Solve 45+5(30div22/45-22)

$$45 + 5 ( \frac { 30 \div 22 } { 45 - 22 } )$$

Evaluate

$$\frac{11460}{253}\approx 45.296442688$$

Solution Steps

Reduce the fraction \frac{30}{22} to lowest terms by extracting and canceling out 2.

$$45+5\times \frac{\frac{15}{11}}{45-22}$$

Subtract 22 from 45 to get 23.

$$45+5\times \frac{\frac{15}{11}}{23}$$

Express \frac{\frac{15}{11}}{23} as a single fraction.

$$45+5\times \frac{15}{11\times 23}$$

Multiply 11 and 23 to get 253.

$$45+5\times \frac{15}{253}$$

Express 5\times \frac{15}{253} as a single fraction.

$$45+\frac{5\times 15}{253}$$

Multiply 5 and 15 to get 75.

$$45+\frac{75}{253}$$

Convert 45 to fraction \frac{11385}{253}.

$$\frac{11385}{253}+\frac{75}{253}$$

Since \frac{11385}{253} and \frac{75}{253} have the same denominator, add them by adding their numerators.

$$\frac{11385+75}{253}$$

Add 11385 and 75 to get 11460.

$$\frac{11460}{253}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 5 \cdot 191}{11 \cdot 23} = 45\frac{75}{253} = 45.29644268774704$$