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Chapter 5: Problem 90

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(2 \frac{1}{8}+3 \frac{3}{4}\)

Short Answer

Expert verified
The answer to the given operation \(2 \frac{1}{8}+3 \frac{3}{4}\) is \(5 \frac{7}{8}\).

Step by step solution

01

Convert mixed numbers into improper fractions

Firstly, convert each mixed number into an improper fraction. An improper fraction is a fraction in which the numerator is greater than the denominator. For \(2 \frac{1}{8}\), multiply the whole number (2) with the denominator (8) and add the numerator (1): \(2*8+1 = 17\). So, it becomes \(\frac{17}{8}\). Do the same with \(3 \frac{3}{4}\): multiplying the whole number (3) with the denominator (4) and then adding the numerator (3): \(3*4+3 = 15\), thus it becomes \(\frac{15}{4}\).
02

Add the improper fractions

Next, add the two improper fractions \(\frac{17}{8} + \frac{15}{4}\). Before adding these two fractions, the denominators must be the same. To make denominators the same, multiply the numerator and denominator of the second fraction by 2. It becomes \(\frac{30}{8}\). Now, both fractions have the same denominator, therefore they can be added: \(\frac{17}{8} + \frac{30}{8} = \frac{47}{8}\).
03

Convert back into a mixed number

Once the addition has been performed, convert the resulting improper fraction back into a mixed number. This entails dividing the numerator (47) by the denominator (8) to get a quotient and a remainder. The quotient becomes the whole number part, the remainder becomes the numerator, and the denominator stays the same: \(47 梅 8 = 5\) remainder 7, thus the mixed number becomes \(5 \frac{7}{8}\).

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Most popular questions from this chapter

What is the common difference in an arithmetic sequence?

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. \(0.0007,-0.007,0.07,-0.7, \ldots\)

What is an arithmetic sequence? Give an example with your description.

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. \(3,12,48,192, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=10, r=-4\)
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