evaluate the expression ( m + np - q ) if ( m=\frac{7}{15},n = -\frac{2}{3},p=-0.4 ), and ( q = 3\frac{1}{3}…

Explanation:

Step1: Substitute the values

Substitute (m = \frac{7}{15}), (n=-\frac{2}{3}), (p = - 0.4=-\frac{2}{5}), and (q=\frac{1}{3}) into the expression (m+np - q). [ \begin{align*} m+np - q&=\frac{7}{15}+\left(-\frac{2}{3}\right)\times\left(-\frac{2}{5}\right)-\frac{1}{3}\ \end{align*} ]

Step2: Calculate the product

Calculate (\left(-\frac{2}{3}\right)\times\left(-\frac{2}{5}\right)). According to the rule of multiplying two negative fractions ((-\frac{a}{b})\times(-\frac{c}{d})=\frac{ac}{bd}), we have (\left(-\frac{2}{3}\right)\times\left(-\frac{2}{5}\right)=\frac{(- 2)\times(-2)}{3\times5}=\frac{4}{15}). The expression becomes (\frac{7}{15}+\frac{4}{15}-\frac{1}{3}).

Step3: Add the first two fractions

Add (\frac{7}{15}+\frac{4}{15}). Since (\frac{a}{c}+\frac{b}{c}=\frac{a + b}{c}) ((c\neq0)), (\frac{7}{15}+\frac{4}{15}=\frac{7 + 4}{15}=\frac{11}{15}). The expression is now (\frac{11}{15}-\frac{1}{3}).

Step4: Make the denominators the same and subtract

Rewrite (\frac{1}{3}) with a denominator of 15. (\frac{1}{3}=\frac{1\times5}{3\times5}=\frac{5}{15}). Then (\frac{11}{15}-\frac{5}{15}=\frac{11-5}{15}=\frac{6}{15}).

Step5: Simplify the fraction

Simplify (\frac{6}{15}) by dividing both the numerator and denominator by their greatest - common divisor 3. (\frac{6\div3}{15\div3}=\frac{2}{5}=0.4).

Answer:

(0.4)