David created two expressions and says that 6×2+2÷3 and 3×(4-2)+6 are equivalent.
To determine if the two expressions, 6×2+2÷3 and 3×(4-2)+6, are equivalent, we need to evaluate both expressions and see if they yield the same result.
Let's start with the first expression, 6×2+2÷3:
1. Multiply 6 by 2: 6×2 = 12.
2. Divide 2 by 3: 2÷3 ≈ 0.6667 (rounded to four decimal places).
3. Add the results of steps 1 and 2: 12 + 0.6667 ≈ 12.6667 (rounded to four decimal places).
Now, let's evaluate the second expression, 3×(4-2)+6:
1. Solve the parentheses: 4 - 2 = 2.
2. Multiply 3 by the result of step 1: 3 × 2 = 6.
3. Add 6 to 6: 6 + 6 = 12.
After evaluating both expressions, we obtained 12.6667 and 12, respectively. These two values are not equal, which means that the expressions 6×2+2÷3 and 3×(4-2)+6 are NOT equivalent. Thus, David's claim is incorrect.