Problem 88 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{7}{30}-\frac{5}{24}$$

Step-by-Step Solution

Answer

The result of the operation \(\frac{7}{30}-\frac{5}{24}\) is \(\frac{1}{40}\).

Step 1: Find a common denominator

To add or subtract fractions, they must have the same denominator. In this case 30 and 24 are not the same, so a common denominator needs to be found. This can be done by finding the Least Common Multiple (LCM) of the two denominators. Given the numbers 30 and 24, the LCM is \(30*24 = 720\). So, the common denominator is 720.

Step 2: Convert the fractions

Next is to express the two fractions in terms of the common denominator. The first fraction becomes \(\frac{7}{30} * \frac{24}{24} = \frac{168}{720}\) and the second fraction becomes \(\frac{5}{24} * \frac{30}{30} = \frac{150}{720}\). So now the problem is \(\frac{168}{720}-\frac{150}{720}\).

Step 3: Perform the subtraction

Now that the fractions have the same denominators, we can proceed to subtract the numerators: \(168 - 150 = 18\). This gives the fraction \(\frac{18}{720}\) as a result of the subtraction.

Step 4: Reduce to Simplest Form

The final step is to simplify the resulting fraction to its lowest terms. The numerator 18 and the denominator 720 have a greatest common divisor of 18. When we divide both by this number, we get \(\frac{18}{720} = \frac{1}{40}\). This is the simplest form of the fraction.