The two expressions on either side of the equal sign will have the same value if two numbers on the left-hand side are interchanged and two signs on the right-hand side are interchanged. What are those two numbers (not digits) and the two signs? 4 × 3 ÷ 6 + 2 - 8 = 10 + 2 × 3 ÷ 5 - 18
4 and 8; + and ÷
To solve this problem, we need to find which numbers on the left-hand side of the equation can be interchanged with which numbers on the right-hand side and also identify which signs can be interchanged so that both sides of the equation equal the same value.
Initially, the equation is:
4 × 3 ÷ 6 + 2 - 8 = 10 + 2 × 3 ÷ 5 - 18
We are given options for the numbers and signs interchange. Let's check the correct option: "4 and 8; + and ÷".
Step 1: Interchange the numbers 4 and 8
The new equation becomes:
8 × 3 ÷ 6 + 2 - 4 = 10 + 2 × 3 ÷ 5 - 18
Step 2: Interchange the signs + and ÷ on the right-hand side
The revised equation is:
8 × 3 ÷ 6 + 2 - 4 = 10 ÷ 2 × 3 + 5 - 18
Step 3: Calculate both sides
Left side calculation:
8 × 3 = 24
24 ÷ 6 = 4
4 + 2 = 6
6 - 4 = 2
Right side calculation:
10 ÷ 2 = 5
5 × 3 = 15
15 + 5 = 20
20 - 18 = 2
Both sides of the equation equal 2, thus confirming that interchanging the numbers 4 and 8 on the left-hand side and the operators + and ÷ on the right-hand side makes the equation equivalently balanced.
Therefore, the correct answer is:
4 and 8; + and ÷
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