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Simplify: 2/7(1/4+3/8) using the distributive property.

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Final answer:

To simplify 2/7(1/4+3/8), distribute 2/7 to both fractions, convert to a common denominator, and then add the results. The simplified expression is 5/28.

Step-by-step explanation:

To simplify the expression 2/7(1/4+3/8) using the distributive property, follow these steps:

  1. First, distribute the 2/7 to both terms inside the parenthesis, which means you multiply 2/7 by 1/4 and 2/7 by 3/8 separately.
  2. Next, multiply the numerators together and the denominators together for each term. So 2/7 times 1/4 is 2/28, which simplifies to 1/14 after dividing both the numerator and denominator by 2. For 2/7 times 3/8, you get 6/56, which simplifies to 3/28 after dividing both by 2.
  3. Now, combine the two results: 1/14 + 3/28. Since 14 is not a multiple of 28, convert 1/14 to 2/28 so you have a common denominator.
  4. Finally, add the two fractions with a common denominator: 2/28 + 3/28 equals 5/28.

The simplified expression is 5/28.

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