I posted this problem the other day and someone answered it but when I checked my book I realized that I wrote the problem wrong. The answer is suppose to be 43/128 and I can't get it. Thanks
(1/4)^2/(1/2-3/4)+ 3/2^3
I think it is not correct yet. I can't make any way for those numbers to equal 43/128
I'm so sorry it's suppose to be 1/8
To solve the expression (1/4)^2 / (1/2 - 3/4) + 3/2^3 and obtain the answer of 43/128, you need to follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
1. First, simplify any operations within parentheses. Since there are no parentheses in this expression, proceed to the next step.
2. Next, evaluate any exponents. In this case, we have (1/4)^2. To simplify, square the numerator and the denominator separately: (1^2)/(4^2) = 1/16.
3. Moving on to division, divide the numerator by the denominator within the main fraction: (1/16) / (1/2 - 3/4).
4. To simplify (1/2 - 3/4), you need to find a common denominator, which is 4. Multiply the numerator and denominator of 1/2 by 2 to get 2/4. Therefore, (1/2 - 3/4) becomes (2/4 - 3/4). Subtract the numerators while keeping the common denominator: -1/4.
5. Substitute this result back into the fraction and evaluate 1/16 / -1/4: Multiply the first fraction by the reciprocal of the second fraction, which means flipping the second fraction and multiplying: (1/16) * (-4/1) = -4/16 = -1/4.
6. Moving on to addition, add -1/4 to 3/2^3.
7. The value of 2^3 is 8. Therefore, the fraction becomes 3/8.
8. Finally, substitute the simplified fraction back into the previous step: -1/4 + 3/8.
9. To add these fractions, you need to find a common denominator, which is 8. Multiply the numerator and denominator of -1/4 by 2 to get -2/8.
10. The expression now becomes -2/8 + 3/8 = 1/8.
Hence, the correct answer to the expression (1/4)^2 / (1/2 - 3/4) + 3/2^3 is 1/8, not 43/128. It seems that there might be an error in the original problem or its solution.