NCERT Solutions for Class 4 Maths Mela Chapter 09 Equal Groups

Page 128

Animal Jumps

Question 1. The frog jumps 3 steps at a time. Which numbers will the frog touch? Will it touch 67?
Answer: The numbers the frog touches are all multiples of 3: 0, 3, 6, 9, 12, 15, 21, 24, 27, 30… To check if 67 will be touched: 67 ÷ 3 = 22 remainder 1. Since there is a remainder, 67 is not a multiple of 3. Therefore, the frog will not touch 67.
In simple words: The frog lands on numbers you get by counting by 3s. The number 67 cannot be made by counting by 3s, so the frog will skip it.

Exam Tip: To check if a number is a multiple of another, divide and look for a remainder. If there is a remainder, it is not a multiple.

Question 2. The squirrel jumps 4 steps at a time. Which numbers will the squirrel touch? How many times should the squirrel jump to reach 60?
Answer: The numbers the squirrel touches are all multiples of 4: 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60. To reach 60: 60 ÷ 4 = 15 jumps.
In simple words: The squirrel lands by counting by 4s. It takes 15 jumps to land on 60.

Exam Tip: Division helps you find how many jumps an animal needs to reach a target number.

Question 3. 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?
Answer: The numbers the rabbit touches are all multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102… The smallest 3-digit number is 102. To reach 102: 102 ÷ 6 = 17 jumps.
In simple words: The rabbit lands by counting by 6s. The first 3-digit number it reaches is 102. This takes 17 jumps.

Exam Tip: Find the smallest 3-digit number by listing multiples until you reach 100 or more.

Question 4. The kangaroo jumps 8 steps at a time. Which numbers will the kangaroo touch?
Answer: The numbers the kangaroo touches are all multiples of 8: 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96… Numbers that both the rabbit and kangaroo will touch are: 0, 24, 48, 72, 96… (These are common multiples of 6 and 8, which are all multiples of 24).
In simple words: The kangaroo lands by counting by 8s. When the rabbit and kangaroo land on the same numbers, those are numbers both 6 and 8 divide into evenly.

Exam Tip: Common multiples are numbers that two or more numbers divide into evenly.

Question 5. To reach 48, how many times did the rabbit jump?
Answer: To reach 48, the rabbit jumps: 48 ÷ 6 = 8 times.
In simple words: The rabbit needs 8 jumps to reach 48.

Exam Tip: Use division to find how many jumps are needed to reach a number.

Question 6. How many times did the kangaroo jump to reach the same number?
Answer: To reach 48, the kangaroo jumps: 48 ÷ 8 = 6 times.
In simple words: The kangaroo needs 6 jumps to reach 48.

Exam Tip: When an animal takes bigger steps, it needs fewer jumps to reach the same number.

Question 7. What did you observe? Share your thoughts.
Answer: I noticed that the animal which takes larger steps at a time needs fewer jumps to reach the same number. Since the kangaroo jumps more steps than the rabbit, it reached 48 in fewer jumps.
In simple words: Bigger steps mean fewer jumps needed.

Exam Tip: Compare jump sizes and jump counts - they have an inverse relationship.

Question 8. To reach 60, how many times did the frog jump?
Answer: To reach 60, the frog jumps: 60 ÷ 3 = 20 times.
In simple words: The frog needs 20 jumps to reach 60.

Exam Tip: Division shows the number of jumps required.

Question 9. How many times did the rabbit jump to reach the same number?
Answer: To reach 60, the rabbit jumps: 60 ÷ 6 = 10 times.
In simple words: The rabbit needs 10 jumps to reach 60.

Exam Tip: Compare how different animals need different numbers of jumps for the same distance.

Question 10. What do you observe? Share your thoughts.
Answer: The frog takes twice as many jumps as the rabbit to reach the same number because its step size is half the size of the rabbit's step size.
In simple words: If one animal's steps are smaller, it has to jump more times.

Exam Tip: When step size is halved, the number of jumps doubles.

