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\frac{2+\frac{1}{3}}{3-\frac{1}{2+\frac{2}{3}}}=
[#permalink]
20 Jul 2026, 03:21
20 Jul 2026, 03:21
1
Expert Reply
00:00
Question Stats:
50% (00:35) correct
50% (01:44) wrong based on 4 sessions
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\(\frac{2+\frac{1}{3}}{3-\frac{1}{2+\frac{2}{3}}}=\)
A. \(\frac{5}{6}\)
B. \(\frac{6}{7}
\)
C. \(\frac{7}{8}\)
D. \(\frac{8}{9}\)
E. \(\frac{9}{10}\)
A. \(\frac{5}{6}\)
B. \(\frac{6}{7}
\)
C. \(\frac{7}{8}\)
D. \(\frac{8}{9}\)
E. \(\frac{9}{10}\)
- Part of the project: GRE Daily Quant Challenge ALL 4 CORE QUANT AREAS
- Also replying to the unanswered questions
Re: \frac{2+\frac{1}{3}}{3-\frac{1}{2+\frac{2}{3}}}=
[#permalink]
21 Jul 2026, 04:00
21 Jul 2026, 04:00
Expert Reply
Step-by-Step Solution
Step 1 - Simplify the numerator
\(2+\frac{1}{3}=\frac{6}{3}+\frac{1}{3}=\frac{7}{3}\)
Step 2 - Simplify the nested part in the denominator
Start with the innermost fraction:
\(2+\frac{2}{3}=\frac{6}{3}+\frac{2}{3}=\frac{8}{3}\)
Now take its reciprocal:
\(\frac{1}{2+\frac{2}{3}}=\frac{1}{\frac{8}{3}}=\frac{3}{8}\)
Step 3 - Simplify the full denominator
\(3-\frac{1}{2+\frac{2}{3}}=3-\frac{3}{8}=\frac{24}{8}-\frac{3}{8}=\frac{21}{8}\)
Step 4 - Divide the numerator by the denominator
\(\frac{2+\frac{1}{3}}{3-\frac{1}{2+\frac{2}{3}}}=\frac{\frac{7}{3}}{\frac{21}{8}}=\frac{7}{3} \times \frac{8}{21}\)
Step 5 - Multiply and simplify
\(\frac{7 \times 8}{3 \times 21}=\frac{56}{63}\)
Divide numerator and denominator by 7:
\(\begin{gathered}
\frac{56}{63}=\frac{8}{9} \\
\end{gathered}\)
Step 1 - Simplify the numerator
\(2+\frac{1}{3}=\frac{6}{3}+\frac{1}{3}=\frac{7}{3}\)
Step 2 - Simplify the nested part in the denominator
Start with the innermost fraction:
\(2+\frac{2}{3}=\frac{6}{3}+\frac{2}{3}=\frac{8}{3}\)
Now take its reciprocal:
\(\frac{1}{2+\frac{2}{3}}=\frac{1}{\frac{8}{3}}=\frac{3}{8}\)
Step 3 - Simplify the full denominator
\(3-\frac{1}{2+\frac{2}{3}}=3-\frac{3}{8}=\frac{24}{8}-\frac{3}{8}=\frac{21}{8}\)
Step 4 - Divide the numerator by the denominator
\(\frac{2+\frac{1}{3}}{3-\frac{1}{2+\frac{2}{3}}}=\frac{\frac{7}{3}}{\frac{21}{8}}=\frac{7}{3} \times \frac{8}{21}\)
Step 5 - Multiply and simplify
\(\frac{7 \times 8}{3 \times 21}=\frac{56}{63}\)
Divide numerator and denominator by 7:
\(\begin{gathered}
\frac{56}{63}=\frac{8}{9} \\
\end{gathered}\)
gmatclubot
Re: \frac{2+\frac{1}{3}}{3-\frac{1}{2+\frac{2}{3}}}= [#permalink]
21 Jul 2026, 04:00
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