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Use the equation \(\frac{1}{5} + s = \frac{32}{40}\) to answer the questions.

**Part A:** Find possible values of \(s\) using mathematical reasoning. Support your answer using the correct vocabulary. (2 points)

**Part B:** Solve for the variable. Show your work. (2 points)

Answer :

The question involves solving for 's' in the equation 'one fifth plus s equals 32 over 40'. The possible value for 's' is '3 over 5' or '0.6', confirmed by simplifying the fraction and isolating 's' in the equation.

The student's question involves finding possible values for a variable 's' using the equation one fifth plus s equals 32 over 40 and then solving for 's'.

Part A: Finding possible values of 's'

To find possible values for 's', we can use the concept of equivalent fractions. The fraction 32 over 40 can be simplified to 4 over 5 by dividing both the numerator and the denominator by 8. Since one fifth plus s equals 4 over 5, we know that s must be the difference between 4/5 and 1/5, which is 3 over 5 or 0.6.

Part B: Solving for 's'

  1. Convert the given equation into fractions: 1/5 + s = 32/40.
  2. Simplify the right side of the equation by reducing the fraction: 32/40 = 4/5.
  3. Write the equation with the simplified fraction: 1/5 + s = 4/5.
  4. Subtract 1/5 from both sides of the equation to isolate 's': s = 4/5 - 1/5.
  5. Solve for 's': s = 3/5 or s = 0.6.

Upon solving, we find that the value of 's' is 3 over 5 or 0.6. We can check this by substituting the value back into the original equation to verify if the equality holds true, which it does.

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