(6) \( a+\frac{1}{4} a-1 \frac{1}{6} \)
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Mind Expander
To simplify the expression \( a + \frac{1}{4} a - 1 \frac{1}{6} \), first, convert \( 1 \frac{1}{6} \) into an improper fraction. This gives us \( 1 \frac{1}{6} = \frac{7}{6} \). Now, the expression becomes \( a + \frac{1}{4} a - \frac{7}{6} \). Next, combine like terms. To do so, express \( a \) as \( \frac{4}{4} a \), so we have: \[ \frac{4}{4} a + \frac{1}{4} a = \frac{5}{4} a \] Now, your expression looks like \( \frac{5}{4} a - \frac{7}{6} \). To combine these, find a common denominator, which would be 12 here. Thus, converting \( \frac{5}{4} a \) gives \( \frac{15}{12} a \) and \( -\frac{7}{6} \) becomes \( -\frac{14}{12} \). Finally, combine them: \[ \frac{15}{12} a - \frac{14}{12} = \frac{15a - 14}{12} \] So the simplified expression is \( \frac{15a - 14}{12} \). Keep practicing combining fractions and keep an eye on improper fractions—they'll pop up more than you think! You'll turn equation gymnastics into a flawless performance in no time. Also, don't forget your arithmetic rules! They’re like the cheat codes of algebra; they’ll save you from minor mistakes and make your calculations a breeze.
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