Solve =[15*7*8+1/2*22/7*7/2*7/2*15]_{m}

$$= [ 15 \times 7 \times 8 + \frac { 1 } { 2 } \times \frac { 22 } { 7 } \times \frac { 7 } { 2 } \times \frac { 7 } { 2 } \times 15 ] _ { m }$$

Evaluate

$$\frac{4515}{4}=1128.75$$

Solution Steps

Multiply 15 and 7 to get 105.

$$105\times 8+\frac{1}{2}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 15$$

Multiply 105 and 8 to get 840.

$$840+\frac{1}{2}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 15$$

Multiply \frac{1}{2} times \frac{22}{7} by multiplying numerator times numerator and denominator times denominator.

$$840+\frac{1\times 22}{2\times 7}\times \frac{7}{2}\times \frac{7}{2}\times 15$$

Do the multiplications in the fraction \frac{1\times 22}{2\times 7}.

$$840+\frac{22}{14}\times \frac{7}{2}\times \frac{7}{2}\times 15$$

Reduce the fraction \frac{22}{14} to lowest terms by extracting and canceling out 2.

$$840+\frac{11}{7}\times \frac{7}{2}\times \frac{7}{2}\times 15$$

Multiply \frac{11}{7} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$840+\frac{11\times 7}{7\times 2}\times \frac{7}{2}\times 15$$

Cancel out 7 in both numerator and denominator.

$$840+\frac{11}{2}\times \frac{7}{2}\times 15$$

Multiply \frac{11}{2} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$840+\frac{11\times 7}{2\times 2}\times 15$$

Do the multiplications in the fraction \frac{11\times 7}{2\times 2}.

$$840+\frac{77}{4}\times 15$$

Express \frac{77}{4}\times 15 as a single fraction.

$$840+\frac{77\times 15}{4}$$

Multiply 77 and 15 to get 1155.

$$840+\frac{1155}{4}$$

Convert 840 to fraction \frac{3360}{4}.

$$\frac{3360}{4}+\frac{1155}{4}$$

Since \frac{3360}{4} and \frac{1155}{4} have the same denominator, add them by adding their numerators.

$$\frac{3360+1155}{4}$$

Add 3360 and 1155 to get 4515.

$$\frac{4515}{4}$$

Factor

$$\frac{3 \cdot 5 \cdot 7 \cdot 43}{2 ^ {2}} = 1128\frac{3}{4} = 1128.75$$