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Chapter 5: Problem 8

Perform the indicated operation. \(12 \frac{1}{4}-7 \frac{1}{8}\)

Short Answer

Expert verified
Answer: The result of the subtraction is 5 1/8.

Step by step solution

01

Convert mixed fractions to improper fractions

To convert a mixed fraction to an improper fraction, we use the formula: \(\text{improper}_\text{numerator}= \text{whole part} \times \text{denominator}+\text{numerator}\). Then, put that result over the original denominator to get the improper fraction. For the first fraction: \(12 \frac{1}{4}= \frac{(12\times 4)+1}{4}= \frac{49}{4}\) For the second fraction: \(7 \frac{1}{8}= \frac{(7\times 8)+1}{8}= \frac{57}{8}\) So, the subtraction problem becomes: \(\frac{49}{4} - \frac{57}{8}\)
02

Find a common denominator and subtract the numerators

The least common multiple (LCM) of 4 and 8 is 8. So, we will convert the first fraction to have a denominator of 8. \(\frac{49}{4} \times \frac{2}{2}= \frac{98}{8}\) Now we can perform the subtraction: \(\frac{98}{8} - \frac{57}{8}= \frac{98-57}{8}= \frac{41}{8}\)
03

Convert the resulting improper fraction to a mixed fraction

To convert an improper fraction to a mixed fraction, divide the numerator by the denominator and write the remainder as a fraction. In this case, \(41 \div 8 = 5 \text{ R } 1\). So, our mixed fraction is: \(5 \frac{1}{8}\) Therefore, the result of the subtraction \(12 \frac{1}{4}-7 \frac{1}{8}\) is \(5 \frac{1}{8}\).

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Most popular questions from this chapter

Convert 287 centimeters into meters.
Translate each of the following verbal statements into equations and solve. Let \(x\) represent the unknown number. a. The quotient of a number and 5.3 is \(-6.7\) b. A number times 3.6 is 23.4 c. 42.75 is the product of a number and \(-7.5\) d. A number divided by 2.3 is 13.2 e. \(-9.4\) times a number is 47
Calculate using the order of operations. Check the results using a calculator. $$48.5-10.34+4.66$$
To convert a positive improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number part of the mixed number and the remainder becomes the numerator of the fraction part; the denominator remains unchanged.
Convert 236 grams into kilograms.
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