Mathematical Reasoning
When calculating 60 ÷ (4 + 2), Lily wrote the expression as 60 ÷ 4 + 2. What is the difference between the re…
Question 1 · Multiple choice
Question
When calculating 60 ÷ (4 + 2), Lily wrote the expression as 60 ÷ 4 + 2. What is the difference between the results of the two calculations?
Options
- A.5
- B.6
- C.7
- D.8
- E.9
Correct answer
Explanation
Step 1: Calculate the correct expression (with brackets)
60 ÷ (4 + 2)
Brackets always go first — add 4 + 2:
60 ÷ 6 = 10
Step 2: Calculate Lily's expression (without brackets)
60 ÷ 4 + 2
Without brackets, division comes before addition (this is the order of operations rule).
Divide first: 60 ÷ 4 = 15
Then add: 15 + 2 = 17
Step 3: Compare the two results
Expression Steps Result
─────────────────────────────────────
60 ÷ (4 + 2) 60 ÷ 6 10 ← correct
60 ÷ 4 + 2 15 + 2 17 ← Lily's version
Step 4: Find the difference
17 − 10 = 7
The brackets changed the answer by 7! This shows how important it is to place brackets correctly.
Answer: The difference is 7
| Option | Value | Why it is wrong |
|---|---|---|
| A | 5 | Used Lily's result as 15: 15−10=5. ✗ |
| B | 6 | Used Lily's result as 16: 16−10=6. ✗ |
| C | 7 | 17−10=7. ✓ |
| D | 8 | Used 60÷4=16 (arithmetic slip): 18−10=8. ✗ |
| E | 9 | Used 60÷4+4=19 as Lily's result: 19−10=9. ✗ |