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Chapter 5: Problem 6

Add \(\frac{2}{7}\) and \(\frac{1}{5}\) without using a calculator.

Short Answer

Expert verified
Answer: \(\frac{17}{35}\)

Step by step solution

01

Find the least common multiple (LCM) of 7 and 5

To add two fractions, we need a common denominator. We will find the LCM of 7 and 5. Since 7 and 5 are prime numbers, their LCM is simply the product of the two numbers. LCM(7,5) = 7*5 = 35 So, we will express both fractions with a common denominator of 35.
02

Express each fraction with the common denominator 35

Now, let's express both fractions with a common denominator of 35. For \(\frac{2}{7}\), we will multiply both the numerator and the denominator by (35/7) = 5. \(\frac{2}{7} \times \frac{5}{5} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}\) For \(\frac{1}{5}\), we will multiply both the numerator and the denominator by (35/5) = 7. \(\frac{1}{5} \times \frac{7}{7} = \frac{1 \times 7}{5 \times 7} = \frac{7}{35}\) So, we now have: \(\frac{2}{7} = \frac{10}{35}\) and \(\frac{1}{5} = \frac{7}{35}\)
03

Add the two fractions with a common denominator

Now that we have both fractions with a common denominator of 35, we can add them by adding the numerators and keeping the denominator the same. \(\frac{10}{35} + \frac{7}{35} = \frac{10 + 7}{35} = \frac{17}{35}\)
04

Check if the result can be simplified

We need to check if the resulting fraction \(\frac{17}{35}\) can be simplified further. Since 17 is a prime number and has no common factors with 35, the fraction is already in its simplest form. The result of adding \(\frac{2}{7}\) and \(\frac{1}{5}\) is \(\frac{17}{35}\).

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Most popular questions from this chapter

Make the specified variable the subject of the formula: (a) \(h=c+d+2 e\), for \(e\) (b) \(S=2 \pi r^{2}+2 \pi r h\), for \(h\) (c) \(Q=\sqrt{\frac{c+d}{c-d}}\), for \(c\) (d) \(\frac{x+y}{3}=\frac{x-y}{7}+2\), for \(x\)

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