The rabbit jumps 6 steps at a time. Which numbers will the rabbit touch? What is the smallest 3-digit number on which the rabbit will land? How many times did the rabbit jump to reach this number?
Step 1: The rabbit jumps 6 steps at a time, landing on multiples of 6. Numbers: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
Step 2: Find the smallest 3-digit multiple of 6. Smallest 3-digit number = 100
Step 3: Check if 100 is a multiple of 6. 100 ÷ 6 = 16 remainder 4 ∴ 100 is not a multiple of 6.
Step 4: Find the next multiple of 6. Previous multiple: 96 Next multiple: 96 + 6 = 102
Step 5: Verify 102 is a multiple of 6. 102 ÷ 6 = 17 (no remainder) ∴ 102 is a multiple of 6.
Answer: The smallest 3-digit number is 102 and the rabbit needs 17 jumps to reach it.
Explanation
The rabbit jumps 6 steps at a time, landing on multiples of 6. The smallest 3-digit number is 100. To find the smallest 3-digit multiple of 6, we check: 100 ÷ 6 = 16 remainder 4, so 100 is not a multiple of 6. The next multiple is 96 + 6 = 102. To verify: 102 ÷ 6 = 17, so 102 is a multiple of 6 and the rabbit needs 17 jumps to reach it.
Solution Steps
Rabbit jumps 6 steps at a time, landing on multiples of 6.
Find the smallest 3-digit multiple of 6.
Check if 100 is a multiple of 6: 100 ÷ 6 = 16 remainder 4 (not a multiple).
Find the next multiple: 96 + 6 = 102.
Verify: 102 ÷ 6 = 17 (no remainder), so 102 is a multiple of 6.
Answer: Smallest 3-digit number is 102, requiring 17 jumps.