which cards are equivalent to 1\\frac{3}{5}+\\frac{1}{4}? choose all the correct answers. 1\\frac{3}{20}+2\\f…

Explanation:

Step1: Convert mixed - numbers to improper fractions

First, convert (1\frac{3}{5}) and (2\frac{1}{4}) to improper fractions. (1\frac{3}{5}=\frac{1\times5 + 3}{5}=\frac{8}{5}), (2\frac{1}{4}=\frac{2\times4+1}{4}=\frac{9}{4}). Then find a common denominator, which is (20). (\frac{8}{5}=\frac{8\times4}{5\times4}=\frac{32}{20}), (\frac{9}{4}=\frac{9\times5}{4\times5}=\frac{45}{20}). So (1\frac{3}{5}+2\frac{1}{4}=\frac{32}{20}+\frac{45}{20}=\frac{32 + 45}{20}=\frac{77}{20}=3\frac{17}{20}).

Step2: Check each option

• For (1\frac{3}{20}+2\frac{1}{20}), convert to improper fractions: (\frac{1\times20 + 3}{20}+\frac{2\times20+1}{20}=\frac{23}{20}+\frac{41}{20}=\frac{23 + 41}{20}=\frac{64}{20}=3\frac{4}{20}), not equivalent.
• For (1\frac{15}{20}+2\frac{4}{20}), convert to improper fractions: (\frac{1\times20 + 15}{20}+\frac{2\times20+4}{20}=\frac{35}{20}+\frac{44}{20}=\frac{35 + 44}{20}=\frac{79}{20}=3\frac{19}{20}), not equivalent.
• For (1\frac{12}{20}+2\frac{5}{20}), convert to improper fractions: (\frac{1\times20 + 12}{20}+\frac{2\times20+5}{20}=\frac{32}{20}+\frac{45}{20}=\frac{32 + 45}{20}=\frac{77}{20}=3\frac{17}{20}), equivalent.
• For (3\frac{19}{20}), it is not equivalent.
• For (3\frac{17}{20}), it is equivalent.
• For (3\frac{4}{20}), it is not equivalent.

Answer:

(1\frac{12}{20}+2\frac{5}{20}), (3\frac{17}{20})