Final answer:
To add the fractions (4/7), (5/12), and (1/5), find a common denominator, which is 420. Convert each fraction and then add the numerators together. The simplified form of the sum is 1 79/420.
Step-by-step explanation:
To add the three fractions (4/7) + (5/12) + (1/5), we need to find a common denominator. The common denominators for 7, 12, and 5 would be their least common multiple (LCM), which is 420. Now we convert each fraction to an equivalent fraction with the denominator of 420:
- (4/7) becomes (4×60) / (7×60) = 240/420
- (5/12) becomes (5×35) / (12×35) = 175/420
- (1/5) becomes (1×84) / (5×84) = 84/420
Adding these equivalent fractions together:
240/420 + 175/420 + 84/420 = (240 + 175 + 84) / 420 = 499/420.
When added, the sum is greater than 1, so it could be simplified to a mixed number by dividing the numerator by the denominator:
499 ÷ 420 = 1 with a remainder of 79.
Therefore, the simplified form is:
1 whole and 79/420, which can be further simplified to:
179/420