Solve 14*13/8+0.314*25/4-31.4*0.2=143/40

$$14 \times 1 \frac { 3 } { 8 } + 0.314 \times \frac { 25 } { 4 } - 31.4 \times 0.2 = 14 \frac { 3 } { 40 }$$

Verify

Solution Steps

Multiply both sides of the equation by 40, the least common multiple of 8,4,40.

$$40\left(14\times \frac{1\times 8+3}{8}+0.314\times \frac{25}{4}\right)-1256\times 0.2=14\times 40+3$$

Multiply 1 and 8 to get 8.

$$40\left(14\times \frac{8+3}{8}+0.314\times \frac{25}{4}\right)-1256\times 0.2=14\times 40+3$$

Add 8 and 3 to get 11.

$$40\left(14\times \frac{11}{8}+0.314\times \frac{25}{4}\right)-1256\times 0.2=14\times 40+3$$

Express 14\times \frac{11}{8} as a single fraction.

$$40\left(\frac{14\times 11}{8}+0.314\times \frac{25}{4}\right)-1256\times 0.2=14\times 40+3$$

Multiply 14 and 11 to get 154.

$$40\left(\frac{154}{8}+0.314\times \frac{25}{4}\right)-1256\times 0.2=14\times 40+3$$

Reduce the fraction \frac{154}{8} to lowest terms by extracting and canceling out 2.

$$40\left(\frac{77}{4}+0.314\times \frac{25}{4}\right)-1256\times 0.2=14\times 40+3$$

Convert decimal number 0.314 to fraction \frac{314}{1000}. Reduce the fraction \frac{314}{1000} to lowest terms by extracting and canceling out 2.

$$40\left(\frac{77}{4}+\frac{157}{500}\times \frac{25}{4}\right)-1256\times 0.2=14\times 40+3$$

Multiply \frac{157}{500} times \frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$40\left(\frac{77}{4}+\frac{157\times 25}{500\times 4}\right)-1256\times 0.2=14\times 40+3$$

Do the multiplications in the fraction \frac{157\times 25}{500\times 4}.

$$40\left(\frac{77}{4}+\frac{3925}{2000}\right)-1256\times 0.2=14\times 40+3$$

Reduce the fraction \frac{3925}{2000} to lowest terms by extracting and canceling out 25.

$$40\left(\frac{77}{4}+\frac{157}{80}\right)-1256\times 0.2=14\times 40+3$$

Least common multiple of 4 and 80 is 80. Convert \frac{77}{4} and \frac{157}{80} to fractions with denominator 80.

$$40\left(\frac{1540}{80}+\frac{157}{80}\right)-1256\times 0.2=14\times 40+3$$

Since \frac{1540}{80} and \frac{157}{80} have the same denominator, add them by adding their numerators.

$$40\times \frac{1540+157}{80}-1256\times 0.2=14\times 40+3$$

Add 1540 and 157 to get 1697.

$$40\times \frac{1697}{80}-1256\times 0.2=14\times 40+3$$

Express 40\times \frac{1697}{80} as a single fraction.

$$\frac{40\times 1697}{80}-1256\times 0.2=14\times 40+3$$

Multiply 40 and 1697 to get 67880.

$$\frac{67880}{80}-1256\times 0.2=14\times 40+3$$

Reduce the fraction \frac{67880}{80} to lowest terms by extracting and canceling out 40.

$$\frac{1697}{2}-1256\times 0.2=14\times 40+3$$

Multiply 1256 and 0.2 to get 251.2.

$$\frac{1697}{2}-251.2=14\times 40+3$$

Convert decimal number 251.2 to fraction \frac{2512}{10}. Reduce the fraction \frac{2512}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1697}{2}-\frac{1256}{5}=14\times 40+3$$

Least common multiple of 2 and 5 is 10. Convert \frac{1697}{2} and \frac{1256}{5} to fractions with denominator 10.

$$\frac{8485}{10}-\frac{2512}{10}=14\times 40+3$$

Since \frac{8485}{10} and \frac{2512}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8485-2512}{10}=14\times 40+3$$

Subtract 2512 from 8485 to get 5973.

$$\frac{5973}{10}=14\times 40+3$$

Multiply 14 and 40 to get 560.

$$\frac{5973}{10}=560+3$$

Add 560 and 3 to get 563.

$$\frac{5973}{10}=563$$

Convert 563 to fraction \frac{5630}{10}.

$$\frac{5973}{10}=\frac{5630}{10}$$

Compare \frac{5973}{10} and \frac{5630}{10}.

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