The following equation is incorrect. Which two signs should be interchanged to correct the equation?
2×12+15÷4−14=33
- A+ and ×
- B+ and ÷
- C− and +
- D÷ and ×
Solution & Step-by-step Explanation
Let's test the options to find the correct interchange:
Option B: Interchange + and ÷
The equation becomes:
2×12÷15+4−14=33
2×
15
12
+4−14=
15
24
−10
=33
(Incorrect)
Option D: Interchange ÷ and ×
The equation becomes:
2÷12+15×4−14=33
12
2
+60−14=
6
1
+46
=33
(Incorrect)
Option C: Interchange − and +
The equation becomes:
2×12−15÷4+14=33
24−3.75+14=34.25
=33
(Incorrect)
Let's re-verify Option A: Interchange + and ×:
The equation becomes:
2+12×15÷4−14=33
Applying BODMAS:
First, division:
15÷4=3.75
Then, multiplication:
12×3.75=45
Now rewrite the expression:
2+45−14
47−14=33
LHS = RHS. Thus, interchanging + and × corrects the equation.
Option B: Interchange + and ÷
The equation becomes:
2×12÷15+4−14=33
2×
15
12
+4−14=
15
24
−10
=33
(Incorrect)
Option D: Interchange ÷ and ×
The equation becomes:
2÷12+15×4−14=33
12
2
+60−14=
6
1
+46
=33
(Incorrect)
Option C: Interchange − and +
The equation becomes:
2×12−15÷4+14=33
24−3.75+14=34.25
=33
(Incorrect)
Let's re-verify Option A: Interchange + and ×:
The equation becomes:
2+12×15÷4−14=33
Applying BODMAS:
First, division:
15÷4=3.75
Then, multiplication:
12×3.75=45
Now rewrite the expression:
2+45−14
47−14=33
LHS = RHS. Thus, interchanging + and × corrects the equation.