use the order of operations to simplify the expression.\n-\\frac{5}{4}(\\frac{1}{3})+\\frac{5}{8}+\\frac{7}{6…

use the order of operations to simplify the expression.\n-\\frac{5}{4}(\\frac{1}{3})+\\frac{5}{8}+\\frac{7}{6}\n-\\frac{5}{4}(\\frac{1}{3})+\\frac{5}{8}+\\frac{7}{6}=\\frac{11}{8} (type a fraction. simplify your answer.)

use the order of operations to simplify the expression.\n-\\frac{5}{4}(\\frac{1}{3})+\\frac{5}{8}+\\frac{7}{6}\n-\\frac{5}{4}(\\frac{1}{3})+\\frac{5}{8}+\\frac{7}{6}=\\frac{11}{8} (type a fraction. simplify your answer.)

Answer

Explanation:

Step1: Calculate the multiplication

First, calculate (-\frac{5}{4}\times\frac{1}{3}). According to the rule of fraction multiplication (\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}), we have (-\frac{5}{4}\times\frac{1}{3}=-\frac{5\times1}{4\times3}=-\frac{5}{12}). The expression becomes (-\frac{5}{12}+\frac{5}{8}+\frac{7}{6}).

Step2: Find the common denominator

The common denominator of (12), (8) and (6) is (24). Rewrite each fraction with the common denominator: (-\frac{5}{12}=-\frac{5\times2}{12\times2}=-\frac{10}{24}), (\frac{5}{8}=\frac{5\times3}{8\times3}=\frac{15}{24}), (\frac{7}{6}=\frac{7\times4}{6\times4}=\frac{28}{24}). The expression is now (-\frac{10}{24}+\frac{15}{24}+\frac{28}{24}).

Step3: Add the fractions

According to the rule of fraction addition (\frac{a}{c}+\frac{b}{c}=\frac{a + b}{c}), we have (\frac{- 10 + 15+28}{24}=\frac{(-10)+(15 + 28)}{24}=\frac{-10 + 43}{24}=\frac{33}{24}). Simplify (\frac{33}{24}) by dividing both the numerator and denominator by (3), (\frac{33\div3}{24\div3}=\frac{11}{8}).

Answer:

(\frac{11}{8})