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Chapter 5: Problem 79

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(\frac{3}{4}+\frac{3}{20}\)

Short Answer

Expert verified
\(\frac{9}{10}\)

Step by step solution

01

Identify the Least Common Multiple (LCM)

To find the LCM of the two denominators, which are 4 and 20, begin by listing the multiples of the largest number (20), and then check if the smaller number (4) can divide any of these multiples without leaving a remainder. The smallest multiple which both can divide into evenly is 20. So, the LCM of 4 and 20 is 20.
02

Convert the Fractions

Convert each fraction to an equivalent fraction with a denominator of 20. For the first fraction, multiply both the numerator and denominator by 5 because \(5 \times 4 = 20\). For the second fraction, the denominator is already 20, so no change is needed. Therefore, \(\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}\), and \(\frac{3}{20} = \frac{3}{20}\).
03

Add the Converted Fractions

Now that both fractions have the same denominator, they can be added together by keeping the denominator constant and adding the numerators. That is, \(\frac{15}{20} + \frac{3}{20} = \frac{15+3}{20} = \frac{18}{20}\).
04

Simplify the Result

The result of \(\frac{18}{20}\) can be simplified by dividing both the numerator and denominator by their common factor, 2. Doing this yields \(\frac{18 \div 2}{20 \div 2} = \frac{9}{10}\).

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Most popular questions from this chapter

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{30}\), when \(a_{1}=8000, r=-\frac{1}{2}\).

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-6, r=-5\)

Use the appropriate formula shown above to find \(2+4+6+8+\cdots+200\), the sum of the first 100 positive even integers.

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{7}\), when \(a_{1}=5, r=-2\).

If you are given a sequence that is arithmetic or geometric, how can you determine which type of sequence it is?
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