What is the rational number between (1)/(2) and (1)/(3)?

Identify fractions: Identify the two fractions between which we need to find a rational number.Average calculation: Understand that to find a rational number between two fractions, we can simply find the average of the two fractions.Calculate average: Calculate the average of the two fractions (1/2) and (1/3) by adding them together and dividing by 2. Average = ((1/2) + (1/3)) / 2Find common denominator: Find a common denominator for the fractions to add them together. The common denominator for 2 and 3 is 6. (1/2) becomes (3/6) and (1/3) becomes (2/6).Add fractions: Add the two fractions with the common denominator. (3/6) + (2/6) = (5/6)Divide sum: Divide the sum by 2 to find the average. (5/6) / 2 = (5/6) * (1/2) = (5/12)Check validity: Check if (5/12) is indeed between (1/2) and (1/3). (1/3) < (5/12) < (1/2) is true because (1/3) = (4/12) and (1/2) = (6/12).

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What is the rational number between
(1)/(2) and
(1)/(3)?

What is the rational number between $\frac{1}{2}$ and $\frac{1}{3} ?$

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Algebra 2

Evaluate rational exponents

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Q. What is the rational number between

\frac{1}{2}

and

\frac{1}{3} ?

Identify fractions: Identify the two fractions between which we need to find a rational number.
Average calculation: Understand that to find a rational number between two fractions, we can simply find the average of the two fractions by calculating \frac{\text{fraction}_1 + \text{fraction}_2}{2}.
Calculate average: Calculate the average of the two fractions $(\frac{1}{2})$ and $(\frac{1}{3})$ by adding them together and dividing by $2$ . $\newline$ Average = $\left(\frac{1}{2} + \frac{1}{3}\right) / 2$
Find common denominator: Find a common denominator for the fractions to add them together. The common denominator for $2$ and $3$ is $6$ . $(\frac{1}{2})$ becomes $(\frac{3}{6})$ and $(\frac{1}{3})$ becomes $(\frac{2}{6})$ .
Add fractions: Add the two fractions with the common denominator. $\newline$ $(\frac{3}{6}) + (\frac{2}{6}) = (\frac{5}{6})$
Divide sum: Divide the sum by $2$ to find the average. $\newline$ $\left(\frac{5}{6}\right) / 2 = \left(\frac{5}{6}\right) \cdot \left(\frac{1}{2}\right) = \left(\frac{5}{12}\right)$
Check validity: Check if $(\frac{5}{12})$ is indeed between $(\frac{1}{2})$ and $(\frac{1}{3})$ .\frac{1}{3} < \frac{5}{12} < \frac{1}{2} is true because $\frac{1}{3} = \frac{4}{12}$ and $\frac{1}{2} = \frac{6}{12}$ .