Question

drag each tile to the correct box.
place the complex fractions in order
from least to greatest.
\\(\frac{\frac{2}{3} + 1}{1 - \frac{3}{5}}\\) \\(\frac{\frac{4}{5}}{\frac{11}{9} - 1}\\) \\(\frac{\frac{3}{4} + 1}{\frac{2}{5}}\\)
\\(square\\) < \\(square\\) < \\(square\\)
reset submit
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Explanation:

Step1: Simplify the first complex fraction

First, simplify the numerator and denominator of \(\frac{\frac{2}{3}+1}{1 - \frac{3}{5}}\).

• Numerator: \(\frac{2}{3}+1=\frac{2}{3}+\frac{3}{3}=\frac{5}{3}\)
• Denominator: \(1-\frac{3}{5}=\frac{5}{5}-\frac{3}{5}=\frac{2}{5}\)

So the first fraction becomes \(\frac{\frac{5}{3}}{\frac{2}{5}}=\frac{5}{3}\times\frac{5}{2}=\frac{25}{6}\approx4.17\)

Step2: Simplify the second complex fraction

Simplify \(\frac{\frac{4}{5}}{\frac{11}{9}-1}\).

• Denominator: \(\frac{11}{9}-1=\frac{11}{9}-\frac{9}{9}=\frac{2}{9}\)

So the second fraction becomes \(\frac{\frac{4}{5}}{\frac{2}{9}}=\frac{4}{5}\times\frac{9}{2}=\frac{36}{10}=\frac{18}{5} = 3.6\)

Step3: Simplify the third complex fraction

Simplify \(\frac{\frac{3}{4}+1}{\frac{2}{5}}\).

• Numerator: \(\frac{3}{4}+1=\frac{3}{4}+\frac{4}{4}=\frac{7}{4}\)

So the third fraction becomes \(\frac{\frac{7}{4}}{\frac{2}{5}}=\frac{7}{4}\times\frac{5}{2}=\frac{35}{8}=4.375\)

Step4: Compare the values

Now we have the three values: \(\frac{18}{5}=3.6\), \(\frac{25}{6}\approx4.17\), \(\frac{35}{8} = 4.375\)

Ordering from least to greatest: \(3.6<4.17<4.375\), which corresponds to \(\frac{\frac{4}{5}}{\frac{11}{9}-1}<\frac{\frac{2}{3}+1}{1 - \frac{3}{5}}<\frac{\frac{3}{4}+1}{\frac{2}{5}}\)

Answer:

\(\boldsymbol{\frac{\frac{4}{5}}{\frac{11}{9}-1}}\) < \(\boldsymbol{\frac{\frac{2}{3}+1}{1 - \frac{3}{5}}}\) < \(\boldsymbol{\frac{\frac{3}{4}+1}{\frac{2}{5}}}\)