Solved Exercises on Division Facts with No Remainder in Grade 3

Master division facts with no remainder: understanding exact division, solving division problems with no remainder, and identifying division facts with no remainder through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Understanding exact division
Exercise 1
Is 18 ÷ 3 = 6 an example of division with no remainder? Explain why or why not.
Definition:

Division with no remainder: When one number divides evenly into another, leaving zero leftover.

Checking method:
  1. Multiply the quotient by the divisor
  2. Compare the result to the dividend
  3. If they match exactly, there's no remainder
  4. If not, there would be a remainder
Problem
18 ÷ 3 = 6
Check
6 × 3 = 18
Step 1: Perform the division

18 ÷ 3 = 6

Step 2: Check by multiplying

Quotient × Divisor = 6 × 3 = 18

Step 3: Compare with dividend

Result (18) equals dividend (18)

Step 4: Conclusion

Since 6 × 3 = 18 exactly, there is no remainder.

18 ÷ 3 = 6 with no remainder
Final answer:

Yes, 18 ÷ 3 = 6 is division with no remainder because 6 × 3 = 18 exactly.

Applied rules:

• Exact division: When dividend ÷ divisor = whole number

• Checking: Quotient × Divisor = Dividend (no remainder)

• Multiplication connection: Division and multiplication are inverses

Tip: Always multiply to check division with no remainder.
Tip: Numbers that divide evenly are called "divisible."
2 Solving division problems with no remainder
Exercise 2
Emma has 24 pencils and wants to put them equally into 6 pencil boxes. Will there be any pencils left over? How many pencils will go in each box?
Definition:

Word problem with no remainder: A real-life situation where division results in a whole number with zero leftover.

Problem
24 ÷ 6 = ?
Solution
24 ÷ 6 = 4
Step 1: Identify the total and groups

Total pencils = 24 (dividend)

Number of boxes = 6 (divisor)

Step 2: Set up the division

24 ÷ 6 = ?

Step 3: Use multiplication facts

What number times 6 equals 24?

4 × 6 = 24

Step 4: Check for remainder

4 × 6 = 24 exactly, so no remainder

Step 5: Answer the questions

Each box gets 4 pencils, and there are 0 pencils left over.

24 ÷ 6 = 4 with no remainder
Final answer:

No pencils will be left over. Each box will contain 4 pencils.

Applied rules:

• Equal sharing: Divide total items equally among groups

• No remainder: When items divide evenly

• Checking: 4 × 6 = 24 ✓

Tip: In word problems, look for words like "equally" or "share."
Tip: Always check if your answer makes sense in context.
3 Identifying division facts with no remainder
Exercise 3
Which of these division facts have no remainder: 25÷5, 27÷3, 28÷4, 30÷7? Show your work.
Definition:

Division facts with no remainder: Division equations where the dividend is exactly divisible by the divisor.

Check each
25÷5, 27÷3, 28÷4, 30÷7
Results
5, 9, 7, 4 r2
Step 1: Check 25 ÷ 5

25 ÷ 5 = 5

Check: 5 × 5 = 25 ✓ No remainder

Step 2: Check 27 ÷ 3

27 ÷ 3 = 9

Check: 9 × 3 = 27 ✓ No remainder

Step 3: Check 28 ÷ 4

28 ÷ 4 = 7

Check: 7 × 4 = 28 ✓ No remainder

Step 4: Check 30 ÷ 7

30 ÷ 7 = 4 remainder 2

Check: 4 × 7 = 28, and 30 - 28 = 2 (remainder)

Step 5: Identify results

Division facts with no remainder: 25÷5, 27÷3, 28÷4

25÷5=5, 27÷3=9, 28÷4=7 (no remainder); 30÷7=4 r2 (with remainder)
Final answer:

Division facts with no remainder: 25÷5=5, 27÷3=9, 28÷4=7. The fact 30÷7 has a remainder.

Applied rules:

• Checking divisibility: Multiply quotient by divisor

• Remainder rule: If result ≠ dividend, there's a remainder

• Exact division: Result is a whole number only

Tip: Test each division by multiplying to check for remainder.
Tip: Practice recognizing numbers that divide evenly.
Division Facts with No Remainder
Dividend ÷ Divisor = Quotient (remainder 0)
Exact Division
Division by 2
4÷2=2, 6÷2=3, 8÷2=4
All even numbers
Division by 3
6÷3=2, 9÷3=3, 12÷3=4
Sum of digits multiple of 3
Division by 5
10÷5=2, 15÷5=3, 20÷5=4
Ends in 0 or 5
Key definitions:

Dividend: The number being divided

Divisor: The number dividing the dividend

Quotient: The result of division

No remainder: When division results in a whole number only

Divisibility: When one number divides another evenly

Methods to identify no remainder:
  1. Multiplication check: Multiply quotient by divisor, result should equal dividend
  2. Pattern recognition: Look for divisibility patterns (even numbers for 2, sums for 3, etc.)
  3. Visual grouping: Try to form equal groups without leftovers
  4. Repeated subtraction: Keep subtracting divisor until reaching zero
Tip 1: Even numbers are always divisible by 2.
Tip 2: Numbers ending in 0 or 5 are divisible by 5.
Tip 3: If sum of digits is divisible by 3, the number is divisible by 3.
Tip 4: Always verify: quotient × divisor = dividend.
Common errors: Forgetting to check for remainders, confusing dividends and divisors, not verifying answers.
Memorization: Practice division tables focusing on exact divisions.
Divisibility rules:

• Divisible by 2: Number is even (ends in 0, 2, 4, 6, 8)

• Divisible by 3: Sum of digits is divisible by 3

• Divisible by 4: Last two digits form a number divisible by 4

• Divisible by 5: Number ends in 0 or 5

• Divisible by 10: Number ends in 0

Detailed Summary: Division Facts with No Remainder
Key Concepts:

Division with No Remainder: Also called "exact division," occurs when one number divides evenly into another, leaving zero leftover.

Divisibility: When one number is divisible by another, it means the division results in a whole number with no remainder.

Parts of Division: Dividend ÷ Divisor = Quotient (remainder 0)

Remainder: The amount left over when division is not exact (remainder = 0 for exact division).

Core Methods:
  1. Multiplication Verification: After dividing, multiply the quotient by the divisor to see if you get the dividend. If yes, there's no remainder.
  2. Visual Grouping: Represent the dividend with objects and try to form equal groups of the divisor size. If no objects remain, there's no remainder.
  3. Repeated Subtraction: Keep subtracting the divisor from the dividend until reaching zero. If you reach exactly zero, there's no remainder.
  4. Divisibility Rules: Use shortcuts to determine if a number is divisible by another without performing the full division.
Examples of Exact Division:
  • Easy facts: 4÷2=2, 6÷3=2, 8÷4=2 (no remainder)
  • Medium facts: 12÷3=4, 15÷5=3, 18÷6=3 (no remainder)
  • Advanced facts: 24÷8=3, 36÷9=4, 40÷8=5 (no remainder)
Divisibility Patterns:
  • Divisible by 2: All even numbers (2, 4, 6, 8, 10, 12...)
  • Divisible by 3: Numbers whose digits sum to a multiple of 3 (12: 1+2=3)
  • Divisible by 5: Numbers ending in 0 or 5 (5, 10, 15, 20...)
  • Divisible by 10: Numbers ending in 0 (10, 20, 30, 40...)
Tips for Success:
  • Always verify your answer: quotient × divisor should equal dividend
  • Learn divisibility rules to quickly identify exact divisions
  • Practice with visual representations to understand the concept
  • Memorize common division facts for faster calculations
Common Mistakes to Avoid:
  • Assuming all divisions have no remainder
  • Not checking answers by multiplying
  • Confusing which number is the dividend vs. divisor
  • Forgetting that division with no remainder means a whole number result
Key Takeaways for Memorization:

• Exact division occurs when dividend ÷ divisor = whole number only

• Always verify by multiplying: quotient × divisor = dividend

• Learning divisibility rules helps quickly identify exact divisions

• Common patterns exist for 2, 3, 4, 5, and 10 that make division easier

• Practice with visual models reinforces understanding of no remainder

Questions & Answers

Question: How can I quickly tell if a division problem will have no remainder without doing the full calculation?

Answer: There are several divisibility rules you can use to quickly identify if division will result in no remainder:

  • By 2: If the number is even (ends in 0, 2, 4, 6, 8), it's divisible by 2
  • By 3: Add all digits; if the sum is divisible by 3, the number is divisible by 3
  • By 5: If the number ends in 0 or 5, it's divisible by 5
  • By 10: If the number ends in 0, it's divisible by 10

For example, to check if 24 is divisible by 3: 2 + 4 = 6, and 6 is divisible by 3, so 24 is divisible by 3 with no remainder.

These rules save time and help you predict whether division will result in a whole number answer.

Question: What's the difference between "division with no remainder" and "division that results in a whole number"?

Answer: Actually, "division with no remainder" and "division that results in a whole number" describe the same thing! They are two ways of saying that the division is exact:

  • When division has no remainder, the result is a whole number
  • When division results in a whole number, there is no remainder

For example: 15 ÷ 3 = 5 (no remainder) and 5 is a whole number. Both descriptions apply.

The opposite would be division with a remainder, like 16 ÷ 3 = 5 remainder 1, where the result is not a whole number.

Teachers might use different terms, but they mean the same concept: division that divides evenly.

Question: Are there any tricks to memorize division facts that have no remainder?

Answer: Yes, here are effective tricks for memorizing division facts with no remainder:

  • Use multiplication facts: Since 4×6=24, you know 24÷4=6 and 24÷6=4
  • Focus on patterns: Notice that dividing by 2 always gives half the number
  • Group facts by divisor: Master all ÷2 facts first, then ÷3, etc.
  • Use visual associations: Draw groups to represent division facts

Also, practice with related facts together: if you know 12÷3=4, practice 15÷3=5 and 18÷3=6 at the same time.

Regular practice with flashcards or games that focus specifically on exact divisions will strengthen your memory of these facts.