Page 130

Common Multiples

Question 1. Which numbers do both the frog and the squirrel touch? A few common multiples of 3 and 4 are ______.
Answer: The frog and squirrel both land on their common multiples. Common multiples of 3 and 4 are: 12, 24, 36, 48, 60, 72…
In simple words: These numbers can be divided by both 3 and 4 with no remainder.

Exam Tip: Common multiples are numbers that appear in the jump patterns of both animals.

Question 2. Which numbers do both the rabbit and the kangaroo touch? A few common multiples of 6 and 8 are ______.
Answer: The rabbit and kangaroo both land on their common multiples. Common multiples of 6 and 8 are: 24, 48, 72, 96, 120…
In simple words: These numbers work for both the rabbit's 6-step jumps and the kangaroo's 8-step jumps.

Exam Tip: List multiples of both numbers and find where they match.

Question 3. If the cat and the rat land on the same number, the cat will catch the rat. The cat is now on 6 and the rat on 12. When the cat jumps 3 steps forward, the rat jumps 2 steps forward. Will the cat catch the rat? If yes, at which number?
Answer: The cat starts at 6 and jumps 3 steps; the rat starts at 12 and jumps 2 steps. After the first jump: cat at 9, rat at 14. After the second jump: cat at 12, rat at 16. After the third jump: cat at 15, rat at 18. After the fourth jump: cat at 18, rat at 20. After the fifth jump: cat at 21, rat at 22. After the sixth jump: cat at 24, rat at 24. So, the cat will catch the rat at position 24.
In simple words: By tracking each jump, you find they both land on 24 at the same time.

Exam Tip: Keep a running record of positions after each jump to find when they meet.

Question 4. Find multiplication and division sentences below. Shade the sentences. How many can you find? Two examples are done for you.
Answer: Multiplication sentences: 3 × 4 = 12, 4 × 2 = 8, 4 × 2 = 8, 20 ÷ 5 = 4, 3 × 2 = 6, 2 × 6 = 12, 2 × 2 = 4, 12 ÷ 8 = 1, 3 × 2 = 6, 2 × 3 = 6, 2 × 3 = 6, 18 ÷ 6 = 3, 10 ÷ 3 = 4, 12 ÷ 2 = 6, 20 ÷ 5 = 4, 2 × 2 = 4, 10 ÷ 7 = 14, 8 ÷ 2 = 4, 2 ÷ 2 = 1, 10 ÷ 5 = 2.
In simple words: Look for facts that show times (multiply) or share (divide) numbers.

Exam Tip: Multiplication uses × and division uses ÷ signs.

Page 131

Gulabo's Garden

Question 1. Gulabo's garden has lily flowers. Each lily flower has 3 petals. How many petals are there in 12 flowers? Show how you found your answer. Gulabo will have 12 × 3 petals. Petals in 10 lilies 10 × 3 = 30 petals. Petals in 2 lilies ______. Petals in 12 lilies ______.
Answer: Gulabo will have 12 × 3 petals. Petals in 10 lilies = 10 × 3 = 30 petals. Petals in 2 lilies = 2 × 3 = 6 petals. Petals in 12 lilies = 30 + 6 = 36 petals.
In simple words: Split 12 into 10 and 2. Find petals for each part, then add them together.

Exam Tip: Breaking a number into parts makes it easier to multiply and add.

Question 2. In a hibiscus flower there are 5 petals. Gulabo counted all the petals and found them to be 80. How many flowers did she have? Gulabo has 80 ÷ 5 flowers. 5 petals is 1 flower. 10 petals are 2 flowers. 50 petals are 10 flowers. Then, 80 petals are _____ flowers.
Answer: 5 petals make 1 flower. 10 petals make 2 flowers. 50 petals make 10 flowers. Then, 80 petals are 2 + 4 + 10 flowers = 16 flowers. So there are 80 petals in 16 flowers.
In simple words: Add up the groups: 2 flowers (10 petals) + 4 flowers (20 petals) + 10 flowers (50 petals) = 16 flowers.

Exam Tip: Use known groups to build up to the final number.

