Question

evaluate
(1.8) (3\frac{2}{3}-6)
enter your answer as a simplified mixed number in the box

Explanation:

Step1: Convert mixed - number to improper fraction

First, convert $3\frac{2}{3}$ to an improper fraction. $3\frac{2}{3}=\frac{3\times3 + 2}{3}=\frac{9 + 2}{3}=\frac{11}{3}$.

Step2: Calculate the value inside the parentheses

Calculate $\frac{11}{3}-6$. Rewrite 6 as $\frac{18}{3}$. Then $\frac{11}{3}-6=\frac{11}{3}-\frac{18}{3}=\frac{11 - 18}{3}=-\frac{7}{3}$.

Step3: Convert 1.8 to fraction

$1.8=\frac{18}{10}=\frac{9}{5}$.

Step4: Multiply the two fractions

Multiply $\frac{9}{5}$ by $-\frac{7}{3}$. $\frac{9}{5}\times(-\frac{7}{3})=\frac{9\times(-7)}{5\times3}=\frac{-63}{15}$.

Step5: Simplify the fraction

Simplify $\frac{-63}{15}$ by dividing both the numerator and denominator by 3. $\frac{-63\div3}{15\div3}=-\frac{21}{5}$.

Step6: Convert to mixed - number

Divide 21 by 5. $21\div5 = 4$ with a remainder of 1. So $-\frac{21}{5}=-4\frac{1}{5}$.

Answer:

$-4\frac{1}{5}$