Final answer:
To find equivalent fractions for 2 2/5 and 1 3/4, convert them to improper fractions and then find a common denominator, which is 20. The equivalent fractions are 48/20 for 2 2/5 and 35/20 for 1 3/4.
Step-by-step explanation:
To find equivalent fractions for 2 2/5 and 1 3/4 with a common denominator, we must first convert these mixed numbers into improper fractions. For 2 2/5, the improper fraction is 12/5 because 2 times 5 equals 10, plus 2 equals 12. For 1 3/4, the improper fraction is 7/4 because 1 times 4 equals 4, plus 3 equals 7.
Next, we need to determine the least common denominator (LCD) for the two fractions. Since the denominators are 5 and 4, the LCD is 20 because it's the smallest number that both 5 and 4 can evenly divide into. We now convert the fractions to have the common denominator of 20.
We multiply the numerator and denominator of 12/5 by 4 to get 48/20. Similarly, we multiply the numerator and denominator of 7/4 by 5 to get 35/20. The equivalent fractions with a common denominator of 20 are then 48/20 for 2 2/5 and 35/20 for 1 3/4.