Solve 7*150*3.5+7*69*(7+12+3.5)*2+7*200*(7+12+7+100)*2/7*150+7*69*2+7*200*2

$$\frac { 7 \times 150 \times 3.5 + 7 \times 69 \times ( 7 + 12 + 3.5 ) \times 2 + 7 \times 200 \times ( 7 + 12 + 7 + 100 ) \times 2 } { 7 \times 150 + 7 \times 69 \times 2 + 7 \times 200 \times 2 }$$

Evaluate

$$\frac{27015}{344}\approx 78.531976744$$

Solution Steps

Multiply 7 and 150 to get 1050. Multiply 7 and 69 to get 483. Multiply 7 and 200 to get 1400.

$$\frac{1050\times 3.5+483\left(7+12+3.5\right)\times 2+1400\left(7+12+7+100\right)\times 2}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Multiply 1050 and 3.5 to get 3675.

$$\frac{3675+483\left(7+12+3.5\right)\times 2+1400\left(7+12+7+100\right)\times 2}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Add 7 and 12 to get 19.

$$\frac{3675+483\left(19+3.5\right)\times 2+1400\left(7+12+7+100\right)\times 2}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Add 19 and 3.5 to get 22.5.

$$\frac{3675+483\times 22.5\times 2+1400\left(7+12+7+100\right)\times 2}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Multiply 483 and 22.5 to get 10867.5.

$$\frac{3675+10867.5\times 2+1400\left(7+12+7+100\right)\times 2}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Multiply 10867.5 and 2 to get 21735.

$$\frac{3675+21735+1400\left(7+12+7+100\right)\times 2}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Add 3675 and 21735 to get 25410.

$$\frac{25410+1400\left(7+12+7+100\right)\times 2}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Add 7 and 12 to get 19.

$$\frac{25410+1400\left(19+7+100\right)\times 2}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Add 19 and 7 to get 26.

$$\frac{25410+1400\left(26+100\right)\times 2}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Add 26 and 100 to get 126.

$$\frac{25410+1400\times 126\times 2}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Multiply 1400 and 126 to get 176400.

$$\frac{25410+176400\times 2}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Multiply 176400 and 2 to get 352800.

$$\frac{25410+352800}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Add 25410 and 352800 to get 378210.

$$\frac{378210}{7\times 150+7\times 69\times 2+7\times 200\times 2}$$

Multiply 7 and 150 to get 1050. Multiply 7 and 69 to get 483. Multiply 7 and 200 to get 1400.

$$\frac{378210}{1050+483\times 2+1400\times 2}$$

Multiply 483 and 2 to get 966.

$$\frac{378210}{1050+966+1400\times 2}$$

Add 1050 and 966 to get 2016.

$$\frac{378210}{2016+1400\times 2}$$

Multiply 1400 and 2 to get 2800.

$$\frac{378210}{2016+2800}$$

Add 2016 and 2800 to get 4816.

$$\frac{378210}{4816}$$

Reduce the fraction \frac{378210}{4816} to lowest terms by extracting and canceling out 14.

$$\frac{27015}{344}$$

Factor

$$\frac{3 \cdot 5 \cdot 1801}{43 \cdot 2 ^ {3}} = 78\frac{183}{344} = 78.53197674418605$$