Solve 2frac{79/83/3frac{89{97}}}{511/13/7frac{131{137}}}*1+1=frac{1frac{38}{76}}{3frac{19}{21}}

$$\frac { \frac { 2 \frac { 79 } { 83 } } { 3 \frac { 89 } { 97 } } } { \frac { 5 \frac { 11 } { 13 } } { 7 \frac { 131 } { 137 } } } \times 1 + 1 = \frac { 1 \frac { 38 } { 76 } } { 3 \frac { 19 } { 21 } }$$

Verify

Solution Steps

Divide \frac{\frac{2\times 83+79}{83}}{\frac{3\times 97+89}{97}} by \frac{\frac{5\times 13+11}{13}}{\frac{7\times 137+131}{137}} by multiplying \frac{\frac{2\times 83+79}{83}}{\frac{3\times 97+89}{97}} by the reciprocal of \frac{\frac{5\times 13+11}{13}}{\frac{7\times 137+131}{137}}.

$$\frac{\frac{2\times 83+79}{83}\times \frac{7\times 137+131}{137}}{\frac{3\times 97+89}{97}\times \frac{5\times 13+11}{13}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Multiply 2 and 83 to get 166.

$$\frac{\frac{166+79}{83}\times \frac{7\times 137+131}{137}}{\frac{3\times 97+89}{97}\times \frac{5\times 13+11}{13}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Add 166 and 79 to get 245.

$$\frac{\frac{245}{83}\times \frac{7\times 137+131}{137}}{\frac{3\times 97+89}{97}\times \frac{5\times 13+11}{13}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Multiply 7 and 137 to get 959.

$$\frac{\frac{245}{83}\times \frac{959+131}{137}}{\frac{3\times 97+89}{97}\times \frac{5\times 13+11}{13}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Add 959 and 131 to get 1090.

$$\frac{\frac{245}{83}\times \frac{1090}{137}}{\frac{3\times 97+89}{97}\times \frac{5\times 13+11}{13}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Multiply \frac{245}{83} times \frac{1090}{137} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{245\times 1090}{83\times 137}}{\frac{3\times 97+89}{97}\times \frac{5\times 13+11}{13}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Do the multiplications in the fraction \frac{245\times 1090}{83\times 137}.

$$\frac{\frac{267050}{11371}}{\frac{3\times 97+89}{97}\times \frac{5\times 13+11}{13}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Multiply 3 and 97 to get 291.

$$\frac{\frac{267050}{11371}}{\frac{291+89}{97}\times \frac{5\times 13+11}{13}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Add 291 and 89 to get 380.

$$\frac{\frac{267050}{11371}}{\frac{380}{97}\times \frac{5\times 13+11}{13}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Multiply 5 and 13 to get 65.

$$\frac{\frac{267050}{11371}}{\frac{380}{97}\times \frac{65+11}{13}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Add 65 and 11 to get 76.

$$\frac{\frac{267050}{11371}}{\frac{380}{97}\times \frac{76}{13}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Multiply \frac{380}{97} times \frac{76}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{267050}{11371}}{\frac{380\times 76}{97\times 13}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Do the multiplications in the fraction \frac{380\times 76}{97\times 13}.

$$\frac{\frac{267050}{11371}}{\frac{28880}{1261}}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Divide \frac{267050}{11371} by \frac{28880}{1261} by multiplying \frac{267050}{11371} by the reciprocal of \frac{28880}{1261}.

$$\frac{267050}{11371}\times \frac{1261}{28880}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Multiply \frac{267050}{11371} times \frac{1261}{28880} by multiplying numerator times numerator and denominator times denominator.

$$\frac{267050\times 1261}{11371\times 28880}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Do the multiplications in the fraction \frac{267050\times 1261}{11371\times 28880}.

$$\frac{336750050}{328394480}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Reduce the fraction \frac{336750050}{328394480} to lowest terms by extracting and canceling out 10.

$$\frac{33675005}{32839448}\times 1+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Multiply \frac{33675005}{32839448} and 1 to get \frac{33675005}{32839448}.

$$\frac{33675005}{32839448}+1=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Convert 1 to fraction \frac{32839448}{32839448}.

$$\frac{33675005}{32839448}+\frac{32839448}{32839448}=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Since \frac{33675005}{32839448} and \frac{32839448}{32839448} have the same denominator, add them by adding their numerators.

$$\frac{33675005+32839448}{32839448}=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Add 33675005 and 32839448 to get 66514453.

$$\frac{66514453}{32839448}=\frac{\frac{1\times 76+38}{76}}{\frac{3\times 21+19}{21}}$$

Divide \frac{1\times 76+38}{76} by \frac{3\times 21+19}{21} by multiplying \frac{1\times 76+38}{76} by the reciprocal of \frac{3\times 21+19}{21}.

$$\frac{66514453}{32839448}=\frac{\left(1\times 76+38\right)\times 21}{76\left(3\times 21+19\right)}$$

Multiply 1 and 76 to get 76.

$$\frac{66514453}{32839448}=\frac{\left(76+38\right)\times 21}{76\left(3\times 21+19\right)}$$

Add 76 and 38 to get 114.

$$\frac{66514453}{32839448}=\frac{114\times 21}{76\left(3\times 21+19\right)}$$

Multiply 114 and 21 to get 2394.

$$\frac{66514453}{32839448}=\frac{2394}{76\left(3\times 21+19\right)}$$

Multiply 3 and 21 to get 63.

$$\frac{66514453}{32839448}=\frac{2394}{76\left(63+19\right)}$$

Add 63 and 19 to get 82.

$$\frac{66514453}{32839448}=\frac{2394}{76\times 82}$$

Multiply 76 and 82 to get 6232.

$$\frac{66514453}{32839448}=\frac{2394}{6232}$$

Reduce the fraction \frac{2394}{6232} to lowest terms by extracting and canceling out 38.

$$\frac{66514453}{32839448}=\frac{63}{164}$$

Least common multiple of 32839448 and 164 is 1346417368. Convert \frac{66514453}{32839448} and \frac{63}{164} to fractions with denominator 1346417368.

$$\frac{2727092573}{1346417368}=\frac{517221306}{1346417368}$$

Compare \frac{2727092573}{1346417368} and \frac{517221306}{1346417368}.

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