Question 3. Gulabo plants some marigold saplings in a box as shown in the picture. There are _____ saplings in each row.
Answer: There are 5 saplings in each row.
In simple words: Count the plants across one row.

Exam Tip: Look at one row to count the number in each row.

Question 4. There are _____ rows.
Answer: There are 4 rows.
In simple words: Count the rows from top to bottom.

Exam Tip: Count carefully from one end to the other.

Question 5. How many saplings has she planted? How did you calculate it?
Answer: Total saplings planted: 5 × 4 = 20 saplings.
In simple words: Multiply the number in each row by the number of rows.

Exam Tip: Rows times columns gives the total.

Question 6. Mathematical statement _________.
Answer: Mathematical statement: Number of saplings in each row = 5. Number of rows = 4. So, total saplings = 4 × 5 = 20.
In simple words: Write the parts you know and the multiplication sentence.

Exam Tip: Always write the number sentence that shows your thinking.

Question 7. "Dailyfresh" supermarket has kept boxes of strawberries in a big tray. How many boxes of strawberries does the supermarket have? Show how you found them.
Answer: To find the total number of boxes, I multiply the number of rows by the number of columns: 6 rows × 15 columns = 90 boxes.
In simple words: Rows times columns gives all the boxes.

Exam Tip: Count rows, count columns, then multiply.

Question 8. There are _____ columns of strawberry boxes.
Answer: There are 15 columns of strawberry boxes.
In simple words: Count the columns from left to right.

Exam Tip: Columns go up and down.

Question 9. There are _____ boxes in each column.
Answer: There are 6 boxes in each column.
In simple words: Look at one column and count the boxes.

Exam Tip: Pick one column and count from top to bottom.

Question 10. There are _____ boxes in all.
Answer: There are 90 boxes in all.
In simple words: Multiply rows by columns to get the total.

Exam Tip: This is the main answer to the question.

Question 11. Mathematical statement _________.
Answer: Number of rows = 6. Number of columns = 15. So, total number of boxes = 6 × 15 = 90.
In simple words: Write what you know and the multiplication you did.

Exam Tip: Write the number sentence to show your work.

Question 12. Radha runs a bakery shop. She bakes 18 cupcakes in one tray of the size shown below. Complete arranging the cupcakes in the two trays given below.
Answer: The trays show 18 cupcakes arranged in 3 rows and 6 columns per tray (3 × 6 = 18).
In simple words: Arrange cupcakes so each tray has the same number in rows and columns.

Exam Tip: Equal rows and columns must multiply to 18.

Question 13. She can use two such trays in her oven at a time. How many cupcakes can she make in one attempt?
Answer: Number of cupcakes in one tray = 18. So, the number of cupcakes in 2 trays = 2 × 18 = 36 cupcakes. Hence, she can make 36 cupcakes in one attempt.
In simple words: One tray holds 18. Two trays hold twice as many.

Exam Tip: Multiply the number in one tray by the number of trays used.

Question 14. Today she received a special order. She has made 108 cupcakes. How many trays has she baked?
Answer: She has to make 108 cupcakes in total. We know that there are 18 cupcakes in one tray. So, the number of trays required for 108 cupcakes = 108 ÷ 18 = 6 trays. Hence, she has baked 6 trays of cupcakes.
In simple words: Divide the total cupcakes by the number in each tray to find how many trays.

Exam Tip: Division tells you how many trays you need.

Question 15. She has another square baking tray. She can bake 36 mini cupcakes in such a tray. Complete the arrangement below. Number of columns: _______.
Answer: Number of columns: 6
In simple words: Count the columns in the square arrangement.

Exam Tip: In a square, rows and columns are equal.

Question 16. Number of cupcakes in each column: _______.
Answer: Number of cupcakes in each column: 6
In simple words: Count down one column.

Exam Tip: In a square with 36 items, 6 × 6 = 36.

Question 17. Multiplication statement _______.
Answer: Number of columns = 6. Number of cupcakes in each column = 6. So, total number of cupcakes = 6 × 6 = 36.
In simple words: Write the number sentence for the square arrangement.

