Which two numbers need to be interchanged to make the following equation correct?
24+22×12÷16–8=32
- A22 and 24
- B24 and 12
- C22 and 16
- D12 and 8
Solution & Step-by-step Explanation
Let's test the options using the BODMAS rule to find the one that equals 32.
Test Option B (Interchange 24 and 12):
The new equation becomes:
12+22×24÷16−8=32
Applying BODMAS:
Division: 24÷16=
2
3
Multiplication: 22×
2
3
=11×3=33
Addition and Subtraction: 12+33−8=45−8=37
=32
Test Option C (Interchange 22 and 16):
The new equation becomes:
24+16×12÷22−8=32
This leaves a fraction (192÷22), which won't yield an integer 32.
Test Option A (Interchange 22 and 24):
The new equation becomes:
22+24×12÷16−8=32
Applying BODMAS:
Division & Multiplication: 24×
16
12
=24×
4
3
=6×3=18
Equation is now: 22+18−8
40−8=32
Since 32=32, interchanging 22 and 24 makes the equation correct.
Test Option B (Interchange 24 and 12):
The new equation becomes:
12+22×24÷16−8=32
Applying BODMAS:
Division: 24÷16=
2
3
Multiplication: 22×
2
3
=11×3=33
Addition and Subtraction: 12+33−8=45−8=37
=32
Test Option C (Interchange 22 and 16):
The new equation becomes:
24+16×12÷22−8=32
This leaves a fraction (192÷22), which won't yield an integer 32.
Test Option A (Interchange 22 and 24):
The new equation becomes:
22+24×12÷16−8=32
Applying BODMAS:
Division & Multiplication: 24×
16
12
=24×
4
3
=6×3=18
Equation is now: 22+18−8
40−8=32
Since 32=32, interchanging 22 and 24 makes the equation correct.