Evaluate each expression if \( a=\frac{5}{6} b=-\frac{3}{4}, c \equiv 0,4 \), and \( d=\frac{1}{2} \), (Example 1) \( \frac{h}{c}+a-d \) 2. \( a+b+c+d \) 3. \( c=a+\frac{b}{a} \) \( \frac{a}{b}+\frac{a}{c} \) 5. \( b^{2}-d \) 6. \( a+\frac{a}{b}-c \) \[ a^{2}+b \] 8. \( b-c+d \) 9. \( \frac{c}{a}-b^{2} \)

Evaluate the expression by following steps: - step0: Evaluate: \(b^{2}-d\) - step1: Substitute: \(\left(-\frac{3}{4}\right)^{2}-\frac{1}{2}\) - step2: Simplify: \(\frac{3^{2}}{4^{2}}-\frac{1}{2}\) - step3: Evaluate the power: \(\frac{9}{16}-\frac{1}{2}\) - step4: Reduce fractions to a common denominator: \(\frac{9}{16}-\frac{8}{2\times 8}\) - step5: Multiply the numbers: \(\frac{9}{16}-\frac{8}{16}\) - step6: Transform the expression: \(\frac{9-8}{16}\) - step7: Subtract the numbers: \(\frac{1}{16}\) Substitute \( a=\frac{5}{6},b=-\frac{3}{4} \) into the expression \( a^{2}+b \). Evaluate the expression by following steps: - step0: Evaluate: \(a^{2}+b\) - step1: Substitute: \(\left(\frac{5}{6}\right)^{2}-\frac{3}{4}\) - step2: Simplify: \(\frac{5^{2}}{6^{2}}-\frac{3}{4}\) - step3: Evaluate the power: \(\frac{25}{36}-\frac{3}{4}\) - step4: Reduce fractions to a common denominator: \(\frac{25}{36}-\frac{3\times 9}{4\times 9}\) - step5: Multiply the numbers: \(\frac{25}{36}-\frac{3\times 9}{36}\) - step6: Transform the expression: \(\frac{25-3\times 9}{36}\) - step7: Multiply the numbers: \(\frac{25-27}{36}\) - step8: Subtract the numbers: \(\frac{-2}{36}\) - step9: Reduce the fraction: \(\frac{-1}{18}\) - step10: Rewrite the fraction: \(-\frac{1}{18}\) Substitute \( a=\frac{5}{6},b=-\frac{3}{4},c=0.4,d=\frac{1}{2} \) into the expression \( b-c+d \). Evaluate the expression by following steps: - step0: Evaluate: \(b-c+d\) - step1: Substitute: \(-\frac{3}{4}-0.4+\frac{1}{2}\) - step2: Rewrite the expression: \(-\frac{3}{4}-\frac{2}{5}+\frac{1}{2}\) - step3: Reduce fractions to a common denominator: \(-\frac{3\times 5}{4\times 5}-\frac{2\times 4}{5\times 4}+\frac{10}{2\times 10}\) - step4: Multiply the numbers: \(-\frac{3\times 5}{20}-\frac{2\times 4}{5\times 4}+\frac{10}{2\times 10}\) - step5: Multiply the numbers: \(-\frac{3\times 5}{20}-\frac{2\times 4}{20}+\frac{10}{2\times 10}\) - step6: Multiply the numbers: \(-\frac{3\times 5}{20}-\frac{2\times 4}{20}+\frac{10}{20}\) - step7: Transform the expression: \(\frac{-3\times 5-2\times 4+10}{20}\) - step8: Multiply the numbers: \(\frac{-15-2\times 4+10}{20}\) - step9: Multiply the numbers: \(\frac{-15-8+10}{20}\) - step10: Calculate: \(\frac{-13}{20}\) - step11: Rewrite the fraction: \(-\frac{13}{20}\) Substitute \( a=\frac{5}{6},b=-\frac{3}{4},c=0.4 \) into the expression \( \frac{c}{a}-b^{2} \). Evaluate the expression by following steps: - step0: Evaluate: \(\frac{c}{a}-b^{2}\) - step1: Substitute: \(\frac{0.4}{\frac{5}{6}}-\left(-\frac{3}{4}\right)^{2}\) - step2: Divide the terms: \(\frac{12}{25}-\left(-\frac{3}{4}\right)^{2}\) - step3: Rewrite the expression: \(\frac{12}{25}-\frac{3^{2}}{4^{2}}\) - step4: Evaluate the power: \(\frac{12}{25}-\frac{9}{16}\) - step5: Reduce fractions to a common denominator: \(\frac{12\times 16}{25\times 16}-\frac{9\times 25}{16\times 25}\) - step6: Multiply the numbers: \(\frac{12\times 