Solve 229.5div1000*(x-298.15)-483.636

$$229.5 \div 1000 \times (x-298.15)-483.636$$

Evaluate

$$\frac{459x}{2000}-552.061425$$

Solution Steps

Expand \frac{229.5}{1000} by multiplying both numerator and the denominator by 10.

$$\frac{2295}{10000}\left(x-298.15\right)-483.636$$

Reduce the fraction \frac{2295}{10000} to lowest terms by extracting and canceling out 5.

$$\frac{459}{2000}\left(x-298.15\right)-483.636$$

Use the distributive property to multiply \frac{459}{2000} by x-298.15.

$$\frac{459}{2000}x+\frac{459}{2000}\left(-298.15\right)-483.636$$

Convert decimal number -298.15 to fraction -\frac{29815}{100}. Reduce the fraction -\frac{29815}{100} to lowest terms by extracting and canceling out 5.

$$\frac{459}{2000}x+\frac{459}{2000}\left(-\frac{5963}{20}\right)-483.636$$

Multiply \frac{459}{2000} times -\frac{5963}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{459}{2000}x+\frac{459\left(-5963\right)}{2000\times 20}-483.636$$

Do the multiplications in the fraction \frac{459\left(-5963\right)}{2000\times 20}.

$$\frac{459}{2000}x+\frac{-2737017}{40000}-483.636$$

Fraction \frac{-2737017}{40000} can be rewritten as -\frac{2737017}{40000} by extracting the negative sign.

$$\frac{459}{2000}x-\frac{2737017}{40000}-483.636$$

Convert decimal number 483.636 to fraction \frac{483636}{1000}. Reduce the fraction \frac{483636}{1000} to lowest terms by extracting and canceling out 4.

$$\frac{459}{2000}x-\frac{2737017}{40000}-\frac{120909}{250}$$

Least common multiple of 40000 and 250 is 40000. Convert -\frac{2737017}{40000} and \frac{120909}{250} to fractions with denominator 40000.

$$\frac{459}{2000}x-\frac{2737017}{40000}-\frac{19345440}{40000}$$

Since -\frac{2737017}{40000} and \frac{19345440}{40000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{459}{2000}x+\frac{-2737017-19345440}{40000}$$

Subtract 19345440 from -2737017 to get -22082457.

$$\frac{459}{2000}x-\frac{22082457}{40000}$$

Expand

$$\frac{459x}{2000}-552.061425$$

Solution Steps

Expand \frac{229.5}{1000} by multiplying both numerator and the denominator by 10.

$$\frac{2295}{10000}\left(x-298.15\right)-483.636$$

Reduce the fraction \frac{2295}{10000} to lowest terms by extracting and canceling out 5.

$$\frac{459}{2000}\left(x-298.15\right)-483.636$$

Use the distributive property to multiply \frac{459}{2000} by x-298.15.

$$\frac{459}{2000}x+\frac{459}{2000}\left(-298.15\right)-483.636$$

Convert decimal number -298.15 to fraction -\frac{29815}{100}. Reduce the fraction -\frac{29815}{100} to lowest terms by extracting and canceling out 5.

$$\frac{459}{2000}x+\frac{459}{2000}\left(-\frac{5963}{20}\right)-483.636$$

Multiply \frac{459}{2000} times -\frac{5963}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{459}{2000}x+\frac{459\left(-5963\right)}{2000\times 20}-483.636$$

Do the multiplications in the fraction \frac{459\left(-5963\right)}{2000\times 20}.

$$\frac{459}{2000}x+\frac{-2737017}{40000}-483.636$$

Fraction \frac{-2737017}{40000} can be rewritten as -\frac{2737017}{40000} by extracting the negative sign.

$$\frac{459}{2000}x-\frac{2737017}{40000}-483.636$$

Convert decimal number 483.636 to fraction \frac{483636}{1000}. Reduce the fraction \frac{483636}{1000} to lowest terms by extracting and canceling out 4.

$$\frac{459}{2000}x-\frac{2737017}{40000}-\frac{120909}{250}$$

Least common multiple of 40000 and 250 is 40000. Convert -\frac{2737017}{40000} and \frac{120909}{250} to fractions with denominator 40000.

$$\frac{459}{2000}x-\frac{2737017}{40000}-\frac{19345440}{40000}$$

Since -\frac{2737017}{40000} and \frac{19345440}{40000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{459}{2000}x+\frac{-2737017-19345440}{40000}$$

Subtract 19345440 from -2737017 to get -22082457.

$$\frac{459}{2000}x-\frac{22082457}{40000}$$