Example Question - commutative property
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Check Commutative Property in Addition
<p>Para verificar la propiedad conmutativa en la adición:</p> <p>a) \( \frac{10}{8} + \frac{3}{5} = \frac{3}{5} + \frac{10}{8} \)</p> <p>Calculemos:</p> <p>Primero, \( \frac{10}{8} + \frac{3}{5} = \frac{25}{20} + \frac{12}{20} = \frac{37}{20} \)</p> <p>Luego, \( \frac{3}{5} + \frac{10}{8} = \frac{12}{20} + \frac{25}{20} = \frac{37}{20} \)</p> <p>Ambos resultados son iguales, por lo tanto, se cumple la propiedad conmutativa.</p> <p>b) \( \frac{7}{8} + \left( \frac{2}{9} + \frac{5}{4} \right) \) debe ser igual a \( \left( \frac{2}{9} + \frac{7}{8} \right) + \frac{5}{4} \)</p> <p>Calculemos ambos lados: </p> <p>Izquierda: \( \frac{7}{8} + \left( \frac{2}{9} + \frac{5}{4} \right) = \frac{7}{8} + \left( \frac{2}{9} + \frac{45}{36} \right) \approx \frac{7}{8} + \frac{47}{36} = \frac{63}{72} + \frac{47}{72} = \frac{110}{72} \)</p> <p>Derecha: \( \left( \frac{2}{9} + \frac{7}{8} \right) + \frac{5}{4} = \left( \frac{47}{36} + \frac{90}{72} \right) \approx \frac{110}{72} \)</p> <p>Ambos resultados son iguales, se cumple la propiedad conmutativa.</p>
Properties of Addition
The image shows three separate equations, each representing a different property of addition. Here they are in textual form: 1. \( 0 + b = b \) 2. \( 2 + (x + 8) = (2 + x) + 8 \) 3. \( (3 + 1) + 9 = 9 + (3 + 1) \) Now, let's identify the property of addition that each equation represents: 1. The first equation, \( 0 + b = b \), is an example of the Identity Property of Addition, which states that the sum of any number and zero is the original number. 2. The second equation, \( 2 + (x + 8) = (2 + x) + 8 \), demonstrates the Associative Property of Addition. This property states that when three or more numbers are added together, the sum is the same regardless of the grouping of the addends. 3. The third equation, \( (3 + 1) + 9 = 9 + (3 + 1) \), illustrates the Commutative Property of Addition. This property states that the order of the addends can be changed without changing the sum. So, for each equation: 1. Identity Property of Addition 2. Associative Property of Addition 3. Commutative Property of Addition
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