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Which expressión is equivalent to \( 5 / 6-3 / 6 \) ? \( \begin{array}{ll}\text { a. } 1 / 6+1 / 6 & \text { b. } 8 / 6-2.6\end{array} \)

Ask by Li Tran. in the United States
Feb 25,2025

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Answer

Option a (\( \frac{1}{6} + \frac{1}{6} \)) is equivalent to \( \frac{5}{6} - \frac{3}{6} \).

Solution

To simplify 5/6 - 3/6, notice that the denominators are the same so you can subtract the numerators directly:   (5 - 3)/6 = 2/6 Now, simplify 2/6 by dividing the numerator and the denominator by their greatest common divisor, which is 2:   2/6 = (2 ÷ 2)/(6 ÷ 2) = 1/3 Next, evaluate option a:   1/6 + 1/6 = (1 + 1)/6 = 2/6 = 1/3 Since both the simplified form of 5/6 - 3/6 and option a result in 1/3, option a is equivalent to the original expression.

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Beyond the Answer

First, let's simplify \( 5 / 6 - 3 / 6 \). When you subtract these two fractions with the same denominator, you subtract the numerators: \[ \frac{5 - 3}{6} = \frac{2}{6} \] Now, simplifying \( \frac{2}{6} \) gives us \( \frac{1}{3} \). To check the expression options, we can simplify the first expression \( 1/6 + 1/6 \); \[ \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \] The second expression \( 8 / 6 - 2.6 \) is more complicated. First, converting \( 2.6 \) into a fraction gives us \( 2.6 = \frac{26}{10} = \frac{13}{5} \). Finding a common denominator with \( \frac{8}{6} \) is a bit tricky here, which may lead to complications. Thus, it turns out \( 1 / 6 + 1 / 6 \) is equivalent to \( 5 / 6 - 3 / 6 \).

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