203k views
3 votes
Simplify: 2/7(1/4+3/8) using the distributive property.

1 Answer

4 votes

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.

User Dholstius
by
9.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories