Mr. Rijo bought 49 bags of soil one week and 28 bags of soil the next week. Which expression correctly applies the distributive property to show equivalent expressions for the number of bags of soil he bought?

49 + 28 = 4 (7 + 7)
49 + 28 = (7) (7) + (14) (2)
49 + 28 = (7) (14) + (7) (7)
49 + 28 = 7 (7 + 4)

1 answer

To find the expression that correctly applies the distributive property to show equivalent expressions for the number of bags of soil Mr. Rijo bought (49 + 28), we can first factor out the common factor from 49 and 28.

Both numbers can be expressed as multiples of 7:

  • \( 49 = 7 \times 7 \)
  • \( 28 = 7 \times 4 \)

So, we can write: \[ 49 + 28 = 7 \times 7 + 7 \times 4 \]

Using the distributive property: \[ 49 + 28 = 7 (7 + 4) \]

Now, let’s evaluate the provided options:

  1. 49 + 28 = 4 (7 + 7): This is incorrect.
  2. 49 + 28 = (7)(7) + (14)(2): This does not use the distributive property correctly.
  3. 49 + 28 = (7)(14) + (7)(7): This does not correctly represent the original addition.
  4. 49 + 28 = 7 (7 + 4): This correctly applies the distributive property.

The correct expression that applies the distributive property is: 49 + 28 = 7 (7 + 4).