numerator of (1 + 3/4)/(1/2) by the reciprocal of the denominator. (1 + 3/4)/(1/2) = ((1 + 3/4)×2)/1:
(3/4 + 1) 2 - (1/2 + 1)^3
Hint: | Put the fractions in 1 + 1/2 over a common denominator.
Put 1 + 1/2 over the common denominator 2. 1 + 1/2 = 2/2 + 1/2:
(1 + 3/4) 2 - (2/2 + 1/2)^3
Hint: | Add the fractions over a common denominator to a single fraction.
2/2 + 1/2 = (2 + 1)/2:
(1 + 3/4) 2 - ((2 + 1)/2)^3
Hint: | Evaluate 2 + 1.
2 + 1 = 3:
(1 + 3/4) 2 - (3/2)^3
Hint: | Put the fractions in 1 + 3/4 over a common denominator.
Put 1 + 3/4 over the common denominator 4. 1 + 3/4 = 4/4 + 3/4:
4/4 + 3/4 2 - (3/2)^3
Hint: | Add the fractions over a common denominator to a single fraction.
4/4 + 3/4 = (4 + 3)/4:
(4 + 3)/4×2 - (3/2)^3
Hint: | Evaluate 4 + 3.
4 + 3 = 7:
7/4×2 - (3/2)^3
Hint: | Express 7/4×2 as a single fraction.
7/4×2 = (7×2)/4:
(7×2)/4 - (3/2)^3
Hint: | In (7×2)/4, divide 4 in the denominator by 2 in the numerator.
2/4 = 2/(2×2) = 1/2:
7/2 - (3/2)^3
Hint: | Simplify (3/2)^3 using the rule (p/q)^n = p^n/q^n.
(3/2)^3 = 3^3/2^3:
7/2 - 3^3/2^3
Hint: | In order to evaluate 3^3 express 3^3 as 3×3^2.
3^3 = 3×3^2:
7/2 - (3×3^2)/2^3
Hint: | In order to evaluate 2^3 express 2^3 as 2×2^2.
2^3 = 2×2^2:
7/2 - (3×3^2)/(2×2^2)
Hint: | Evaluate 2^2.
2^2 = 4:
7/2 - (3×3^2)/(2×4)
Hint: | Evaluate 3^2.
3^2 = 9:
7/2 - (3×9)/(2×4)
Hint: | Multiply 2 and 4 together.
2×4 = 8:
7/2 - (3×9)/8
Hint: | Multiply 3 and 9 together.
3×9 = 27:
7/2 - 27/8
Hint: | Put the fractions in 7/2 - 27/8 over a common denominator.
Put 7/2 - 27/8 over the common denominator 8. 7/2 - 27/8 = (4×7)/8 - 27/8:
(4×7)/8 - 27/8
Hint: | Multiply 4 and 7 together.
4×7 = 28:
28/8 - 27/8
Hint: | Subtract the fractions over a common denominator to a single fraction.
28/8 - 27/8 = (28 - 27)/8:
(28 - 27)/8
Hint: | Subtract 27 from 28.
| 2 | 8
- | 2 | 7
| 0 | 1:
Answer: 1/8
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