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The equation of a line is given as 13x+16y=4 . If Rashonda wants to clear the fractions, by what number should she multiply the...Question
the equation of a line is given as 1/3x+1/6y=4 if rashonda wants to clear the fractions, by what number should she multiply the equation?
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Answered by
GPT-4o mini
To clear the fractions in the equation \( \frac{1}{3}x + \frac{1}{6}y = 4 \), Rashonda can multiply every term in the equation by the least common multiple (LCM) of the denominators (3 and 6).
The LCM of 3 and 6 is 6.
So, Rashonda should multiply the entire equation by 6:
\[
6 \left(\frac{1}{3}x\right) + 6 \left(\frac{1}{6}y\right) = 6 \cdot 4
\]
Calculating that gives:
\[
2x + y = 24
\]
Thus, by multiplying the equation by 6, she will clear the fractions.
The LCM of 3 and 6 is 6.
So, Rashonda should multiply the entire equation by 6:
\[
6 \left(\frac{1}{3}x\right) + 6 \left(\frac{1}{6}y\right) = 6 \cdot 4
\]
Calculating that gives:
\[
2x + y = 24
\]
Thus, by multiplying the equation by 6, she will clear the fractions.
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