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Chapter 1: Problem 92

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{3}{4}+\left(-\frac{3}{5}\right)=-\frac{3}{20}$$

Short Answer

Expert verified
The statement is false. The correct statement is \(\frac{3}{4} - \frac{3}{5} = \frac{3}{20}\).

Step by step solution

01

Find a Common Denominator

In order to add fractions, they must have the same denominator. In the given statement, the denominators are 4 and 5. The least common denominator (LCD) of 4 and 5 is their product, which is 20. This is because 4 and 5 have no common factors other than 1.
02

Convert Fractions to Have Common Denominator

Now, convert both fractions to equivalent fractions with denominator 20. Multiply both the numerator and denominator of \(\frac{3}{4}\) by 5 to get \(\frac{15}{20}\). Multiply both the numerator and denominator of \(-\frac{3}{5}\) by 4 to get \(-\frac{12}{20}\). The equation becomes \(\frac{15}{20} - \frac{12}{20} = -\frac{3}{20}\)
03

Perform Addition

After converting the fractions, we can now add them together. Subtract the numerators and keep the same denominator, \(\frac{15}{20}-\frac{12}{20} = \frac{3}{20}\)
04

Check Against Given Result

The result of the addition was \(\frac{3}{20}\), not \(-\frac{3}{20}\) as given in the statement. Therefore, the statement was incorrect.
05

Correct the Statement

Change the given statement from \(\frac{3}{4} + \(-\frac{3}{5}\) =\(-\frac{3}{20}\) to \(\frac{3}{4} + \(-\frac{3}{5}\) =\(\frac{3}{20}\) to make it a true statement.

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