Final answer:
The expression 3×100÷2+5 cannot be made to equal 20 by just adding parentheses and a bracket due to the constraints of mathematical operations. Adding parentheses or a bracket to re-order operations cannot change the inherent value of the calculations that lead to a result different than 20.
Step-by-step explanation:
To make the expression 3×100÷2+5 = 20 true, we need to add parentheses and a bracket in such a way that the operations inside the parentheses and bracket are performed first according to the order of operations (also known as BODMAS/BIDMAS). The order of operations tells us to calculate expressions inside parentheses and brackets first, then exponents, then multiplication and division from left to right, and addition and subtraction from left to right.
To achieve the desired result, we need to adjust the expression so that the division occurs before the multiplication. Here's how we can do it:
Add parentheses around the division operation first: 3 × (100 ÷ 2) + 5. This results in 3 × 50 + 5 since 100 ÷ 2 = 50.
Then we calculate the multiplication: 3 × 50 = 150. Now we have 150 + 5.
Finally, add 5 to 150 to get 155, which is not equal to 20. Hence, it is impossible to make the given expression equal to 20 just by adding parentheses and a bracket.
The correct approach to reach the value of 20 would be to factor in addition before multiplication, for example, by using parentheses or a bracket like this: (3 × 100 ÷ (2 + 5)). But, this operation still does not result in 20, because 2 + 5 equals 7, and 100 ÷ 7 does not yield a whole number. Thus, it's not possible to make the original expression equal to 20 simply by reordering the operations with parentheses and a bracket.