Exam Tip: 6 × 6 is a perfect square.

Question 18. Find different ways of arranging the following numbers of cupcakes in rows and columns in your notebook. 36, 8, 12, and 24.
Answer: 36 cupcakes: 6 rows × 6 columns = 36 cupcakes. 8 cupcakes: 2 rows × 4 columns = 8 cupcakes, or 4 rows × 2 columns = 8 cupcakes. 12 cupcakes: 2 rows × 6 columns = 12 cupcakes, or 6 rows × 2 columns = 12 cupcakes. 24 cupcakes: 4 rows × 6 columns = 24 cupcakes, or 6 rows × 4 columns = 24 cupcakes.
In simple words: Each number can be made with different row and column arrangements.

Exam Tip: A number can have multiple ways to arrange as rows and columns.

Page 133

The Doubling Magic

Question 1. Magician Anvi came one day, To Gulabo's house, ready to play. From her coat, with a grand display, She pulled out 23 flowers, bright and gay! She smiled and said, "Now watch and see, How many flowers will there be?" How many flowers are there now?
Answer: There are now 46 flowers.
In simple words: When you double 23, you get 46.

Exam Tip: Doubling means multiplying by 2.

Question 2. Double of 32 = ______.
Answer: Double of 32 = 64
In simple words: 32 × 2 = 64.

Exam Tip: Double by multiplying by 2.

Question 3. Double of 14 = ______.
Answer: Double of 14 = 28
In simple words: 14 × 2 = 28.

Exam Tip: Quick doubling helps with multiplication facts.

Question 4. Double of 26 = ______.
Answer: Double of 26 = 52
In simple words: 26 × 2 = 52.

Exam Tip: Doubling is one of the fastest multiplication tricks.

Question 5. Double of 17 = ______.
Answer: Double of 17 = 34
In simple words: 17 × 2 = 34.

Exam Tip: Doubling is the same as multiplying by 2.

Question 6. Double of 39 = ______.
Answer: Double of 39 = 78
In simple words: 39 × 2 = 78.

Exam Tip: Use mental math: double the tens and the ones separately.

Question 7. Double of 45 = ______.
Answer: Double of 45 = 90
In simple words: 45 × 2 = 90.

Exam Tip: Look for numbers ending in 5 - they double to end in 0.

Question 8. Guess what will be the ones digit of the following numbers when doubled. Write the ones digit in the space provided. a) 28 ______. b) 56 ______. c) 45 ______. d) 17 ______.
Answer: a) 8 × 2 = 16, ones digit: 6. b) 6 × 2 = 12, ones digit: 2. c) 5 × 2 = 10, ones digit: 0. d) 7 × 2 = 14, ones digit: 4.
In simple words: Only look at the ones digit and double it.

Exam Tip: To find the ones digit, double just the last digit.

Question 9. Give examples of numbers that when doubled give the following digits in the ones place. a) 0 _______. b) 2 _______. c) 4 _______. d) 6 _______. e) 8 _______.
Answer: a) 0 as ones digit: 5, 15, 25, 35, 45. b) 2 as ones digit: 1, 11, 21, 31, 41. c) 4 as ones digit: 2, 12, 22, 32, 42. d) 6 as ones digit: 3, 13, 23, 33, 43. e) 8 as ones digit: 4, 14, 24, 34, 44.
In simple words: If you want a ones digit of 0 when doubled, start with a number ending in 5.

Exam Tip: Pattern: ones digit 0 comes from doubling 5; digit 2 from doubling 1; digit 4 from doubling 2, and so on.

Question 10. What do we notice about the numbers that we get after doubling? Even or Odd?
Answer: After doubling, we can only get even digits (0, 2, 4, 6, 8) in the ones place. We cannot get 3, 5, 7, or 9 as ones digits after doubling.
In simple words: When you double any number, the answer always ends in an even digit.

Exam Tip: Doubling always produces an even number.

Page 135

Multiplication Table