NCERT Solutions for Class 5th Maths Chapter 13 A rabbit jumps 4, a frog jumps 3 — Animal Jumps
Book page 165 Updated on2026-09-19
Q1.
A rabbit takes a jump of 4 each time. A frog takes a jump of 3 each time. Use the number line to figure out the numbers they will both touch. If the rabbit and the frog start from 0, the numbers both of them will touch are called the common multiples of 3 and 4.Page 165 — the number line. Both animals start at 0. The frog’s first jump is shown in blue and the rabbit’s first jump in red.
Answer
Between 0 and 12 they both touch only one number — 12.
The frog lands on 3, 6, 9, 12. The rabbit lands on 4, 8, 12. The circled 12 is the only spot they share.
Draw the frog's jumps. Starting at 0 and jumping 3: 3, 6, 9, 12.
Draw the rabbit's jumps. Starting at 0 and jumping 4: 4, 8, 12.
Look for a number in both lists. Only 12 is in both.
Frog (3s): 3, 6, 9, 12 Rabbit (4s): 4, 8, 12
First common landing spot = 12
Why it happens: 12 is in the 3 times table (3 × 4 = 12) and also in the 4 times table (4 × 3 = 12). A number that is a multiple of both numbers is called a common multiple. The word "common" here just means "shared".
Tip: The frog reaches 12 in 4 jumps; the rabbit reaches it in 3 jumps. They both get there, but the rabbit gets there first because its jumps are longer.
Q2.
12 is the first common multiple of 3 and 4. What are some other common multiples of 3 and 4? You can continue the number line or take help from the times tables of 3 and 4.Page 165 — the number line. Both animals start at 0. The frog’s first jump is shown in blue and the rabbit’s first jump in red.
Answer
The next common multiples are 24, 36, 48, 60 and 72 — and they go on for ever.
Why it happens: Once the frog and the rabbit meet at 12, the whole pattern starts again from there. So they meet again 12 steps later at 24, then at 36, and so on — every 12 steps.
Q3.
What do you notice about the common multiples of 3 and 4? Discuss in class.
Answer
Sample answer: Every common multiple of 3 and 4 is a multiple of 12. The list is simply the 12 times table — 12, 24, 36, 48, 60 … The smallest one is 12, and every other one is made by adding 12 again and again. There is no biggest one; the list never ends.
Three things the class should notice:
The first common multiple is 12, and 12 = 3 × 4. When two numbers share no factor except 1, their first common multiple is simply the two numbers multiplied together.
All the others are multiples of the first one. 24 = 12 × 2, 36 = 12 × 3, 48 = 12 × 4.
The list goes on for ever. Two numbers always have endless common multiples — unlike common factors, of which there are only a few.
Why it happens: To land on the same spot, the number must be reachable by 3-jumps and by 4-jumps. Only the numbers in the 12 times table can do both, because 12 is the smallest number that both 3 and 4 divide exactly.