Simplifying Fractions: 1/7 + 2/5 in Simplest Form
When it comes to adding fractions, one of the most crucial steps is to find the least common multiple (LCM) of the denominators involved. In this case, we have two fractions: 1/7 and 2/5. Our goal is to add them and simplify the result to its simplest form.
Step 1: Find the Least Common Multiple (LCM)
To add these fractions, we need to find the LCM of 7 and 5. The multiples of 7 are: 7, 14, 21, 28, 35, ... . The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, ... . The first number that appears in both lists is 35, which is the LCM of 7 and 5.
Step 2: Convert Both Fractions to Have the LCM as the Denominator
Now that we have the LCM, we can convert both fractions to have 35 as the denominator.
- Convert 1/7: Multiply numerator and denominator by 5
1/7 = (1 × 5) / (7 × 5) = 5/35
- Convert 2/5: Multiply numerator and denominator by 7
2/5 = (2 × 7) / (5 × 7) = 14/35
Step 3: Add the Fractions
Now that both fractions have the same denominator, we can add them:
5/35 + 14/35 = (5 + 14) / 35 = 19/35
Simplified Result
The simplified form of 1/7 + 2/5 is 19/35.
