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