Solve 21/3div11/6text{of}(5/4-5/5*1frac{-1}{4})

$$2 \frac { 1 } { 3 } \div 1 \frac { 1 } { 6 } \text { of } ( \frac { 5 } { 4 } - \frac { 5 } { 5 } \times 1 \frac { - 1 } { 4 } )$$

Evaluate

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Solution Steps

Divide 5 by 5 to get 1.

$$\frac{\frac{2\times 3+1}{3}}{\frac{1\times 6+1}{6}}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Divide \frac{2\times 3+1}{3} by \frac{1\times 6+1}{6} by multiplying \frac{2\times 3+1}{3} by the reciprocal of \frac{1\times 6+1}{6}.

$$\frac{\left(2\times 3+1\right)\times 6}{3\left(1\times 6+1\right)}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\left(1+2\times 3\right)}{1+6}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{2\left(1+6\right)}{1+6}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Add 1 and 6 to get 7.

$$\frac{2\times 7}{1+6}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Multiply 2 and 7 to get 14.

$$\frac{14}{1+6}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Add 1 and 6 to get 7.

$$\frac{14}{7}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Divide 14 by 7 to get 2.

$$2of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Multiply 1 and 4 to get 4.

$$2of\left(\frac{5}{4}-1\times \frac{4-1}{4}\right)$$

Subtract 1 from 4 to get 3.

$$2of\left(\frac{5}{4}-1\times \frac{3}{4}\right)$$

Multiply 1 and \frac{3}{4} to get \frac{3}{4}.

$$2of\left(\frac{5}{4}-\frac{3}{4}\right)$$

Since \frac{5}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$2of\times \frac{5-3}{4}$$

Subtract 3 from 5 to get 2.

$$2of\times \frac{2}{4}$$

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

$$2of\times \frac{1}{2}$$

Cancel out 2 and 2.

$$of$$

Expand

$$fo$$

Solution Steps

Divide 5 by 5 to get 1.

$$\frac{\frac{2\times 3+1}{3}}{\frac{1\times 6+1}{6}}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Divide \frac{2\times 3+1}{3} by \frac{1\times 6+1}{6} by multiplying \frac{2\times 3+1}{3} by the reciprocal of \frac{1\times 6+1}{6}.

$$\frac{\left(2\times 3+1\right)\times 6}{3\left(1\times 6+1\right)}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\left(1+2\times 3\right)}{1+6}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{2\left(1+6\right)}{1+6}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Add 1 and 6 to get 7.

$$\frac{2\times 7}{1+6}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Multiply 2 and 7 to get 14.

$$\frac{14}{1+6}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Add 1 and 6 to get 7.

$$\frac{14}{7}of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Divide 14 by 7 to get 2.

$$2of\left(\frac{5}{4}-1\times \frac{1\times 4-1}{4}\right)$$

Multiply 1 and 4 to get 4.

$$2of\left(\frac{5}{4}-1\times \frac{4-1}{4}\right)$$

Subtract 1 from 4 to get 3.

$$2of\left(\frac{5}{4}-1\times \frac{3}{4}\right)$$

Multiply 1 and \frac{3}{4} to get \frac{3}{4}.

$$2of\left(\frac{5}{4}-\frac{3}{4}\right)$$

Since \frac{5}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$2of\times \frac{5-3}{4}$$

Subtract 3 from 5 to get 2.

$$2of\times \frac{2}{4}$$

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

$$2of\times \frac{1}{2}$$

Cancel out 2 and 2.

$$of$$