Question

select all the expressions that show a way to decompose \\(\frac{5}{12}\\). \\(\square\\) \\(\frac{3}{12} + \frac{2}{12}\\) \\(\square\\) \\(\frac{3}{6} + \frac{2}{6}\\) \\(\square\\) \\(\frac{1}{12} + \frac{2}{12} + \frac{2}{12}\\) \\(\square\\) \\(\frac{1}{12} + \frac{1}{12} + \frac{3}{12}\\) \\(\square\\) \\(\frac{1}{12} + \frac{1}{12} + \frac{2}{12} + \frac{2}{12}\\)

Explanation:

Step1: Check $\frac{3}{12} + \frac{2}{12}$

Add the numerators: $3 + 2 = 5$, denominator remains 12. So $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$. Valid.

Step2: Check $\frac{3}{6} + \frac{2}{6}$

Add numerators: $3 + 2 = 5$, denominator 6. $\frac{5}{6}
eq \frac{5}{12}$. Invalid.

Step3: Check $\frac{1}{12} + \frac{2}{12} + \frac{2}{12}$

Add numerators: $1 + 2 + 2 = 5$, denominator 12. $\frac{5}{12}$. Valid.

Step4: Check $\frac{1}{12} + \frac{1}{12} + \frac{3}{12}$

Add numerators: $1 + 1 + 3 = 5$, denominator 12. $\frac{5}{12}$. Valid.

Step5: Check $\frac{1}{12} + \frac{1}{12} + \frac{2}{12} + \frac{2}{12}$

Add numerators: $1 + 1 + 2 + 2 = 6$, denominator 12. $\frac{6}{12}
eq \frac{5}{12}$. Invalid.

Answer:

• $\frac{3}{12} + \frac{2}{12}$
• $\frac{1}{12} + \frac{2}{12} + \frac{2}{12}$
• $\frac{1}{12} + \frac{1}{12} + \frac{3}{12}$