Question

Question : reduce answers as much as possible by finding the common factors

#1. 2/5+3/7

Answer 1

To add the fractions 2/5 and 3/7, find a common denominator, convert each fraction, and then add the numerators. The answer, which is 29/35, is already in its simplest form as there are no common factors between 29 and 35.

Step-by-step explanation:

To add fractions with different denominators, such as 2/5 and 3/7, you first need to find a common denominator. For these two fractions, the smallest common denominator would be 35, which is the product of 5 and 7. After finding the common denominator, you convert each fraction to an equivalent fraction with the common denominator and then add the numerators together while keeping the denominator the same.

1. Multiply the numerators and denominators to find a common denominator:
   2/5 becomes (2×7)/(5×7) = 14/35
   3/7 becomes (3×5)/(7×5) = 15/35
2. Add the numerators together:
   14/35 + 15/35 = (14+15)/35 = 29/35
3. There are no common factors between 29 and 35, so the fraction is already in its simplest form.
   The answer is 29/35.

By checking that the answer is reasonable, we understand that the sum is less than 1 since each fraction is less than 1.