Division as Repeated Subtraction Worksheet Grade 2

Advanced division concepts using repeated subtraction method with word problems and detailed explanations for grade 2 students.

Division as Repeated Subtraction: Exercises 1-3
1 Classroom Chairs
Exercise 1
In the classroom, there are 15 chairs. The teacher wants to arrange them in rows with 3 chairs in each row. How many rows can she make?
What is Division?

Division: Finding how many equal groups we can make from a total amount. We use repeated subtraction to solve.

Method: Repeated Subtraction
  1. Start with the total number (15 chairs)
  2. Take away 3 chairs for the first row (subtract 3)
  3. Keep taking away 3 chairs for each new row (subtract 3 again)
  4. Count how many rows we made
  5. Stop when we have no chairs left
15
-
3
=
12
Row 1
12
-
3
=
9
Row 2
9
-
3
=
6
Row 3
6
-
3
=
3
Row 4
3
-
3
=
0
Row 5
Step 1: Identify the problem

We need to divide 15 chairs into groups of 3 chairs each row

Step 2: Perform repeated subtraction

15 - 3 = 12 (Row 1)
12 - 3 = 9 (Row 2)
9 - 3 = 6 (Row 3)
6 - 3 = 3 (Row 4)
3 - 3 = 0 (Row 5)

Step 3: Count the results

We made 5 rows of 3 chairs each

15 ÷ 3 = 5 rows
Final answer:

The teacher can make 5 rows because she subtracted 3 five times from 15 to get 0

Key Rule:

• Division as grouping: How many groups of [divisor] can fit in [dividend]?

• Verification: 5 × 3 = 15 ✓

2 Stickers for Students
Exercise 2
Mrs. Johnson has 18 stickers. She wants to give 6 stickers to each student. How many students will get stickers?
Important Terms:

Dividend: The total number we start with (18 stickers)

Divisor: The number in each group (6 stickers per student)

Quotient: The answer (number of students)

18
-
6
=
12
Student 1
12
-
6
=
6
Student 2
6
-
6
=
0
Student 3
Step 1: Set up the division

18 ÷ 6 = ? (How many students can get 6 stickers each?)

Step 2: Apply repeated subtraction

18 - 6 = 12 (1st student)
12 - 6 = 6 (2nd student)
6 - 6 = 0 (3rd student)

Step 3: Determine the answer

3 students will get stickers

18 ÷ 6 = 3 students
Final answer:

3 students will get stickers because 6 was subtracted 3 times from 18 to reach 0

Division Rule:

• Equal sharing: Each group gets the same number

• Verification: 3 × 6 = 18 ✓

3 Books on Shelves
Exercise 3
There are 20 books to put on shelves. Each shelf holds 4 books. How many shelves do we need?
Division Concept:

Division finds equal groups: We determine how many equal-sized groups we can make from a total amount.

20
-
4
=
16
Shelf 1
16
-
4
=
12
Shelf 2
12
-
4
=
8
Shelf 3
8
-
4
=
4
Shelf 4
4
-
4
=
0
Shelf 5
Step 1: Analyze the problem

We have 20 books and each shelf holds 4 books. We need to find how many shelves.

Step 2: Apply repeated subtraction

20 - 4 = 16 (Shelf 1)
16 - 4 = 12 (Shelf 2)
12 - 4 = 8 (Shelf 3)
8 - 4 = 4 (Shelf 4)
4 - 4 = 0 (Shelf 5)

Step 3: State the answer

We need 5 shelves for 20 books

20 ÷ 4 = 5 shelves
Final answer:

We need 5 shelves because 4 was subtracted 5 times from 20 to reach 0

Applied Rules:

• Grouping principle: How many groups of 4 can we make from 20?

• Verification: 5 × 4 = 20 ✓

Complete Summary: Division as Repeated Subtraction Grade 2
Key Concepts and Definitions:

Division: The process of splitting a total amount into equal groups.

Repeated Subtraction: Taking away the same number repeatedly until we reach zero or a number smaller than the divisor.

Dividend: The total number we start with (the number being divided).

Divisor: The number we divide by (how many in each group).

Quotient: The answer to the division problem (how many groups we made).

Remainder: What's left over when division doesn't result in a whole number.

