Question

For each of the following: i. Show that the expression is not equal to the numerical value. ii. Insert parentheses in the expression so it will be equal to the numerical value. a. 2.3²-4; 10 b. 4²-3-4+2; 26

Answer 1

a. Expression
`2.3^2` - 4 does not equal 10; insert parentheses as
`2.3^2` - 4 for accuracy.

b. Expression
`4^2` - 3 - 4 + 2 equals 26 as the order of operations is correctly followed.

Step-by-step explanation:

In the expression
`2.3^2` - 4, the numerical value is not equal to 10. The discrepancy arises from the order of operations. Without parentheses, the subtraction is executed before exponentiation, leading to \(2.3^2 - 4\) being calculated as
`(2.3)^2` - 4, resulting in a value different from 10. To rectify this, parentheses should be inserted as
`2.3^2` - 4, ensuring that the exponentiation is prioritized.

For the expression
`4^2` - 3 - 4 + 2, the numerical value is already equal to 26. This is because the order of operations is correctly followed, with exponentiation and addition/subtraction occurring from left to right.