Final answer:
The smallest common denominator for the fractions 2/5 and 3/4 is 20. It is found by determining the least common multiple of the original denominators, which in this case are 5 and 4. Upon rewriting, fractions become 8/20 and 15/20 respectively.
Step-by-step explanation:
To find a common denominator for the fractions 2/5 and 3/4, we are looking for the smallest number that both 5 and 4 can divide into without leaving a remainder.
The denominators of the fractions are 5 and 4. The least common multiple (LCM) of these numbers is 20, as 20 is the smallest number that both 5 and 4 can divide into evenly (5 × 4 = 20). Therefore, the common denominator that should be used is 20. Viable denominators are calculated by finding multiples of each of the original denominators (5 and 4) until we find a match; in this case, the first common multiple we encounter is 20.
When you rewrite the fractions with the common denominator, 2/5 becomes 8/20, and 3/4 becomes 15/20, as 2 × 4 = 8 and 3 × 5 = 15. Now both fractions have a denominator of 20, allowing for easy addition or comparison.