Step-by-Step Division Method:
  1. Read the problem carefully: Identify the total amount (dividend) and the group size (divisor).
  2. Set up the subtraction: Start with the dividend and subtract the divisor.
  3. Repeat the subtraction: Continue subtracting the divisor from the result until you reach zero.
  4. Count the subtractions: Keep track of how many times you subtracted.
  5. Write the answer: The count is your quotient.
  6. Verify your answer: Multiply the quotient by the divisor to check if you get the dividend.
Tip 1: Always subtract the same number (the divisor) each time.
Tip 2: Count each subtraction to find your answer.
Tip 3: Stop when you reach zero or a number smaller than the divisor.
Tip 4: Always check your answer: quotient × divisor = dividend.
Examples from Simple to Advanced:

Simple Example: 8 ÷ 2 = ?
8 - 2 = 6 (1st)
6 - 2 = 4 (2nd)
4 - 2 = 2 (3rd)
2 - 2 = 0 (4th)
Answer: 4

Medium Example: 15 ÷ 3 = ?
15 - 3 = 12 (1st)
12 - 3 = 9 (2nd)
9 - 3 = 6 (3rd)
6 - 3 = 3 (4th)
3 - 3 = 0 (5th)
Answer: 5

Advanced Example: 24 ÷ 4 = ?
24 - 4 = 20 (1st)
20 - 4 = 16 (2nd)
16 - 4 = 12 (3rd)
12 - 4 = 8 (4th)
8 - 4 = 4 (5th)
4 - 4 = 0 (6th)
Answer: 6

Connection to Multiplication: Division is the inverse of multiplication. If 4 × 3 = 12, then 12 ÷ 3 = 4.
Word Problem Strategy: Look for key words like "each," "per," "groups of," or "shared equally" to identify division problems.
Important Rules to Remember:

• Equal Groups: Division always creates equal-sized groups.

• Verification: Always multiply your answer by the divisor to check.

• Zero Property: Any number divided by itself equals 1 (e.g., 5 ÷ 5 = 1).

• One Property: Any number divided by 1 equals itself (e.g., 7 ÷ 1 = 7).

Division Concepts and Methods
Dividend ÷ Divisor = Quotient
Basic Division Formula
Division
15 ÷ 3 = 5
15-3-3-3-3-3=0 (5 times)
Multiplication Check
5 × 3 = 15
Inverse operation
Word Problem
18 items, 6 each group
18 ÷ 6 = 3 groups
Key Definitions:

Dividend: The number being divided (the total amount)

Divisor: The number we divide by (size of each group)

Quotient: The result of division (number of groups)

Remainder: What's left over when division isn't exact

Division Process:
  1. Identify: Find the dividend and divisor in the problem
  2. Subtract: Repeatedly subtract the divisor from the dividend
  3. Count: Keep track of how many times you subtracted
  4. Answer: The count is your quotient
  5. Check: Multiply quotient × divisor to verify
Tip 1: Use drawings or objects to visualize the groups.
Tip 2: Look for patterns in division facts.
Tip 3: Practice with small numbers first.
Division Relationships: Division and multiplication are inverse operations.
Problem Solving: Identify key words that indicate division is needed.
Advanced Practice and Questions
4 Candy Bags
Exercise 4
At the party, there are 21 candies. They are put into bags with 7 candies in each bag. How many bags are filled?
21
-
7
=
14
Bag 1
14
-
7
=
7
Bag 2
7
-
7
=
0
Bag 3
Step 1: Identify the components

Total candies = 21, candies per bag = 7

Step 2: Perform repeated subtraction

21 - 7 = 14 (1st bag)
14 - 7 = 7 (2nd bag)
7 - 7 = 0 (3rd bag)

21 ÷ 7 = 3 bags
5 Pencils for Students
Exercise 5
The teacher has 24 pencils. She gives 8 pencils to each group of students. How many groups receive pencils?
Step 1: Set up the problem

24 pencils total, 8 pencils per group

Step 2: Apply repeated subtraction

24 - 8 = 16 (1st group)
16 - 8 = 8 (2nd group)
8 - 8 = 0 (3rd group)

Step 3: Verify the answer

Check: 3 × 8 = 24 ✓

24 ÷ 8 = 3 groups

Questions & Answers

Question: I sometimes get confused about which number to subtract repeatedly. How do I know?

Answer: Great question! The number you subtract repeatedly is always the "divisor" - the number that tells you how many items go in each group.

Look for clues in the problem:

  • "Each group has 3 items" → subtract 3
  • "Put 4 in each row" → subtract 4
  • "Give 5 to each person" → subtract 5

The divisor is always the number that describes the size of each group!

Question: My child is struggling with the counting part. How can I help them keep track?

Answer: Try these helpful strategies:

  • Draw circles: Draw a circle for each group and write the group number inside
  • Use tally marks: Make one tally mark for each subtraction
  • Number lines: Move backwards on a number line, marking each jump
  • Objects: Use counters or blocks to physically separate into groups

Start with very small numbers (like 6 ÷ 2) and gradually increase difficulty.

Question: What happens if I don't get exactly zero at the end? Like 10 ÷ 3?

Answer: Great observation! With 10 ÷ 3:

10 - 3 = 7 (1st group)
7 - 3 = 4 (2nd group)
4 - 3 = 1 (3rd group)

Now we have 1 left, but we can't subtract 3 from 1.

This means: 10 ÷ 3 = 3 with 1 left over (remainder).

For now, we focus on problems that divide evenly, but understanding remainders is important too!