College

Use the equation [tex]\frac{1}{5} + s = \frac{32}{40}[/tex] to answer the questions.

Part A: Find possible values of [tex]s[/tex] using mathematical reasoning. Support your answer using the correct vocabulary. (2 points)

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

Answer :

Sure! Let's break down the solution to the equation [tex]\(\frac{1}{5} + s = \frac{32}{40}\)[/tex] step-by-step.

Part A: Understand and Simplify the Equation

1. Simplify [tex]\(\frac{32}{40}\)[/tex]:

Start by simplifying the fraction [tex]\(\frac{32}{40}\)[/tex]. Both the numerator (32) and the denominator (40) can be divided by 8, their greatest common divisor.

[tex]\[
\frac{32}{40} = \frac{32 \div 8}{40 \div 8} = \frac{4}{5}
\][/tex]

So, [tex]\(\frac{32}{40}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].

2. Rewrite the Equation:

Now, rewrite the given equation using the simplified fraction:

[tex]\[
\frac{1}{5} + s = \frac{4}{5}
\][/tex]

Part B: Solve for [tex]\(s\)[/tex]

1. Isolate [tex]\(s\)[/tex]:

To solve for [tex]\(s\)[/tex], subtract [tex]\(\frac{1}{5}\)[/tex] from both sides of the equation to isolate [tex]\(s\)[/tex]:

[tex]\[
s = \frac{4}{5} - \frac{1}{5}
\][/tex]

2. Perform the Subtraction:

Since the fractions have the same denominator, subtract the numerators directly:

[tex]\[
s = \frac{4 - 1}{5} = \frac{3}{5}
\][/tex]

So, the value of [tex]\(s\)[/tex] is [tex]\(\frac{3}{5}\)[/tex].

Since [tex]\(\frac{3}{5}\)[/tex] can also be written as a decimal, the value of [tex]\(s\)[/tex] is [tex]\(0.6\)[/tex].

Therefore, the solution to the equation is [tex]\(s = \frac{3}{5}\)[/tex] or [tex]\(s = 0.6\)[/tex].

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