Solve [0.4-6.65div5)3*(15-4.8-1.8)+8]-3

$$[ 0.4 - 6.65 \div 5 ) 3 \times ( 15 - 4.8 - 1.8 ) + 8 ] - 3$$

Evaluate

$$-15.436$$

Solution Steps

Expand \frac{6.65}{5} by multiplying both numerator and the denominator by 100.

$$\left(0.4-\frac{665}{500}\right)\times 3\left(15-4.8-1.8\right)+8$$

Reduce the fraction \frac{665}{500} to lowest terms by extracting and canceling out 5.

$$\left(0.4-\frac{133}{100}\right)\times 3\left(15-4.8-1.8\right)+8$$

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\left(\frac{2}{5}-\frac{133}{100}\right)\times 3\left(15-4.8-1.8\right)+8$$

Least common multiple of 5 and 100 is 100. Convert \frac{2}{5} and \frac{133}{100} to fractions with denominator 100.

$$\left(\frac{40}{100}-\frac{133}{100}\right)\times 3\left(15-4.8-1.8\right)+8$$

Since \frac{40}{100} and \frac{133}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40-133}{100}\times 3\left(15-4.8-1.8\right)+8$$

Subtract 133 from 40 to get -93.

$$-\frac{93}{100}\times 3\left(15-4.8-1.8\right)+8$$

Express -\frac{93}{100}\times 3 as a single fraction.

$$\frac{-93\times 3}{100}\left(15-4.8-1.8\right)+8$$

Multiply -93 and 3 to get -279.

$$\frac{-279}{100}\left(15-4.8-1.8\right)+8$$

Fraction \frac{-279}{100} can be rewritten as -\frac{279}{100} by extracting the negative sign.

$$-\frac{279}{100}\left(15-4.8-1.8\right)+8$$

Subtract 4.8 from 15 to get 10.2.

$$-\frac{279}{100}\left(10.2-1.8\right)+8$$

Subtract 1.8 from 10.2 to get 8.4.

$$-\frac{279}{100}\times 8.4+8$$

Convert decimal number 8.4 to fraction \frac{84}{10}. Reduce the fraction \frac{84}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{279}{100}\times \frac{42}{5}+8$$

Multiply -\frac{279}{100} times \frac{42}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-279\times 42}{100\times 5}+8$$

Do the multiplications in the fraction \frac{-279\times 42}{100\times 5}.

$$\frac{-11718}{500}+8$$

Reduce the fraction \frac{-11718}{500} to lowest terms by extracting and canceling out 2.

$$-\frac{5859}{250}+8$$

Convert 8 to fraction \frac{2000}{250}.

$$-\frac{5859}{250}+\frac{2000}{250}$$

Since -\frac{5859}{250} and \frac{2000}{250} have the same denominator, add them by adding their numerators.

$$\frac{-5859+2000}{250}$$

Add -5859 and 2000 to get -3859.

$$-\frac{3859}{250}$$

Factor

$$-15.436$$