Solve (phi)11/4*7div(127/12-111/3)

$$( \phi ) 1 \frac { 1 } { 4 } \times 7 \div ( 12 \frac { 7 } { 12 } - 11 \frac { 1 } { 3 } )$$

Evaluate

$$7ϕ$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{ϕ\times \frac{4+1}{4}\times 7}{\frac{12\times 12+7}{12}-\frac{11\times 3+1}{3}}$$

Add 4 and 1 to get 5.

$$\frac{ϕ\times \frac{5}{4}\times 7}{\frac{12\times 12+7}{12}-\frac{11\times 3+1}{3}}$$

Express \frac{5}{4}\times 7 as a single fraction.

$$\frac{ϕ\times \frac{5\times 7}{4}}{\frac{12\times 12+7}{12}-\frac{11\times 3+1}{3}}$$

Multiply 5 and 7 to get 35.

$$\frac{ϕ\times \frac{35}{4}}{\frac{12\times 12+7}{12}-\frac{11\times 3+1}{3}}$$

Multiply 12 and 12 to get 144.

$$\frac{ϕ\times \frac{35}{4}}{\frac{144+7}{12}-\frac{11\times 3+1}{3}}$$

Add 144 and 7 to get 151.

$$\frac{ϕ\times \frac{35}{4}}{\frac{151}{12}-\frac{11\times 3+1}{3}}$$

Multiply 11 and 3 to get 33.

$$\frac{ϕ\times \frac{35}{4}}{\frac{151}{12}-\frac{33+1}{3}}$$

Add 33 and 1 to get 34.

$$\frac{ϕ\times \frac{35}{4}}{\frac{151}{12}-\frac{34}{3}}$$

Least common multiple of 12 and 3 is 12. Convert \frac{151}{12} and \frac{34}{3} to fractions with denominator 12.

$$\frac{ϕ\times \frac{35}{4}}{\frac{151}{12}-\frac{136}{12}}$$

Since \frac{151}{12} and \frac{136}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{ϕ\times \frac{35}{4}}{\frac{151-136}{12}}$$

Subtract 136 from 151 to get 15.

$$\frac{ϕ\times \frac{35}{4}}{\frac{15}{12}}$$

Reduce the fraction \frac{15}{12} to lowest terms by extracting and canceling out 3.

$$\frac{ϕ\times \frac{35}{4}}{\frac{5}{4}}$$

Divide ϕ\times \frac{35}{4} by \frac{5}{4} by multiplying ϕ\times \frac{35}{4} by the reciprocal of \frac{5}{4}.

$$\frac{ϕ\times \frac{35}{4}\times 4}{5}$$

Cancel out 4 and 4.

$$\frac{ϕ\times 35}{5}$$

Divide ϕ\times 35 by 5 to get ϕ\times 7.

$$ϕ\times 7$$

Expand

$$7ϕ$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{ϕ\times \frac{4+1}{4}\times 7}{\frac{12\times 12+7}{12}-\frac{11\times 3+1}{3}}$$

Add 4 and 1 to get 5.

$$\frac{ϕ\times \frac{5}{4}\times 7}{\frac{12\times 12+7}{12}-\frac{11\times 3+1}{3}}$$

Express \frac{5}{4}\times 7 as a single fraction.

$$\frac{ϕ\times \frac{5\times 7}{4}}{\frac{12\times 12+7}{12}-\frac{11\times 3+1}{3}}$$

Multiply 5 and 7 to get 35.

$$\frac{ϕ\times \frac{35}{4}}{\frac{12\times 12+7}{12}-\frac{11\times 3+1}{3}}$$

Multiply 12 and 12 to get 144.

$$\frac{ϕ\times \frac{35}{4}}{\frac{144+7}{12}-\frac{11\times 3+1}{3}}$$

Add 144 and 7 to get 151.

$$\frac{ϕ\times \frac{35}{4}}{\frac{151}{12}-\frac{11\times 3+1}{3}}$$

Multiply 11 and 3 to get 33.

$$\frac{ϕ\times \frac{35}{4}}{\frac{151}{12}-\frac{33+1}{3}}$$

Add 33 and 1 to get 34.

$$\frac{ϕ\times \frac{35}{4}}{\frac{151}{12}-\frac{34}{3}}$$

Least common multiple of 12 and 3 is 12. Convert \frac{151}{12} and \frac{34}{3} to fractions with denominator 12.

$$\frac{ϕ\times \frac{35}{4}}{\frac{151}{12}-\frac{136}{12}}$$

Since \frac{151}{12} and \frac{136}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{ϕ\times \frac{35}{4}}{\frac{151-136}{12}}$$

Subtract 136 from 151 to get 15.

$$\frac{ϕ\times \frac{35}{4}}{\frac{15}{12}}$$

Reduce the fraction \frac{15}{12} to lowest terms by extracting and canceling out 3.

$$\frac{ϕ\times \frac{35}{4}}{\frac{5}{4}}$$

Divide ϕ\times \frac{35}{4} by \frac{5}{4} by multiplying ϕ\times \frac{35}{4} by the reciprocal of \frac{5}{4}.

$$\frac{ϕ\times \frac{35}{4}\times 4}{5}$$

Cancel out 4 and 4.

$$\frac{ϕ\times 35}{5}$$

Divide ϕ\times 35 by 5 to get ϕ\times 7.

$$ϕ\times 7$$