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Use the equation 1 over 5 + s = 32 over 40 to answer the following 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

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Answer :

  • s = 3/5

Explanation :

firstly, let's rewrite the equation mathematically :

  • 1/5 + s = 32/40

part A :

In order to find the possible value of s ,we are required to isolate the variable s and solve for it .

firstly, we can carry away 1/5 to the other side i.s. the right side by changing it's symbol i.e. negative from positive

now, we can solve further by finding the least common factor of the two denominators i.e. 40 and 5 that is 40 itself and then perform the function to find the answer .

part B :

  • 1/5 + s = 32/40
  • s = 32/40 - 1/5
  • s = (32 - 8)/40
  • s = 24/40
  • s = 3/5

thus, the value of the variable 's' is 3/5.

Part A:

To find possible values of \( s \) in the equation \(\frac{1}{5} + s = \frac{32}{40}\), we can use mathematical reasoning:

1. **Common Denominator:** First, get a common denominator for both fractions. The common denominator for 5 and 40 is 40.

2. **Equivalent Fractions:** Rewrite the equation with the common denominator:
\[\frac{1}{5} + s = \frac{8}{40}.\]

3. **Subtraction:** Subtract \(\frac{1}{5}\) from both sides of the equation:
\[s = \frac{8}{40} - \frac{1}{5}.\]

4. **Simplify:** Simplify the expression on the right side to find the possible values of \( s \).

Part B:

\[ s = \frac{8}{40} - \frac{1}{5} \]

To subtract the fractions, find a common denominator (which is 40 in this case):

\[ s = \frac{8}{40} - \frac{8}{40} \]

Now subtract the numerators:

\[ s = \frac{0}{40} \]

Since the numerator is 0, the solution is:

\[ s = 0 \]

So, \( s = 0 \) is the solution to the given equation.