Pregunta
2. Express as a single fraction \[ \frac{w}{2}-\frac{w+1}{7} \]
Ask by Davey Sullivan. in South Africa
Feb 24,2025
Solución de inteligencia artificial de Upstudy
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The single fraction is \( \frac{5w - 2}{14} \).
Solución
To combine the fractions into a single fraction, we first identify a common denominator. The denominators are 2 and 7, and their least common denominator is 14.
Rewrite each term with denominator 14:
w/2 = (7w)/14 (multiply numerator and denominator by 7)
(w + 1)/7 = (2(w + 1))/14 (multiply numerator and denominator by 2)
Now, subtract the fractions:
(7w)/14 − 2(w + 1)/14 = [7w − 2(w + 1)]/14
Distribute the 2 in the numerator:
7w − 2w − 2 = 5w − 2
So the combined fraction is:
(5w − 2)/14
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Simplifique esta solución Mind Expander
To combine the fractions \( \frac{w}{2} \) and \( -\frac{w+1}{7} \), we first need to find a common denominator, which in this case is 14. Rewriting the fractions, we have: \[ \frac{w}{2} = \frac{7w}{14} \] \[ -\frac{w+1}{7} = -\frac{2(w+1)}{14} = -\frac{2w + 2}{14} \] Now we can combine them: \[ \frac{7w}{14} - \frac{2w + 2}{14} = \frac{7w - (2w + 2)}{14} \] Simplifying the numerator: \[ 7w - 2w - 2 = 5w - 2 \] So the combined fraction is: \[ \frac{5w - 2}{14} \] Thus, the final answer is: \[ \frac{5w - 2}{14} \]
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