Final answer:
The correct operations to fill in the blanks are addition (+) and multiplication (×). This follows from the distributive property, where the added result of two products on one side must equal the combined products using addition on the other side.
Step-by-step explanation:
To determine the correct signs that should be placed in the blanks, we need to understand the properties of arithmetic operations - addition, and multiplication, and how they relate to grouping symbols. We compare each side of the equation and apply the appropriate operations.
On the left side, we need an operation that combines 5 with (8 operation 4) so that it equals the right side; (5x8) operation (5x4). We know that multiplication distributes over addition, which is stated in the distributive property of multiplication. This distribution will result in two products on the right side that are being combined. Thus, the operation that combines 5 with the result of (8 operations 4) must be addition so that it mirrors the addition that happens after we distribute multiplication on the right side.
On the right side, after distribution occurs, as illustrated with (5x8) + (5x4), multiplication has already been applied inside the parentheses. Therefore, before the distribution, the sign inside the parentheses must be the multiplication sign to match the (5x4) term.
Therefore, replacing the blanks with the correct operations gives us:
5 + (8 × 4) = (5x8) + (5× 4)