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\frac{3T}{16}+\frac{50}{3}
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\frac{3T}{16}+\frac{50}{3}
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\frac{T\times 3}{5\times 3+1}+\frac{5\times 8+1}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}
Divide T by \frac{5\times 3+1}{3} by multiplying T by the reciprocal of \frac{5\times 3+1}{3}.
\frac{T\times 3}{15+1}+\frac{5\times 8+1}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}
Multiply 5 and 3 to get 15.
\frac{T\times 3}{16}+\frac{5\times 8+1}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}
Add 15 and 1 to get 16.
\frac{T\times 3}{16}+\frac{40+1}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}
Multiply 5 and 8 to get 40.
\frac{T\times 3}{16}+\frac{41}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}
Add 40 and 1 to get 41.
\frac{T\times 3}{16}+\frac{41}{8}+\frac{18+2}{3}+\frac{4\times 8+7}{8}
Multiply 6 and 3 to get 18.
\frac{T\times 3}{16}+\frac{41}{8}+\frac{20}{3}+\frac{4\times 8+7}{8}
Add 18 and 2 to get 20.
\frac{T\times 3}{16}+\frac{123}{24}+\frac{160}{24}+\frac{4\times 8+7}{8}
Least common multiple of 8 and 3 is 24. Convert \frac{41}{8} and \frac{20}{3} to fractions with denominator 24.
\frac{T\times 3}{16}+\frac{123+160}{24}+\frac{4\times 8+7}{8}
Since \frac{123}{24} and \frac{160}{24} have the same denominator, add them by adding their numerators.
\frac{T\times 3}{16}+\frac{283}{24}+\frac{4\times 8+7}{8}
Add 123 and 160 to get 283.
\frac{T\times 3}{16}+\frac{283}{24}+\frac{32+7}{8}
Multiply 4 and 8 to get 32.
\frac{T\times 3}{16}+\frac{283}{24}+\frac{39}{8}
Add 32 and 7 to get 39.
\frac{T\times 3}{16}+\frac{283}{24}+\frac{117}{24}
Least common multiple of 24 and 8 is 24. Convert \frac{283}{24} and \frac{39}{8} to fractions with denominator 24.
\frac{T\times 3}{16}+\frac{283+117}{24}
Since \frac{283}{24} and \frac{117}{24} have the same denominator, add them by adding their numerators.
\frac{T\times 3}{16}+\frac{400}{24}
Add 283 and 117 to get 400.
\frac{T\times 3}{16}+\frac{50}{3}
Reduce the fraction \frac{400}{24} to lowest terms by extracting and canceling out 8.
\frac{3T\times 3}{48}+\frac{50\times 16}{48}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 16 and 3 is 48. Multiply \frac{T\times 3}{16} times \frac{3}{3}. Multiply \frac{50}{3} times \frac{16}{16}.
\frac{3T\times 3+50\times 16}{48}
Since \frac{3T\times 3}{48} and \frac{50\times 16}{48} have the same denominator, add them by adding their numerators.
\frac{9T+800}{48}
Do the multiplications in 3T\times 3+50\times 16.
\frac{T\times 3}{5\times 3+1}+\frac{5\times 8+1}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}
Divide T by \frac{5\times 3+1}{3} by multiplying T by the reciprocal of \frac{5\times 3+1}{3}.
\frac{T\times 3}{15+1}+\frac{5\times 8+1}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}
Multiply 5 and 3 to get 15.
\frac{T\times 3}{16}+\frac{5\times 8+1}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}
Add 15 and 1 to get 16.
\frac{T\times 3}{16}+\frac{40+1}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}
Multiply 5 and 8 to get 40.
\frac{T\times 3}{16}+\frac{41}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}
Add 40 and 1 to get 41.
\frac{T\times 3}{16}+\frac{41}{8}+\frac{18+2}{3}+\frac{4\times 8+7}{8}
Multiply 6 and 3 to get 18.
\frac{T\times 3}{16}+\frac{41}{8}+\frac{20}{3}+\frac{4\times 8+7}{8}
Add 18 and 2 to get 20.
\frac{T\times 3}{16}+\frac{123}{24}+\frac{160}{24}+\frac{4\times 8+7}{8}
Least common multiple of 8 and 3 is 24. Convert \frac{41}{8} and \frac{20}{3} to fractions with denominator 24.
\frac{T\times 3}{16}+\frac{123+160}{24}+\frac{4\times 8+7}{8}
Since \frac{123}{24} and \frac{160}{24} have the same denominator, add them by adding their numerators.
\frac{T\times 3}{16}+\frac{283}{24}+\frac{4\times 8+7}{8}
Add 123 and 160 to get 283.
\frac{T\times 3}{16}+\frac{283}{24}+\frac{32+7}{8}
Multiply 4 and 8 to get 32.
\frac{T\times 3}{16}+\frac{283}{24}+\frac{39}{8}
Add 32 and 7 to get 39.
\frac{T\times 3}{16}+\frac{283}{24}+\frac{117}{24}
Least common multiple of 24 and 8 is 24. Convert \frac{283}{24} and \frac{39}{8} to fractions with denominator 24.
\frac{T\times 3}{16}+\frac{283+117}{24}
Since \frac{283}{24} and \frac{117}{24} have the same denominator, add them by adding their numerators.
\frac{T\times 3}{16}+\frac{400}{24}
Add 283 and 117 to get 400.
\frac{T\times 3}{16}+\frac{50}{3}
Reduce the fraction \frac{400}{24} to lowest terms by extracting and canceling out 8.
\frac{3T\times 3}{48}+\frac{50\times 16}{48}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 16 and 3 is 48. Multiply \frac{T\times 3}{16} times \frac{3}{3}. Multiply \frac{50}{3} times \frac{16}{16}.
\frac{3T\times 3+50\times 16}{48}
Since \frac{3T\times 3}{48} and \frac{50\times 16}{48} have the same denominator, add them by adding their numerators.
\frac{9T+800}{48}
Do the multiplications in 3T\times 3+50\times 16.
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