Adding Fractions: 1/5 + 1/6 + 1/7 as a Fraction
When dealing with fractions, it is essential to know how to add them correctly. In this article, we will explore how to add the fractions 1/5, 1/6, and 1/7 and express the result as a single fraction.
Step 1: Find the Least Common Multiple (LCM)
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which are 5, 6, and 7. The LCM of these numbers is 210.
Calculate the LCM
- Multiply the denominators: 5 × 6 × 7 = 210
- Find the prime factors of each denominator:
- 5 = 5
- 6 = 2 × 3
- 7 = 7
- Multiply the highest power of each prime factor: 2 × 3 × 5 × 7 = 210
Step 2: Convert Each Fraction to Have the LCM as the Denominator
Now, we need to convert each fraction to have a denominator of 210.
Convert 1/5
- Multiply numerator and denominator by 42 (210 ÷ 5): 1 × 42 = 42, 5 × 42 = 210
- Result: 42/210
Convert 1/6
- Multiply numerator and denominator by 35 (210 ÷ 6): 1 × 35 = 35, 6 × 35 = 210
- Result: 35/210
Convert 1/7
- Multiply numerator and denominator by 30 (210 ÷ 7): 1 × 30 = 30, 7 × 30 = 210
- Result: 30/210
Step 3: Add the Fractions
Now that we have converted each fraction to have the same denominator, we can add them.
Add the Fractions
- 42/210 + 35/210 + 30/210 = (42 + 35 + 30)/210
- Calculate the sum of the numerators: 42 + 35 + 30 = 107
- Result: 107/210
Therefore, the result of adding the fractions 1/5, 1/6, and 1/7 is:
107/210
In conclusion, we have successfully added the fractions 1/5, 1/6, and 1/7 and expressed the result as a single fraction, 107/210.
