looking at where you got to and got stuck, let's see what we can do, if anything, to further simplify it. the original expression is: 3/4x(1/25/8)+(3/8x) you got: 3/4x(1/8)+(3/8x) looks like you were able to simplify (1/2  5/8) correctly. to simplify further, you have to perform the operations indicated. +(3/8x) is equivalent to 3/8x x(1/8) is equivalent to 1/8x. the expression becomes 3/4 + 1/8x  3/8x 1/8x  3/8x is equal to 2/8x the expression becomes 3/4  2/8x 2/8x is equivalent to 1/4x the expression becomes 3/4  1/4x that looks like selection D. sometimes it's helpful to insert the operational symbols where they are implied. that makes it easier to analyze. your original expression was, once again: 3/4x(1/25/8)+(3/8x) after insertion of implied operational symbols, the expression becomes: 3/4  x * (1/2  5/8) + (3/8 * x) your original simplification was correct, so we'll go with that to get: 3/4  x * (1/8) + (3/8 * x) x * (1/8) is equivalent to 1/8 * x, so the expression becomes: 3/4  (1/8) * x + (3/8 * x) since multiplying a negative by another negative results in a positive, the expression becomes: 3/4 + 1/8 * x + (3/8 * x) since adding a negative is the same as subtracting a positive, the expression becomes: 3/4 + 1/8 * x  3/8 * x you combine like terms by taking + 1/8 * x  3/8 * x and combining them to get 2/8 * x. the expression becomes 3/4  2/8 * x. since 2/8 * x can be simplified to 1/4 * x, the final expression becomes: 3/4  1/4 * x. this is the same as 3/4  1/4x shown in selection D. one way to confirm you did the simplification correctly is to assign a random value to x and evaluate the original expression and the final expression using that value. if the result is the same, then you simplified correctly. i chose x = 13 at random. you can use your calculator for this to avoid unnecessary extra work in resolving fractions. i used my calculator after assigning the value of 13 to x and i got: the original expression of 3/4x(1/25/8)+(3/8x) = 2.5 the final expression of 3/4  1/4 * x = 2.5 the result was the same so i can assume my simplification is correct.
As I said, there are infinite fractions that equal to #3/8#. Therefore, I' m going to show you a way to get a fraction equivalent to #3/8#. Procedure/Step(s): 1) Pick a number that you want and make sure that that number is both numerator and denominator. Example: #4/4# 2) Multiply the fraction that you chose with #3/8# So, an equivalent fraction to#3/8# is #12/32#. I hope that helps!
All the best!
