Answer :
Certainly! Let's solve this equation step by step.
We have the equation:
[tex]\[
\frac{1}{5} + s = \frac{32}{40}
\][/tex]
Part A: Find possible values of [tex]\( s \)[/tex] using mathematical reasoning.
1. First, we need to make sure both fractions [tex]\(\frac{1}{5}\)[/tex] and [tex]\(\frac{32}{40}\)[/tex] have the same denominator so we can compare and solve for [tex]\( s \)[/tex].
2. Convert [tex]\(\frac{1}{5}\)[/tex] to an equivalent fraction with a denominator of 40. We can do this by multiplying both the numerator and the denominator by 8:
[tex]\[
\frac{1}{5} = \frac{1 \times 8}{5 \times 8} = \frac{8}{40}
\][/tex]
3. Now our equation looks like this:
[tex]\[
\frac{8}{40} + s = \frac{32}{40}
\][/tex]
4. To solve for [tex]\( s \)[/tex], subtract [tex]\(\frac{8}{40}\)[/tex] from both sides:
[tex]\[
s = \frac{32}{40} - \frac{8}{40}
\][/tex]
5. Subtract the numerators since the denominators are the same:
[tex]\[
s = \frac{32 - 8}{40} = \frac{24}{40}
\][/tex]
6. Simplifying [tex]\(\frac{24}{40}\)[/tex], we divide both the numerator and the denominator by their greatest common divisor, which is 8:
[tex]\[
\frac{24}{40} = \frac{24 \div 8}{40 \div 8} = \frac{3}{5}
\][/tex]
So, a possible value for [tex]\( s \)[/tex] is [tex]\(\frac{3}{5}\)[/tex].
Part B: Solve for the variable and show your work.
Based on our calculations in Part A, we've already solved for [tex]\( s \)[/tex]:
1. We found [tex]\( s = \frac{24}{40} \)[/tex].
2. Simplifying [tex]\(\frac{24}{40}\)[/tex] gives us [tex]\( \frac{3}{5} \)[/tex].
So, [tex]\( s = \frac{3}{5} \)[/tex].
In decimal form, [tex]\( \frac{3}{5} = 0.6 \)[/tex].
Therefore, the value of [tex]\( s \)[/tex] is [tex]\( 0.6 \)[/tex] or [tex]\( \frac{3}{5} \)[/tex].
We have the equation:
[tex]\[
\frac{1}{5} + s = \frac{32}{40}
\][/tex]
Part A: Find possible values of [tex]\( s \)[/tex] using mathematical reasoning.
1. First, we need to make sure both fractions [tex]\(\frac{1}{5}\)[/tex] and [tex]\(\frac{32}{40}\)[/tex] have the same denominator so we can compare and solve for [tex]\( s \)[/tex].
2. Convert [tex]\(\frac{1}{5}\)[/tex] to an equivalent fraction with a denominator of 40. We can do this by multiplying both the numerator and the denominator by 8:
[tex]\[
\frac{1}{5} = \frac{1 \times 8}{5 \times 8} = \frac{8}{40}
\][/tex]
3. Now our equation looks like this:
[tex]\[
\frac{8}{40} + s = \frac{32}{40}
\][/tex]
4. To solve for [tex]\( s \)[/tex], subtract [tex]\(\frac{8}{40}\)[/tex] from both sides:
[tex]\[
s = \frac{32}{40} - \frac{8}{40}
\][/tex]
5. Subtract the numerators since the denominators are the same:
[tex]\[
s = \frac{32 - 8}{40} = \frac{24}{40}
\][/tex]
6. Simplifying [tex]\(\frac{24}{40}\)[/tex], we divide both the numerator and the denominator by their greatest common divisor, which is 8:
[tex]\[
\frac{24}{40} = \frac{24 \div 8}{40 \div 8} = \frac{3}{5}
\][/tex]
So, a possible value for [tex]\( s \)[/tex] is [tex]\(\frac{3}{5}\)[/tex].
Part B: Solve for the variable and show your work.
Based on our calculations in Part A, we've already solved for [tex]\( s \)[/tex]:
1. We found [tex]\( s = \frac{24}{40} \)[/tex].
2. Simplifying [tex]\(\frac{24}{40}\)[/tex] gives us [tex]\( \frac{3}{5} \)[/tex].
So, [tex]\( s = \frac{3}{5} \)[/tex].
In decimal form, [tex]\( \frac{3}{5} = 0.6 \)[/tex].
Therefore, the value of [tex]\( s \)[/tex] is [tex]\( 0.6 \)[/tex] or [tex]\( \frac{3}{5} \)[/tex].
