Question

select all of the equations below in which \\(\frac{1}{5}\\) is the missing fraction.\
\\(\square\\) a. \\(1\frac{1}{5} = \square + \frac{2}{5} + \frac{2}{5}\\)\
\\(\square\\) b. \\(2 = \frac{5}{5} + \frac{1}{5}+ \\ \square + \frac{1}{5} + \frac{1}{5}\\)\
\\(\square\\) c. \\(2\frac{2}{5} = \square + \frac{4}{5} + \frac{5}{5} + \frac{2}{5}\\)\
\\(\square\\) d. \\(2\frac{1}{5} = 1 + \frac{1}{5}+ \\ \square + \frac{1}{5} + \frac{1}{5}\\)\
\\(\square\\) e. \\(1 = \frac{1}{5} + \\ \square + \frac{1}{5} + \frac{1}{5} + \frac{1}{5}\\)

Explanation:

for each option:

Option A:

Step1: Let the missing fraction be \( x \). The equation is \( 1\frac{1}{5}=x + \frac{2}{5}+\frac{2}{5} \)

Step2: First, simplify the right - hand side: \( x+\frac{2 + 2}{5}=x+\frac{4}{5} \)

Step3: Now, solve for \( x \): \( x=1\frac{1}{5}-\frac{4}{5} \). Convert \( 1\frac{1}{5} \) to improper fraction: \( 1\frac{1}{5}=\frac{6}{5} \). Then \( x=\frac{6}{5}-\frac{4}{5}=\frac{2}{5}

eq\frac{1}{5} \)

Option B:

Step1: Let the missing fraction be \( x \). The equation is \( 2=\frac{5}{5}+\frac{1}{5}+x+\frac{1}{5}+\frac{1}{5} \)

Step2: Simplify the right - hand side: \( \frac{5 + 1+1 + 1}{5}+x=\frac{8}{5}+x \)

Step3: Convert \( 2 \) to fifths: \( 2=\frac{10}{5} \). Then \( x=\frac{10}{5}-\frac{8}{5}=\frac{2}{5}

eq\frac{1}{5} \)

Option C:

Step1: Let the missing fraction be \( x \). The equation is \( 2\frac{2}{5}=x+\frac{4}{5}+\frac{5}{5}+\frac{2}{5} \)

Step2: Simplify the right - hand side: \( x+\frac{4 + 5+2}{5}=x+\frac{11}{5} \)

Step3: Convert \( 2\frac{2}{5} \) to improper fraction: \( 2\frac{2}{5}=\frac{12}{5} \). Then \( x=\frac{12}{5}-\frac{11}{5}=\frac{1}{5} \)

Option D:

Step1: Let the missing fraction be \( x \). The equation is \( 2\frac{1}{5}=1+\frac{1}{5}+x+\frac{1}{5}+\frac{1}{5} \)

Step2: Simplify the right - hand side: \( 1+\frac{1 + 1+1}{5}+x=1+\frac{3}{5}+x=\frac{5 + 3}{5}+x=\frac{8}{5}+x \)

Step3: Convert \( 2\frac{1}{5} \) to improper fraction: \( 2\frac{1}{5}=\frac{11}{5} \). Then \( x=\frac{11}{5}-\frac{8}{5}=\frac{3}{5}

eq\frac{1}{5} \)

Option E:

Step1: Let the missing fraction be \( x \). The equation is \( 1=\frac{1}{5}+x+\frac{1}{5}+\frac{1}{5}+\frac{1}{5} \)

Step2: Simplify the right - hand side: \( x+\frac{1 + 1+1 + 1}{5}=x+\frac{4}{5} \)

Step3: Then \( x = 1-\frac{4}{5}=\frac{1}{5} \)

Answer:

C. \( 2\frac{2}{5}=\square+\frac{4}{5}+\frac{5}{5}+\frac{2}{5} \)
E. \( 1=\frac{1}{5}+\square+\frac{1}{5}+\frac{1}{5}+\frac{1}{5} \)