Question
4. Express as a single fraction \[ \frac{w}{7}-\frac{w+2}{5} \]
Ask by Stephens Bartlett. in South Africa
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
\frac{-2(w + 7)}{35}
\]
Solution
To combine the fractions (w/7) - ((w + 2)/5) into a single fraction, follow these steps:
1. Find the least common denominator (LCD) for 7 and 5, which is 35.
2. Rewrite each fraction with the denominator 35:
w/7 = (5w)/35
(w + 2)/5 = (7(w + 2))/35
3. Now, subtract the second fraction from the first:
(5w - 7(w + 2))/35
4. Distribute the 7 in the numerator:
5w - 7w - 14 = -2w - 14
5. The final expression is:
(-2w - 14)/35
You can factor the numerator if desired:
-2(w + 7)/35
Thus, the given expression as a single fraction is:
-2(w + 7)/35
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Simplify this solution Mind Expander
To combine the fractions, we need a common denominator. The denominators are 7 and 5, so the least common multiple is 35. Now, we can rewrite each fraction: \[ \frac{w}{7} = \frac{5w}{35} \] \[ \frac{w+2}{5} = \frac{7(w+2)}{35} = \frac{7w + 14}{35} \] Now, we can subtract the fractions: \[ \frac{5w}{35} - \frac{7w + 14}{35} = \frac{5w - (7w + 14)}{35} = \frac{5w - 7w - 14}{35} = \frac{-2w - 14}{35} \] Thus, the expression as a single fraction is: \[ \frac{-2w - 14}{35} \]
