Solve 1/3*6+4/3*21/28+31/2*7frac{3}{5}

$$\frac { 1 } { 3 } \cdot 6 + \frac { 4 } { 3 } \cdot \frac { 21 } { 28 } + 3 \frac { 1 } { 2 } \cdot 7 \frac { 3 } { 5 }$$

Evaluate

$$\frac{148}{5}=29.6$$

Solution Steps

Multiply \frac{1}{3} and 6 to get \frac{6}{3}.

$$\frac{6}{3}+\frac{4}{3}\times \frac{21}{28}+\frac{3\times 2+1}{2}\times \frac{7\times 5+3}{5}$$

Divide 6 by 3 to get 2.

$$2+\frac{4}{3}\times \frac{21}{28}+\frac{3\times 2+1}{2}\times \frac{7\times 5+3}{5}$$

Reduce the fraction \frac{21}{28} to lowest terms by extracting and canceling out 7.

$$2+\frac{4}{3}\times \frac{3}{4}+\frac{3\times 2+1}{2}\times \frac{7\times 5+3}{5}$$

Cancel out \frac{4}{3} and its reciprocal \frac{3}{4}.

$$2+1+\frac{3\times 2+1}{2}\times \frac{7\times 5+3}{5}$$

Add 2 and 1 to get 3.

$$3+\frac{3\times 2+1}{2}\times \frac{7\times 5+3}{5}$$

Multiply 3 and 2 to get 6.

$$3+\frac{6+1}{2}\times \frac{7\times 5+3}{5}$$

Add 6 and 1 to get 7.

$$3+\frac{7}{2}\times \frac{7\times 5+3}{5}$$

Multiply 7 and 5 to get 35.

$$3+\frac{7}{2}\times \frac{35+3}{5}$$

Add 35 and 3 to get 38.

$$3+\frac{7}{2}\times \frac{38}{5}$$

Multiply \frac{7}{2} times \frac{38}{5} by multiplying numerator times numerator and denominator times denominator.

$$3+\frac{7\times 38}{2\times 5}$$

Do the multiplications in the fraction \frac{7\times 38}{2\times 5}.

$$3+\frac{266}{10}$$

Reduce the fraction \frac{266}{10} to lowest terms by extracting and canceling out 2.

$$3+\frac{133}{5}$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{15}{5}+\frac{133}{5}$$

Since \frac{15}{5} and \frac{133}{5} have the same denominator, add them by adding their numerators.

$$\frac{15+133}{5}$$

Add 15 and 133 to get 148.

$$\frac{148}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 37}{5} = 29\frac{3}{5} = 29.6$$