Solve Problems Involving Addition, Subtraction, Multiplication and Division 2 - Reasoning

To make the calculation 4 + 32 x 112 – 15 x 24 ÷ 40 equal to 4,023, we need to add a set of brackets in the correct place. The correct placement of the brackets is around the first two numbers and their addition operation, resulting in the expression (4 + 32) x 112 – 15 x 24 ÷ 40. This is because, according to the order of operations (BODMAS/BIDMAS), multiplication and division are performed before addition and subtraction. By adding brackets around 4 + 32, we are changing the order in which the operations are performed, allowing us to add these two numbers together first before multiplying the sum by 112.

The reason for the placement of brackets is to ensure that the addition operation takes precedence over the multiplication, which is not the case in the original expression without brackets. Without the brackets, the multiplication 32 x 112 would be carried out first, leading to a different result. By including the brackets, we calculate the sum of 4 and 32 first, then multiply this result by 112, and finally subtract the product of 15 and 24 divided by 40. This sequence of operations yields the correct answer of 4,023, demonstrating the importance of brackets in altering the order of operations to achieve the desired outcome in a mathematical expression.