16}{400}-\frac{9\times 25}{16\times 25}\) - step7: Multiply the numbers: \(\frac{12\times 16}{400}-\frac{9\times 25}{400}\) - step8: Transform the expression: \(\frac{12\times 16-9\times 25}{400}\) - step9: Multiply the numbers: \(\frac{192-9\times 25}{400}\) - step10: Multiply the numbers: \(\frac{192-225}{400}\) - step11: Subtract the numbers: \(\frac{-33}{400}\) - step12: Rewrite the fraction: \(-\frac{33}{400}\) Substitute \( a=\frac{5}{6},b=-\frac{3}{4},c=0.4,d=\frac{1}{2} \) into the expression \( \frac{h}{c}+a-d \). Evaluate the expression by following steps: - step0: Evaluate: \(\frac{h}{c}+a-d\) - step1: Substitute: \(\frac{h}{0.4}+\frac{5}{6}-\frac{1}{2}\) - step2: Divide the terms: \(\frac{5h}{2}+\frac{5}{6}-\frac{1}{2}\) - step3: Reduce fractions to a common denominator: \(\frac{5h\times 3}{2\times 3}+\frac{5}{6}-\frac{3}{2\times 3}\) - step4: Multiply the numbers: \(\frac{5h\times 3}{6}+\frac{5}{6}-\frac{3}{2\times 3}\) - step5: Multiply the numbers: \(\frac{5h\times 3}{6}+\frac{5}{6}-\frac{3}{6}\) - step6: Transform the expression: \(\frac{5h\times 3+5-3}{6}\) - step7: Multiply the terms: \(\frac{15h+5-3}{6}\) - step8: Subtract the numbers: \(\frac{15h+2}{6}\) Substitute \( a=\frac{5}{6},b=-\frac{3}{4},c=0.4 \) into the expression \( \frac{a}{b}+\frac{a}{c} \). Evaluate the expression by following steps: - step0: Evaluate: \(\frac{a}{b}+\frac{a}{c}\) - step1: Substitute: \(\frac{\frac{5}{6}}{-\frac{3}{4}}+\frac{\frac{5}{6}}{0.4}\) - step2: Divide the terms: \(-\frac{10}{9}+\frac{\frac{5}{6}}{0.4}\) - step3: Divide the numbers: \(-\frac{10}{9}+\frac{25}{12}\) - step4: Reduce fractions to a common denominator: \(-\frac{10\times 4}{9\times 4}+\frac{25\times 3}{12\times 3}\) - step5: Multiply the numbers: \(-\frac{10\times 4}{36}+\frac{25\times 3}{12\times 3}\) - step6: Multiply the numbers: \(-\frac{10\times 4}{36}+\frac{25\times 3}{36}\) - step7: Transform the expression: \(\frac{-10\times 4+25\times 3}{36}\) - step8: Multiply the numbers: \(\frac{-40+25\times 3}{36}\) - step9: Multiply the numbers: \(\frac{-40+75}{36}\) - step10: Add the numbers: \(\frac{35}{36}\) Substitute \( a=\frac{5}{6},b=-\frac{3}{4},c=0.4,d=\frac{1}{2} \) into the expression \( a+b+c+d \). Evaluate the expression by following steps: - step0: Evaluate: \(a+b+c+d\) - step1: Substitute: \(\frac{5}{6}-\frac{3}{4}+0.4+\frac{1}{2}\) - step2: Rewrite the expression: \(\frac{5}{6}-\frac{3}{4}+\frac{2}{5}+\frac{1}{2}\) - step3: Reduce fractions to a common denominator: \(\frac{5\times 2\times 5}{6\times 2\times 5}-\frac{3\times 3\times 5}{4\times 3\times 5}+\frac{2\times 2\times 3\times 2}{5\times 2\times 3\times 2}+\frac{30}{2\times 30}\) - step4: Multiply the terms: \(\frac{5\times 2\times 5}{60}-\frac{3\times 3\times 5}{4\times 3\times 5}+\frac{2\times 2\times 3\times 2}{5\times 2\times 3\times 2}+\frac{30}{2\times 30}\) - step5: Multiply the terms: \(\frac{5\times 2\times 5}{60}-\frac{3\times 3\times 5}{60}+\frac{2\times 2\times 3\times 2}{5\times 2\times 3\times 2}+\frac{30}{2\times 30}\) - step6: Multiply the terms: \(\frac{5\times 2\times 5}{60}-\frac{3\times 3\times 5}{60}+\frac{2\times 2\times 3\times 2}{60}+\frac{30}{2\times 30}\) - step7: Multiply the numbers: \(\frac{5\times 2\times 