Question

which equation is represented by the model? answer \\(\frac{5}{6} \div 2\frac{3}{5} = 2\frac{1}{6}\\) \\(\frac{5}{6} \div 2\frac{1}{6} = 2\frac{3}{5}\\) \\(\frac{1}{6} \div 13 = 2\frac{1}{6}\\) \\(2\frac{1}{6} \div \frac{5}{6} = 2\frac{3}{5}\\)

Explanation:

Step1: Analyze the model

The model shows a total length (the blue part) which we can identify as \(2\frac{1}{6}\) (since it goes beyond 2, with the extra part being \(\frac{1}{6}\)). Each segment of the blue part is \(\frac{5}{6}\)? Wait, no, actually, let's count the number of \(\frac{5}{6}\) segments? Wait, no, looking at the number line, the total blue length is \(2\frac{1}{6}\), and we are dividing it by \(\frac{5}{6}\) to see how many \(\frac{5}{6}\) segments are there. Wait, the last option is \(2\frac{1}{6}\div\frac{5}{6}\). Let's compute that: \(2\frac{1}{6}=\frac{13}{6}\), \(\frac{13}{6}\div\frac{5}{6}=\frac{13}{6}\times\frac{6}{5}=\frac{13}{5}=2\frac{3}{5}\), which matches the idea of dividing the total length \(2\frac{1}{6}\) by \(\frac{5}{6}\) to get the number of segments (which would be \(2\frac{3}{5}\)). Let's check the other options:

• First option: \(\frac{5}{6}\div2\frac{3}{5}=\frac{5}{6}\div\frac{13}{5}=\frac{5}{6}\times\frac{5}{13}=\frac{25}{78}

eq2\frac{1}{6}\)

• Second option: \(\frac{5}{6}\div2\frac{1}{6}=\frac{5}{6}\div\frac{13}{6}=\frac{5}{13}

eq2\frac{3}{5}\)

• Third option: \(\frac{1}{6}\div13=\frac{1}{78}

eq2\frac{1}{6}\)

• Fourth option: \(2\frac{1}{6}\div\frac{5}{6}=\frac{13}{6}\div\frac{5}{6}=\frac{13}{5}=2\frac{3}{5}\), which is correct.

Step2: Verify the division

Convert \(2\frac{1}{6}\) to improper fraction: \(2\frac{1}{6}=\frac{13}{6}\). Then divide by \(\frac{5}{6}\): \(\frac{13}{6}\div\frac{5}{6}=\frac{13}{6}\times\frac{6}{5}=\frac{13}{5}=2\frac{3}{5}\), which matches the result of the division in the fourth option.

Answer:

\(2\frac{1}{6}\div\frac{5}{6}=2\frac{3}{5}\) (the last option, which is \(2\frac{1}{6}\div\frac{5}{6}=2\frac{3}{5}\))