Answer :
Sure! Let's work through this question step by step.
We are given the equation:
[tex]\[\frac{1}{5} + s = \frac{32}{40}\][/tex]
### Part A: Find possible values of [tex]\( s \)[/tex]
To find the possible value of [tex]\( s \)[/tex], we need to isolate [tex]\( s \)[/tex] on one side of the equation. Here’s how we can do that:
1. Start with the equation:
[tex]\[\frac{1}{5} + s = \frac{32}{40}\][/tex]
2. To solve for [tex]\( s \)[/tex], subtract [tex]\(\frac{1}{5}\)[/tex] from both sides:
[tex]\[s = \frac{32}{40} - \frac{1}{5}\][/tex]
3. To subtract these fractions, we should rewrite [tex]\(\frac{1}{5}\)[/tex] with the same denominator as [tex]\(\frac{32}{40}\)[/tex]. Since the denominator 40 is a multiple of 5, we can convert [tex]\(\frac{1}{5}\)[/tex] to a fraction with denominator 40:
[tex]\(\frac{1}{5} = \frac{8}{40}\)[/tex] (since [tex]\(5 \times 8 = 40\)[/tex])
4. Now subtract the fractions:
[tex]\[s = \frac{32}{40} - \frac{8}{40} = \frac{32 - 8}{40} = \frac{24}{40}\][/tex]
So, one possible value for [tex]\( s \)[/tex] is [tex]\(\frac{24}{40}\)[/tex].
### Part B: Solve for the variable [tex]\( s \)[/tex]
To provide the simplest form of the solution, let's simplify the fraction [tex]\(\frac{24}{40}\)[/tex]:
1. Find the greatest common divisor (GCD) of 24 and 40, which is 8.
2. Divide both the numerator and the denominator by 8:
[tex]\[\frac{24}{40} = \frac{24 \div 8}{40 \div 8} = \frac{3}{5}\][/tex]
Therefore, the solution for [tex]\( s \)[/tex] is [tex]\(\frac{3}{5}\)[/tex].
In summary:
- Possible value of [tex]\( s \)[/tex] is [tex]\(\frac{24}{40}\)[/tex].
- Simplified value of [tex]\( s \)[/tex] is [tex]\(\frac{3}{5}\)[/tex].
We are given the equation:
[tex]\[\frac{1}{5} + s = \frac{32}{40}\][/tex]
### Part A: Find possible values of [tex]\( s \)[/tex]
To find the possible value of [tex]\( s \)[/tex], we need to isolate [tex]\( s \)[/tex] on one side of the equation. Here’s how we can do that:
1. Start with the equation:
[tex]\[\frac{1}{5} + s = \frac{32}{40}\][/tex]
2. To solve for [tex]\( s \)[/tex], subtract [tex]\(\frac{1}{5}\)[/tex] from both sides:
[tex]\[s = \frac{32}{40} - \frac{1}{5}\][/tex]
3. To subtract these fractions, we should rewrite [tex]\(\frac{1}{5}\)[/tex] with the same denominator as [tex]\(\frac{32}{40}\)[/tex]. Since the denominator 40 is a multiple of 5, we can convert [tex]\(\frac{1}{5}\)[/tex] to a fraction with denominator 40:
[tex]\(\frac{1}{5} = \frac{8}{40}\)[/tex] (since [tex]\(5 \times 8 = 40\)[/tex])
4. Now subtract the fractions:
[tex]\[s = \frac{32}{40} - \frac{8}{40} = \frac{32 - 8}{40} = \frac{24}{40}\][/tex]
So, one possible value for [tex]\( s \)[/tex] is [tex]\(\frac{24}{40}\)[/tex].
### Part B: Solve for the variable [tex]\( s \)[/tex]
To provide the simplest form of the solution, let's simplify the fraction [tex]\(\frac{24}{40}\)[/tex]:
1. Find the greatest common divisor (GCD) of 24 and 40, which is 8.
2. Divide both the numerator and the denominator by 8:
[tex]\[\frac{24}{40} = \frac{24 \div 8}{40 \div 8} = \frac{3}{5}\][/tex]
Therefore, the solution for [tex]\( s \)[/tex] is [tex]\(\frac{3}{5}\)[/tex].
In summary:
- Possible value of [tex]\( s \)[/tex] is [tex]\(\frac{24}{40}\)[/tex].
- Simplified value of [tex]\( s \)[/tex] is [tex]\(\frac{3}{5}\)[/tex].
