a. $$ \frac{\frac{1}{3}-\frac{1}{9}}{\frac{2}{5}+\frac{1}{6}} $$ b. $$ \left(-\frac{2}{3}+\frac{3}{4} ight) \div\left(-\frac{3}{4}-\frac{1}{5} ight) $$ c. $$ (0.006) imes 20(0,02) imes 1200 $$ d. $$ \frac{\frac{1}{4}-\frac{2}{2}}{5+\frac{4}{3}} $$ e. $$ \left(\frac{5}{7}+0,74 ight)-\frac{1}{3} $$

Question

a. $$ \frac{\frac{1}{3}-\frac{1}{9}}{\frac{2}{5}+\frac{1}{6}} $$ b. $$ \left(-\frac{2}{3}+\frac{3}{4}ight) \div\left(-\frac{3}{4}-\frac{1}{5}ight) $$ c. $$ (0.006) 	imes 20(0,02) 	imes 1200 $$ d. $$ \frac{\frac{1}{4}-\frac{2}{2}}{5+\frac{4}{3}} $$ e. $$ \left(\frac{5}{7}+0,74ight)-\frac{1}{3} $$

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$0.006\times 20\times 0.02\times 1200$$
- step1: Multiply the terms:
  $$0.12\times 0.02\times 1200$$
- step2: Multiply the terms:
  $$0.0024\times 1200$$
- step3: Multiply the numbers:
  $$2.88$$
Calculate or simplify the expression $$ (5/7 + 0.74) - 1/3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{5}{7}+0.74\right)-\frac{1}{3}$$
- step1: Add the numbers:
  $$\frac{509}{350}-\frac{1}{3}$$
- step2: Reduce fractions to a common denominator:
  $$\frac{509\times 3}{350\times 3}-\frac{350}{3\times 350}$$
- step3: Multiply the numbers:
  $$\frac{509\times 3}{1050}-\frac{350}{3\times 350}$$
- step4: Multiply the numbers:
  $$\frac{509\times 3}{1050}-\frac{350}{1050}$$
- step5: Transform the expression:
  $$\frac{509\times 3-350}{1050}$$
- step6: Multiply the numbers:
  $$\frac{1527-350}{1050}$$
- step7: Subtract the numbers:
  $$\frac{1177}{1050}$$
Calculate or simplify the expression $$ (-2/3 + 3/4) / (-3/4 - 1/5) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(\frac{-2}{3}+\frac{3}{4}\right)}{\left(\frac{-3}{4}-\frac{1}{5}\right)}$$
- step1: Remove the parentheses:
  $$\frac{\frac{-2}{3}+\frac{3}{4}}{\frac{-3}{4}-\frac{1}{5}}$$
- step2: Rewrite the fraction:
  $$\frac{-\frac{2}{3}+\frac{3}{4}}{\frac{-3}{4}-\frac{1}{5}}$$
- step3: Rewrite the fraction:
  $$\frac{-\frac{2}{3}+\frac{3}{4}}{-\frac{3}{4}-\frac{1}{5}}$$
- step4: Add the numbers:
  $$\frac{\frac{1}{12}}{-\frac{3}{4}-\frac{1}{5}}$$
- step5: Subtract the numbers:
  $$\frac{\frac{1}{12}}{-\frac{19}{20}}$$
- step6: Multiply by the reciprocal:
  $$\frac{1}{12}\left(-\frac{20}{19}\right)$$
- step7: Multiply the numbers:
  $$-\frac{1}{12}\times \frac{20}{19}$$
- step8: Reduce the numbers:
  $$-\frac{1}{3}\times \frac{5}{19}$$
- step9: Multiply the fractions:
  $$-\frac{5}{3\times 19}$$
- step10: Multiply:
  $$-\frac{5}{57}$$
Calculate or simplify the expression $$ (1/3 - 1/9) / (2/5 + 1/6) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(\frac{1}{3}-\frac{1}{9}\right)}{\left(\frac{2}{5}+\frac{1}{6}\right)}$$
- step1: Remove the parentheses:
  $$\frac{\frac{1}{3}-\frac{1}{9}}{\frac{2}{5}+\frac{1}{6}}$$
- step2: Subtract the numbers:
  $$\frac{\frac{2}{9}}{\frac{2}{5}+\frac{1}{6}}$$
- step3: Add the numbers:
  $$\frac{\frac{2}{9}}{\frac{17}{30}}$$
- step4: Multiply by the reciprocal:
  $$\frac{2}{9}\times \frac{30}{17}$$
- step5: Reduce the numbers:
  $$\frac{2}{3}\times \frac{10}{17}$$
- step6: Multiply the fractions:
  $$\frac{2\times 10}{3\times 17}$$
- step7: Multiply:
  $$\frac{20}{51}$$
Calculate or simplify the expression $$ (1/4 - 2/2) / (5 + 4/3) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(\frac{1}{4}-\frac{2}{2}\right)}{\left(5+\frac{4}{3}\right)}$$
- step1: Remove the parentheses:
  $$\frac{\frac{1}{4}-\frac{2}{2}}{5+\frac{4}{3}}$$
- step2: Divide the terms:
  $$\frac{\frac{1}{4}-1}{5+\frac{4}{3}}$$
- step3: Subtract the numbers:
  $$\frac{-\frac{3}{4}}{5+\frac{4}{3}}$$
- step4: Add the numbers:
  $$\frac{-\frac{3}{4}}{\frac{19}{3}}$$
- step5: Multiply by the reciprocal:
  $$-\frac{3}{4}\times \frac{3}{19}$$
- step6: Multiply the fractions:
  $$-\frac{3\times 3}{4\times 19}$$
- step7: Multiply:
  $$-\frac{9}{76}$$
Aquí están las soluciones a los problemas planteados:

