Question

Consider the expression 25 – 10 ÷ 2 + 3.

Part A
Which shows a way to rewrite the expression using parentheses so that the expression equals 23?
Select all that apply.
A. (25 – 10) ÷ 2 + 3 = 23
B. 25 – 10 ÷ (2 + 3) = 23
C. (25 – 10) ÷ (2 + 3) = 23
D. 25 – (10 ÷ 2) + 3 = 23
Part B
Which shows a way to rewrite the expression using parentheses so that the expression equals 3?
A. (25 – 10) ÷ 2 + 3 = 3
B. 25 – 10 ÷ (2 + 3) = 3
C. (25 – 10) ÷ (2 + 3) = 3
D. 25 – (10 ÷ 2) + 3 = 3

Answer 1

Given:

The expression is:

`25-10/ 2+3`

To find:

Part A: The expression using parentheses so that the expression equals 23.

Part B: The expression using parentheses so that the expression equals 3.

Solution:

Part A:

In option A,

`(25-10)/ 2+3=15/ 2+3`

`(25-10)/ 2+3=7.5+3` [Using BODMAS]

`(25-10)/ 2+3=10.5`

In option B,

`25-10/ (2+3)=25-10/ 5`

`25-10/ (2+3)=25-2` [Using BODMAS]

`25-10/ (2+3)=23`

In option C,

`(25-10)/ (2+3)=15/ 5`

`(25-10)/ (2+3)=3`

In option D,

`25-(10/ 2)+3=25-5+3`

`25-(10/ 2)+3=28-5` [Using BODMAS]

`25-(10/ 2)+3=23`

After the calculation, we have
`25-10/ (2+3)=23` and
`25-(10/ 2)+3=23`.

Therefore, the correct options are B and D.

Part B: From part A, it is clear that

`(25-10)/ (2+3)=3`

Therefore, the correct option is C.