Question

Perform the indicated operation. \(-1 \frac{2}{5}+2 \frac{9}{10}\)

Short answer

Answer: 1 1/2

Step-by-step solution

Convert mixed numbers to improper fractions

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, follow these steps: 1. Multiply the whole number part by the denominator 2. Add the numerator to this result 3. Place the result over the original denominator For \(-1\frac{2}{5}\): 1. \(1 * 5 = 5\) 2. \(5 + 2 = 7\) 3. The improper fraction is: \(\frac{-7}{5}\) For \(2\frac{9}{10}\): 1. \(2 * 10 = 20\) 2. \(20 + 9 = 29\) 3. The improper fraction is: \(\frac{29}{10}\) Now the expression becomes: \(\frac{-7}{5} + \frac{29}{10}\)

Find the common denominator

In order to add the two fractions, we will need a common denominator. The common denominator will be the least common multiple (LCM) of the two denominators. The LCM of 5 and 10 is 10. Now, we will convert both fractions to have the same denominator: \(\frac{-7}{5} = \frac{-7}{5} * \frac{2}{2} = \frac{-14}{10}\) The expression becomes: \(\frac{-14}{10} + \frac{29}{10}\)

Perform the addition

Now we have two fractions with the same denominator and can perform the addition: \(\frac{-14}{10} + \frac{29}{10} = \frac{(-14 + 29)}{10} = \frac{15}{10}\)

Simplify the fraction if necessary

We need to check if the resulting fraction can be simplified. Since the numerator and the denominator have a common factor of 5, we can simplify: \(\frac{15}{10} = \frac{3}{2}\) Now that the fraction is in its simplest form, we can convert it back to a mixed number if necessary. In this case, it is necessary. 1. Divide the numerator by the denominator: \(3 \div 2 = 1\) (remainder 1) 2. The quotient from step 1 becomes the whole number part: \(1\) 3. The remainder from step 1 becomes the numerator of the fraction: \(\frac{1}{2}\) So, \(1 \frac{1}{2}\) is the result of the addition: \(-1 \frac{2}{5} + 2 \frac{9}{10} = 1 \frac{1}{2}\).