Simplify S/9 - 1/6: A Step-by-Step Solution

by Alex Johnson 44 views

Let's break down how to simplify the expression $\frac{s}{9}-\frac{1}{6}$. This involves finding a common denominator and then combining the fractions. This is a fundamental skill in algebra and is crucial for solving more complex equations later on. Understanding these basic operations can greatly improve your confidence and accuracy when dealing with mathematical problems.

Finding the Common Denominator

The first step in subtracting fractions is to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the fractions. In this case, we need to find the LCM of 9 and 6.

The multiples of 9 are: 9, 18, 27, 36, ... The multiples of 6 are: 6, 12, 18, 24, ...

The least common multiple of 9 and 6 is 18. Therefore, we will rewrite both fractions with a denominator of 18.

To convert $\frac{s}{9}$ to a fraction with a denominator of 18, we multiply both the numerator and the denominator by 2:

s9×22=2s18\frac{s}{9} \times \frac{2}{2} = \frac{2s}{18}

To convert $\frac{1}{6}$ to a fraction with a denominator of 18, we multiply both the numerator and the denominator by 3:

16×33=318\frac{1}{6} \times \frac{3}{3} = \frac{3}{18}

Now, our expression looks like this:

2s18−318\frac{2s}{18} - \frac{3}{18}

Combining the Fractions

Now that we have a common denominator, we can subtract the fractions by subtracting the numerators:

2s18−318=2s−318\frac{2s}{18} - \frac{3}{18} = \frac{2s - 3}{18}

So, the simplified expression is $\frac{2s - 3}{18}$.

Analyzing the Given Options

The question provides four options:

A. $\frac{7}{9}$ B. $\frac{13}{3}$ C. $\frac{13}{18}$ D. $\frac{7}{54}$

None of these options match our simplified expression $\frac{2s - 3}{18}$. The options A, B, C, and D are all numerical values, implying that the question might have intended to provide a specific value for 's' to arrive at one of these answers. However, with the given expression, we cannot simplify it further without knowing the value of 's'. Let's explore the possible values of s to match an answer.

Find 's' for Option A: $\frac{7}{9}$

2s−318=79\frac{2s - 3}{18} = \frac{7}{9}

Multiply both sides by 18:

2s−3=79×182s - 3 = \frac{7}{9} \times 18

2s−3=142s - 3 = 14

Add 3 to both sides:

2s=172s = 17

Divide by 2:

s=172s = \frac{17}{2}

Find 's' for Option B: $\frac{13}{3}$

2s−318=133\frac{2s - 3}{18} = \frac{13}{3}

Multiply both sides by 18:

2s−3=133×182s - 3 = \frac{13}{3} \times 18

2s−3=13×62s - 3 = 13 \times 6

2s−3=782s - 3 = 78

Add 3 to both sides:

2s=812s = 81

Divide by 2:

s=812s = \frac{81}{2}

Find 's' for Option C: $\frac{13}{18}$

2s−318=1318\frac{2s - 3}{18} = \frac{13}{18}

Multiply both sides by 18:

2s−3=132s - 3 = 13

Add 3 to both sides:

2s=162s = 16

Divide by 2:

s=8s = 8

Find 's' for Option D: $\frac{7}{54}$

2s−318=754\frac{2s - 3}{18} = \frac{7}{54}

Multiply both sides by 54:

54(2s−3)18=7\frac{54(2s - 3)}{18} = 7

3(2s−3)=73(2s - 3) = 7

6s−9=76s - 9 = 7

6s=166s = 16

s=166=83s = \frac{16}{6} = \frac{8}{3}

Conclusion

Without a specific value for 's', the simplified expression is $\frac{2s - 3}{18}$. However, if we are given that s = 8, then the expression simplifies to $\frac{2(8) - 3}{18} = \frac{16 - 3}{18} = \frac{13}{18}$, which corresponds to option C. In this case, option C would be the correct answer, assuming that s = 8.

Therefore, the simplified expression is $\frac{2s - 3}{18}$. If s=8 then the answer is C.

For further learning and practice on fractions and algebraic expressions, you can visit Khan Academy's Algebra I section. This external resource offers comprehensive lessons and exercises to reinforce your understanding.