a. Para calcular $$ \frac{\frac{1}{3}-\frac{1}{9}}{\frac{2}{5}+\frac{1}{6}} $$:

1. Primero, resolvemos el numerador: 
   $$
   \frac{1}{3} - \frac{1}{9} = \frac{3}{9} - \frac{1}{9} = \frac{2}{9}
   $$

2. Luego, resolvemos el denominador:
   $$
   \frac{2}{5} + \frac{1}{6} = \frac{12}{30} + \frac{5}{30} = \frac{17}{30}
   $$

3. Ahora, dividimos el numerador por el denominador:
   $$
   \frac{\frac{2}{9}}{\frac{17}{30}} = \frac{2}{9} \times \frac{30}{17} = \frac{60}{153} = \frac{20}{51} \approx 0.392157
   $$

b. Para $$ \left(-\frac{2}{3}+\frac{3}{4}\right) \div\left(-\frac{3}{4}-\frac{1}{5}\right) $$:

1. Calculamos el numerador:
   $$
   -\frac{2}{3} + \frac{3}{4} = -\frac{8}{12} + \frac{9}{12} = \frac{1}{12}
   $$

2. Calculamos el denominador:
   $$
   -\frac{3}{4} - \frac{1}{5} = -\frac{15}{20} - \frac{4}{20} = -\frac{19}{20}
   $$

3. Ahora, dividimos el numerador por el denominador:
   $$
   \frac{\frac{1}{12}}{-\frac{19}{20}} = \frac{1}{12} \times -\frac{20}{19} = -\frac{5}{57} \approx -0.087719
   $$

c. Para $$ (0.006) \times 20 \times (0.02) \times 1200 $$:

1. Realizamos la multiplicación:
   $$
   0.006 \times 20 \times 0.02 \times 1200 = 0.006 \times 20 = 0.12
   $$
   $$
   0.12 \times 0.02 = 0.0024
   $$
   $$
   0.0024 \times 1200 = 2.88
   $$

d. Para $$ \frac{\frac{1}{4}-\frac{2}{2}}{5+\frac{4}{3}} $$:

1. Calculamos el numerador:
   $$
   \frac{1}{4} - \frac{2}{2} = \frac{1}{4} - 1 = \frac{1}{4} - \frac{4}{4} = -\frac{3}{4}
   $$

2. Calculamos el denominador:
   $$
   5 + \frac{4}{3} = \frac{15}{3} + \frac{4}{3} = \frac{19}{3}
   $$

3. Ahora, dividimos el numerador por el denominador:
   $$
   \frac{-\frac{3}{4}}{\frac{19}{3}} = -\frac{3}{4} \times \frac{3}{19} = -\frac{9}{76} \approx -0.118421
   $$

e. Para $$ \left(\frac{5}{7}+0.74\right)-\frac{1}{3} $$:

1. Primero, convertimos $$ 0.74 $$ a fracción:
   $$
   0.74 = \frac{74}{100} = \frac{37}{50}
   $$

2. Sumamos:
   $$
   \frac{5}{7} + \frac{37}{50} = \frac{250}{350} + \frac{259}{350} = \frac{1177}{350}
   $$

3. Restamos $$ \frac{1}{3} $$:
   $$
   \frac{1177}{350} - \frac{1}{3} = \frac{1177}{350} - \frac{116.67}{350} = \frac{1177 - 116.67}{350} = \frac{1177}{1050} \approx 1.12
   $$

Así que las respuestas finales son:

a. $$ \frac{20}{51} \approx 0.392157 $$

b. $$ -\frac{5}{57} \approx -0.087719 $$

c. $$ 2.88 $$

d. $$ -\frac{9}{76} \approx -0.118421 $$

e. $$ \frac{1177}{1050} \approx 1.12 $$
a. 0.392157 b. -0.087719 c. 2.88 d. -0.118421 e. 1.12

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