Solve 4/21div(5/99text{of}11/35)-3/4+1frac{1}{3}

$$\frac { 4 } { 21 } \div ( \frac { 5 } { 99 } \text { of } \frac { 11 } { 35 } ) - \frac { 3 } { 4 } + 1 \frac { 1 } { 3 }$$

Evaluate

$$\frac{151}{12}\approx 12.583333333$$

Solution Steps

Multiply \frac{5}{99} times \frac{11}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4}{21}}{\frac{5\times 11}{99\times 35}}-\frac{3}{4}+\frac{1\times 3+1}{3}$$

Do the multiplications in the fraction \frac{5\times 11}{99\times 35}.

$$\frac{\frac{4}{21}}{\frac{55}{3465}}-\frac{3}{4}+\frac{1\times 3+1}{3}$$

Reduce the fraction \frac{55}{3465} to lowest terms by extracting and canceling out 55.

$$\frac{\frac{4}{21}}{\frac{1}{63}}-\frac{3}{4}+\frac{1\times 3+1}{3}$$

Divide \frac{4}{21} by \frac{1}{63} by multiplying \frac{4}{21} by the reciprocal of \frac{1}{63}.

$$\frac{4}{21}\times 63-\frac{3}{4}+\frac{1\times 3+1}{3}$$

Express \frac{4}{21}\times 63 as a single fraction.

$$\frac{4\times 63}{21}-\frac{3}{4}+\frac{1\times 3+1}{3}$$

Multiply 4 and 63 to get 252.

$$\frac{252}{21}-\frac{3}{4}+\frac{1\times 3+1}{3}$$

Divide 252 by 21 to get 12.

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

Convert 12 to fraction \frac{48}{4}.

$$\frac{48}{4}-\frac{3}{4}+\frac{1\times 3+1}{3}$$

Since \frac{48}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{48-3}{4}+\frac{1\times 3+1}{3}$$

Subtract 3 from 48 to get 45.

$$\frac{45}{4}+\frac{1\times 3+1}{3}$$

Multiply 1 and 3 to get 3.

$$\frac{45}{4}+\frac{3+1}{3}$$

Add 3 and 1 to get 4.

$$\frac{45}{4}+\frac{4}{3}$$

Least common multiple of 4 and 3 is 12. Convert \frac{45}{4} and \frac{4}{3} to fractions with denominator 12.

$$\frac{135}{12}+\frac{16}{12}$$

Since \frac{135}{12} and \frac{16}{12} have the same denominator, add them by adding their numerators.

$$\frac{135+16}{12}$$

Add 135 and 16 to get 151.

$$\frac{151}{12}$$

Factor

$$\frac{151}{2 ^ {2} \cdot 3} = 12\frac{7}{12} = 12.583333333333334$$