Solve 0.3528/frac{1.947{3.2}+0.9/3.20.3528}

$$\frac { 0.3528 } { \frac { 1.947 } { 3.2 } + \frac { 0.9 } { 3.2 } 0.3528 }$$

Evaluate

$$\frac{9408}{18871}\approx 0.498542738$$

Solution Steps

Expand \frac{1.947}{3.2} by multiplying both numerator and the denominator by 1000.

$$\frac{0.3528}{\frac{1947}{3200}+\frac{0.9}{3.2}\times 0.3528}$$

Expand \frac{0.9}{3.2} by multiplying both numerator and the denominator by 10.

$$\frac{0.3528}{\frac{1947}{3200}+\frac{9}{32}\times 0.3528}$$

Convert decimal number 0.3528 to fraction \frac{3528}{10000}. Reduce the fraction \frac{3528}{10000} to lowest terms by extracting and canceling out 8.

$$\frac{0.3528}{\frac{1947}{3200}+\frac{9}{32}\times \frac{441}{1250}}$$

Multiply \frac{9}{32} times \frac{441}{1250} by multiplying numerator times numerator and denominator times denominator.

$$\frac{0.3528}{\frac{1947}{3200}+\frac{9\times 441}{32\times 1250}}$$

Do the multiplications in the fraction \frac{9\times 441}{32\times 1250}.

$$\frac{0.3528}{\frac{1947}{3200}+\frac{3969}{40000}}$$

Least common multiple of 3200 and 40000 is 80000. Convert \frac{1947}{3200} and \frac{3969}{40000} to fractions with denominator 80000.

$$\frac{0.3528}{\frac{48675}{80000}+\frac{7938}{80000}}$$

Since \frac{48675}{80000} and \frac{7938}{80000} have the same denominator, add them by adding their numerators.

$$\frac{0.3528}{\frac{48675+7938}{80000}}$$

Add 48675 and 7938 to get 56613.

$$\frac{0.3528}{\frac{56613}{80000}}$$

Divide 0.3528 by \frac{56613}{80000} by multiplying 0.3528 by the reciprocal of \frac{56613}{80000}.

$$0.3528\times \frac{80000}{56613}$$

Convert decimal number 0.3528 to fraction \frac{3528}{10000}. Reduce the fraction \frac{3528}{10000} to lowest terms by extracting and canceling out 8.

$$\frac{441}{1250}\times \frac{80000}{56613}$$

Multiply \frac{441}{1250} times \frac{80000}{56613} by multiplying numerator times numerator and denominator times denominator.

$$\frac{441\times 80000}{1250\times 56613}$$

Do the multiplications in the fraction \frac{441\times 80000}{1250\times 56613}.

$$\frac{35280000}{70766250}$$

Reduce the fraction \frac{35280000}{70766250} to lowest terms by extracting and canceling out 3750.

$$\frac{9408}{18871}$$

Factor

$$\frac{3 \cdot 2 ^ {6} \cdot 7 ^ {2}}{113 \cdot 167} = 0.498542737533782$$