Solve 5(82/12)+6(82/4)-81=7(81/4)

$$5 ( \frac { 82 } { 12 } ) + 6 ( \frac { 82 } { 4 } ) - 81 = 7 ( \frac { 81 } { 4 } )$$

Verify

Solution Steps

Reduce the fraction \frac{82}{12} to lowest terms by extracting and canceling out 2.

$$5\times \frac{41}{6}+6\times \frac{82}{4}-81=7\times \frac{81}{4}$$

Express 5\times \frac{41}{6} as a single fraction.

$$\frac{5\times 41}{6}+6\times \frac{82}{4}-81=7\times \frac{81}{4}$$

Multiply 5 and 41 to get 205.

$$\frac{205}{6}+6\times \frac{82}{4}-81=7\times \frac{81}{4}$$

Reduce the fraction \frac{82}{4} to lowest terms by extracting and canceling out 2.

$$\frac{205}{6}+6\times \frac{41}{2}-81=7\times \frac{81}{4}$$

Express 6\times \frac{41}{2} as a single fraction.

$$\frac{205}{6}+\frac{6\times 41}{2}-81=7\times \frac{81}{4}$$

Multiply 6 and 41 to get 246.

$$\frac{205}{6}+\frac{246}{2}-81=7\times \frac{81}{4}$$

Divide 246 by 2 to get 123.

$$\frac{205}{6}+123-81=7\times \frac{81}{4}$$

Convert 123 to fraction \frac{738}{6}.

$$\frac{205}{6}+\frac{738}{6}-81=7\times \frac{81}{4}$$

Since \frac{205}{6} and \frac{738}{6} have the same denominator, add them by adding their numerators.

$$\frac{205+738}{6}-81=7\times \frac{81}{4}$$

Add 205 and 738 to get 943.

$$\frac{943}{6}-81=7\times \frac{81}{4}$$

Convert 81 to fraction \frac{486}{6}.

$$\frac{943}{6}-\frac{486}{6}=7\times \frac{81}{4}$$

Since \frac{943}{6} and \frac{486}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{943-486}{6}=7\times \frac{81}{4}$$

Subtract 486 from 943 to get 457.

$$\frac{457}{6}=7\times \frac{81}{4}$$

Express 7\times \frac{81}{4} as a single fraction.

$$\frac{457}{6}=\frac{7\times 81}{4}$$

Multiply 7 and 81 to get 567.

$$\frac{457}{6}=\frac{567}{4}$$

Least common multiple of 6 and 4 is 12. Convert \frac{457}{6} and \frac{567}{4} to fractions with denominator 12.

$$\frac{914}{12}=\frac{1701}{12}$$

Compare \frac{914}{12} and \frac{1701}{12}.

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