How do I perform the indicated operation and, if possible, simplify. And show all of my work? 7/12 + (-3/5)
7/12 + (-3/5)
First change the fractions to equivalent fractions with the same denominator.
7/12 = 35/60
3/5 = 36/60
35/60 + (-36/60) = -1/60
To perform the indicated operation of adding fractions, you can follow these steps:
Step 1: Find the least common denominator (LCD).
The LCD is the least common multiple of the denominators. In this case, the denominators are 12 and 5. To find the LCD, you can list the multiples of each denominator until you find a common multiple.
Multiples of 12: 12, 24, 36, 48, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, ...
From the above list, the least common multiple of 12 and 5 is 60. Therefore, the LCD is 60.
Step 2: Convert the fractions to have the same denominator.
To change the denominator of each fraction to the LCD (60), you need to find the equivalent fractions.
To convert 7/12 to have a denominator of 60, you need to multiply both the numerator and denominator by 5 (the result is 35/60).
To convert -3/5 to have a denominator of 60, you need to multiply both the numerator and denominator by 12 (the result is -36/60).
Step 3: Add the fractions.
Now that both fractions have the same denominator, you can add them. Simply add the numerators together while keeping the denominator the same.
35/60 + (-36/60) = (35 - 36)/60 = -1/60
Step 4 (Optional): Simplify the fraction.
In this case, the fraction -1/60 cannot be simplified any further because the numerator (-1) and the denominator (60) have no common factors other than 1.
So, the sum of 7/12 + (-3/5) is equal to -1/60.
Remember to show all your work, including finding the LCD, converting the fractions, and adding them together.