Division as Repeated Subtraction Worksheet

Master division concepts through repeated subtraction method with visual diagrams and step-by-step exercises for 3rd grade students.

Division as Repeated Subtraction: Exercises 1-3
1 Basic Division Practice
Exercise 1
Solve: 12 ÷ 3 using repeated subtraction
Definition:

Division as repeated subtraction: Division means repeatedly subtracting the divisor from the dividend until we reach zero.

Method:
  1. Start with the dividend (12)
  2. Repeatedly subtract the divisor (3) until reaching zero
  3. Count how many times you subtracted
  4. This count is the quotient
12
-
3
=
9
#1
9
-
3
=
6
#2
6
-
3
=
3
#3
3
-
3
=
0
#4
Step 1: Start with dividend

We begin with 12 (the number we want to divide)

Step 2: Subtract the divisor repeatedly

12 - 3 = 9 (1st subtraction)
9 - 3 = 6 (2nd subtraction)
6 - 3 = 3 (3rd subtraction)
3 - 3 = 0 (4th subtraction)

Step 3: Count the subtractions

We subtracted 3 a total of 4 times to reach 0

12 ÷ 3 = 4
Final answer:

12 ÷ 3 = 4 because we subtracted 3 four times from 12 to get 0

Applied rules:

• Division concept: Division is the inverse of multiplication

• Repeated subtraction: Count how many times divisor fits into dividend

• Verification: 4 × 3 = 12 confirms our answer

2 Intermediate Practice
Exercise 2
Solve: 20 ÷ 4 using repeated subtraction
Definition:

Quotient: The result of division, representing how many equal groups we can make.

20
-
4
=
16
#1
16
-
4
=
12
#2
12
-
4
=
8
#3
8
-
4
=
4
#4
4
-
4
=
0
#5
Step 1: Set up the problem

We need to divide 20 by 4, so we'll repeatedly subtract 4 from 20

Step 2: Perform repeated subtraction

20 - 4 = 16 (1st subtraction)
16 - 4 = 12 (2nd subtraction)
12 - 4 = 8 (3rd subtraction)
8 - 4 = 4 (4th subtraction)
4 - 4 = 0 (5th subtraction)

Step 3: Count and conclude

We performed subtraction 5 times to reach 0

20 ÷ 4 = 5
Final answer:

20 ÷ 4 = 5 because we subtracted 4 five times from 20 to get 0

Applied rules:

• Division relationship: 20 ÷ 4 = 5 means 5 groups of 4 make 20

• Verification: 5 × 4 = 20 confirms our answer

• Pattern recognition: Larger dividends require more subtractions

3 Advanced Practice
Exercise 3
Solve: 18 ÷ 6 using repeated subtraction
Key Concept:

Division facts: Understanding that division is finding how many equal groups we can make from a total amount.

18
-
6
=
12
#1
12
-
6
=
6
#2
6
-
6
=
0
#3
Step 1: Identify components

Dividend = 18, Divisor = 6, we need to find the quotient

Step 2: Execute repeated subtraction

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

Step 3: Determine the result

We subtracted 6 three times to reach 0, so the quotient is 3

18 ÷ 6 = 3
Final answer:

18 ÷ 6 = 3 because we subtracted 6 three times from 18 to get 0

Applied rules:

• Division interpretation: 18 items can be divided into 3 groups of 6

• Verification: 3 × 6 = 18 confirms our answer

• Relationship: Division and multiplication are inverse operations

Division Concepts and Methods
Dividend ÷ Divisor = Quotient
Basic Division Formula
Division
12 ÷ 3 = 4
Repeated subtraction: 12-3-3-3-3=0 (4 times)
Multiplication Check
4 × 3 = 12
Inverse operation verification
Remainder
13 ÷ 3 = 4 R1
13-3-3-3-3=1 (remainder)
Key Definitions:

Dividend: The number being divided

Divisor: The number we divide by

Quotient: The result of division

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

Division as Repeated Subtraction Method:
  1. Start: Begin with the dividend (the number to be divided)
  2. Subtract: Repeatedly subtract the divisor from the current number
  3. Count: Keep track of how many times you subtract
  4. Stop: When you reach zero or a number smaller than the divisor
  5. Result: The count is your quotient
Tip 1: Always start with the dividend and subtract the divisor repeatedly.
Tip 2: Count each subtraction to find the quotient.
Tip 3: Verify your answer by multiplying quotient × divisor = dividend.
Tip 4: If you don't reach exactly zero, the remainder is what's left over.
Key Insight: Division shows how many equal groups we can make from a total amount.
Visual Understanding: Repeated subtraction helps visualize the grouping process.
Advanced Exercises and Q&A
4 Challenge Problem
Exercise 4
Solve: 24 ÷ 6 using repeated subtraction and verify your answer
24
-
6
=
18
#1
18
-
6
=
12
#2
12
-
6
=
6
#3
6
-
6
=
0
#4
Step 1: Perform repeated subtraction

24 - 6 = 18 (1st)
18 - 6 = 12 (2nd)
12 - 6 = 6 (3rd)
6 - 6 = 0 (4th)

Step 2: Verify the result

Quotient = 4, so 4 × 6 = 24 ✓

24 ÷ 6 = 4
5 Word Problem
Exercise 5
Sarah has 15 cookies and wants to share them equally among 3 friends. How many cookies does each friend get?
Step 1: Identify the problem

Need to divide 15 cookies among 3 friends: 15 ÷ 3

Step 2: Use repeated subtraction

15 - 3 = 12 (1st group)
12 - 3 = 9 (2nd group)
9 - 3 = 6 (3rd group)
6 - 3 = 3 (4th group)
3 - 3 = 0 (5th group)

Step 3: Interpret the result

Each friend gets 5 cookies

15 ÷ 3 = 5 cookies per friend

Questions & Answers

Question: I don't understand why we subtract the same number over and over again when doing division. Can you explain?

Answer: Great question! Think of division like sharing cookies with friends:

If you have 12 cookies and want to give 3 cookies to each friend, you can think: "How many groups of 3 can I make from 12?"

So you keep taking away 3 cookies (one group) at a time until you run out:

  • Take 3 cookies → 12 - 3 = 9 (1st group)
  • Take 3 cookies → 9 - 3 = 6 (2nd group)
  • Take 3 cookies → 6 - 3 = 3 (3rd group)
  • Take 3 cookies → 3 - 3 = 0 (4th group)

You made 4 groups, so 12 ÷ 3 = 4. Each subtraction represents one group!

Question: What happens if I can't subtract the number evenly? Like 13 ÷ 4?

Answer: That's when we get a remainder! Let's try 13 ÷ 4:

  • 13 - 4 = 9 (1st subtraction)
  • 9 - 4 = 5 (2nd subtraction)
  • 5 - 4 = 1 (3rd subtraction)

Now we have 1 left, but we can't subtract 4 from 1 (because 1 is less than 4).

So: 13 ÷ 4 = 3 remainder 1, written as 3 R1

This means you can make 3 full groups of 4, with 1 left over.

Check: 3 × 4 = 12, and 12 + 1 = 13 ✓

Question: Is repeated subtraction the same as regular division? Why learn this way?

Answer: Yes, repeated subtraction gives the same result as regular division! We learn this way because:

  • Conceptual Understanding: It helps students understand WHAT division actually means (making equal groups)
  • Visual Learning: Students can see the process happening step by step
  • Foundation Building: It connects division to subtraction, which students already know
  • Problem Solving: It reinforces the relationship between addition/subtraction and multiplication/division

Once students understand the concept, they can move to memorizing facts and shortcuts, but the conceptual foundation remains important.