Solve 1000/1+0.15*frac{55{365}}

$$\frac { 1000 } { 1 + 0.15 \times \frac { 55 } { 365 } }$$

Evaluate

$$\frac{1460000}{1493}\approx 977.896851976$$

Solution Steps

Reduce the fraction \frac{55}{365} to lowest terms by extracting and canceling out 5.

$$\frac{1000}{1+0.15\times \frac{11}{73}}$$

Convert decimal number 0.15 to fraction \frac{15}{100}. Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$\frac{1000}{1+\frac{3}{20}\times \frac{11}{73}}$$

Multiply \frac{3}{20} times \frac{11}{73} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1000}{1+\frac{3\times 11}{20\times 73}}$$

Do the multiplications in the fraction \frac{3\times 11}{20\times 73}.

$$\frac{1000}{1+\frac{33}{1460}}$$

Convert 1 to fraction \frac{1460}{1460}.

$$\frac{1000}{\frac{1460}{1460}+\frac{33}{1460}}$$

Since \frac{1460}{1460} and \frac{33}{1460} have the same denominator, add them by adding their numerators.

$$\frac{1000}{\frac{1460+33}{1460}}$$

Add 1460 and 33 to get 1493.

$$\frac{1000}{\frac{1493}{1460}}$$

Divide 1000 by \frac{1493}{1460} by multiplying 1000 by the reciprocal of \frac{1493}{1460}.

$$1000\times \frac{1460}{1493}$$

Express 1000\times \frac{1460}{1493} as a single fraction.

$$\frac{1000\times 1460}{1493}$$

Multiply 1000 and 1460 to get 1460000.

$$\frac{1460000}{1493}$$

Factor

$$\frac{73 \cdot 2 ^ {5} \cdot 5 ^ {4}}{1493} = 977\frac{1339}{1493} = 977.8968519758874$$