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Chapter 5: Problem 108

Find the rational number halfway between the two numbers in each pair. \(\frac{3}{5}\) and \(\frac{2}{3}\)

Short Answer

Expert verified
The rational number halfway between \(\frac{3}{5}\) and \(\frac{2}{3}\) is \(\frac{19}{30}\).

Step by step solution

01

Compute the Sum of two fractions

Firstly, add the given fractions. The sum of \(\frac{3}{5}\) and \(\frac{2}{3}\) is obtained by finding the least common denominator (LCD), which is the least common multiple (LCM) of 5 and 3, in this case, 15. Then the sum is computed as \(\frac{9 + 10}{15}\), which equals \(\frac{19}{15}\).
02

Find the Halfway Point

Now that we have the sum of the two fractions, we can find the 'halfway' point by dividing the sum by 2. So, \(\frac{\frac{19}{15}}{2} = \frac{19}{30}\).

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Most popular questions from this chapter

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=3\)

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(1.5,-3,6,-12, \ldots\)

Write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20 th term of the sequence. \(6,1,-4,-9, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-8, r=-5\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(6,-6,6,-6, \ldots\)
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