Solve 41/2:(11/3-1/6)=41/2:quadfrac{7}{6}=

$$4 \frac { 1 } { 2 } : ( 1 \frac { 1 } { 3 } - \frac { 1 } { 6 } ) = 4 \frac { 1 } { 2 } : \quad \frac { 7 } { 6 } =$$

Verify

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{\frac{8+1}{2}}{\frac{1\times 3+1}{3}-\frac{1}{6}}=\frac{\frac{4\times 2+1}{2}}{\frac{7}{6}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{9}{2}}{\frac{1\times 3+1}{3}-\frac{1}{6}}=\frac{\frac{4\times 2+1}{2}}{\frac{7}{6}}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{9}{2}}{\frac{3+1}{3}-\frac{1}{6}}=\frac{\frac{4\times 2+1}{2}}{\frac{7}{6}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{9}{2}}{\frac{4}{3}-\frac{1}{6}}=\frac{\frac{4\times 2+1}{2}}{\frac{7}{6}}$$

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{\frac{9}{2}}{\frac{8}{6}-\frac{1}{6}}=\frac{\frac{4\times 2+1}{2}}{\frac{7}{6}}$$

Since \frac{8}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9}{2}}{\frac{8-1}{6}}=\frac{\frac{4\times 2+1}{2}}{\frac{7}{6}}$$

Subtract 1 from 8 to get 7.

$$\frac{\frac{9}{2}}{\frac{7}{6}}=\frac{\frac{4\times 2+1}{2}}{\frac{7}{6}}$$

Divide \frac{9}{2} by \frac{7}{6} by multiplying \frac{9}{2} by the reciprocal of \frac{7}{6}.

$$\frac{9}{2}\times \frac{6}{7}=\frac{\frac{4\times 2+1}{2}}{\frac{7}{6}}$$

Multiply \frac{9}{2} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 6}{2\times 7}=\frac{\frac{4\times 2+1}{2}}{\frac{7}{6}}$$

Do the multiplications in the fraction \frac{9\times 6}{2\times 7}.

$$\frac{54}{14}=\frac{\frac{4\times 2+1}{2}}{\frac{7}{6}}$$

Reduce the fraction \frac{54}{14} to lowest terms by extracting and canceling out 2.

$$\frac{27}{7}=\frac{\frac{4\times 2+1}{2}}{\frac{7}{6}}$$

Divide \frac{4\times 2+1}{2} by \frac{7}{6} by multiplying \frac{4\times 2+1}{2} by the reciprocal of \frac{7}{6}.

$$\frac{27}{7}=\frac{\left(4\times 2+1\right)\times 6}{2\times 7}$$

Cancel out 2 in both numerator and denominator.

$$\frac{27}{7}=\frac{3\left(1+2\times 4\right)}{7}$$

Multiply 2 and 4 to get 8.

$$\frac{27}{7}=\frac{3\left(1+8\right)}{7}$$

Add 1 and 8 to get 9.

$$\frac{27}{7}=\frac{3\times 9}{7}$$

Multiply 3 and 9 to get 27.

$$\frac{27}{7}=\frac{27}{7}$$

Compare \frac{27}{7} and \frac{27}{7}.

$$\text{true}$$