5}{60}-\frac{3\times 3\times 5}{60}+\frac{2\times 2\times 3\times 2}{60}+\frac{30}{60}\) - step8: Transform the expression: \(\frac{5\times 2\times 5-3\times 3\times 5+2\times 2\times 3\times 2+30}{60}\) - step9: Multiply the terms: \(\frac{50-3\times 3\times 5+2\times 2\times 3\times 2+30}{60}\) - step10: Multiply the terms: \(\frac{50-45+2\times 2\times 3\times 2+30}{60}\) - step11: Multiply the terms: \(\frac{50-45+24+30}{60}\) - step12: Calculate: \(\frac{59}{60}\) Substitute \( a=\frac{5}{6},b=-\frac{3}{4},c=0.4 \) into the expression \( c=a+\frac{b}{a} \). Evaluate the expression by following steps: - step0: Evaluate: \(c=a+\frac{b}{a}\) - step1: Substitute: \(0.4=\frac{5}{6}+\frac{-\frac{3}{4}}{\frac{5}{6}}\) - step2: Divide the terms: \(0.4=\frac{5}{6}-\frac{9}{10}\) - step3: Subtract the numbers: \(0.4=-\frac{1}{15}\) - step4: Calculate: \(0.4=-0.0\dot{6}\) - step5: Check the equality: \(\textrm{false}\) Substitute \( a=\frac{5}{6},b=-\frac{3}{4},c=0.4 \) into the expression \( a+\frac{a}{b}-c \). Evaluate the expression by following steps: - step0: Evaluate: \(a+\frac{a}{b}-c\) - step1: Substitute: \(\frac{5}{6}+\frac{\frac{5}{6}}{-\frac{3}{4}}-0.4\) - step2: Divide the terms: \(\frac{5}{6}-\frac{10}{9}-0.4\) - step3: Rewrite the expression: \(\frac{5}{6}-\frac{10}{9}-\frac{2}{5}\) - step4: Reduce fractions to a common denominator: \(\frac{5\times 3\times 5}{6\times 3\times 5}-\frac{10\times 2\times 5}{9\times 2\times 5}-\frac{2\times 3\times 2\times 3}{5\times 3\times 2\times 3}\) - step5: Multiply the terms: \(\frac{5\times 3\times 5}{90}-\frac{10\times 2\times 5}{9\times 2\times 5}-\frac{2\times 3\times 2\times 3}{5\times 3\times 2\times 3}\) - step6: Multiply the terms: \(\frac{5\times 3\times 5}{90}-\frac{10\times 2\times 5}{90}-\frac{2\times 3\times 2\times 3}{5\times 3\times 2\times 3}\) - step7: Multiply the terms: \(\frac{5\times 3\times 5}{90}-\frac{10\times 2\times 5}{90}-\frac{2\times 3\times 2\times 3}{90}\) - step8: Transform the expression: \(\frac{5\times 3\times 5-10\times 2\times 5-2\times 3\times 2\times 3}{90}\) - step9: Multiply the terms: \(\frac{75-10\times 2\times 5-2\times 3\times 2\times 3}{90}\) - step10: Multiply the terms: \(\frac{75-100-2\times 3\times 2\times 3}{90}\) - step11: Multiply the terms: \(\frac{75-100-36}{90}\) - step12: Subtract the numbers: \(\frac{-61}{90}\) - step13: Rewrite the fraction: \(-\frac{61}{90}\) Aquí están los resultados de las expresiones evaluadas: 1. \( \frac{h}{c}+a-d \) - Resultado: \( \frac{15h+2}{6} \) 2. \( a+b+c+d \) - Resultado: \( \frac{59}{60} \) o \( 0.98\dot{3} \) 3. \( c=a+\frac{b}{a} \) - Resultado: \( \text{false} \) (esto indica que la ecuación no se cumple con los valores dados) 4. \( \frac{a}{b}+\frac{a}{c} \) - Resultado: \( \frac{35}{36} \) o \( 0.97\dot{2} \) 5. \( b^{2}-d \) - Resultado: \( \frac{1}{16} \) o \( 0.0625 \) 6. \( a+\frac{a}{b}-c \) - Resultado: \( -\frac{61}{90} \) o \( -0.6\dot{7} \) 7. \( a^{2}+b \) - Resultado: \( -\frac{1}{18} \) o \( -0.0\dot{5} \) 8. \( b-c+d \) - Resultado: \( -\frac{13}{20} \) o \( -0.65 \) 9. \( \frac{c}{a}-b^{2} \) - Resultado: \( -\frac{33}{400} \) o \( -0.0825 \) Si necesitas más detalles sobre algún cálculo específico, házmelo saber.