Division with Remainders Mastery Course for Year 4 Students

Comprehensive division with remainders course for Year 4 students: long division, word problems, and advanced concepts for 4th grade mastery.

Year 4 Division with Remainders Mastery

Welcome to Year 4 Division Mastery!

Advanced division with remainders using long division method, complex word problems, and multi-step reasoning for Year 4 students.

1 Long Division (Intermediate)
1
Calculate: 84 ÷ 6
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6 ) 84
- 6
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24
- 24
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0
Solution:

Step 1: 6 goes into 8 once (6 × 1 = 6)

Step 2: 8 - 6 = 2, bring down 4 to make 24

Step 3: 6 goes into 24 four times (6 × 4 = 24)

Step 4: 24 - 24 = 0

Therefore: 84 ÷ 6 = 14 R 0

Verification:

(6 × 14) + 0 = 84 + 0 = 84 ✓

2 Long Division (Intermediate)
2
Calculate: 97 ÷ 8
______
8 ) 97
- 8
--
17
- 16
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1
Solution:

Step 1: 8 goes into 9 once (8 × 1 = 8)

Step 2: 9 - 8 = 1, bring down 7 to make 17

Step 3: 8 goes into 17 twice (8 × 2 = 16)

Step 4: 17 - 16 = 1

Therefore: 97 ÷ 8 = 12 R 1

Verification:

(8 × 12) + 1 = 96 + 1 = 97 ✓

3 Long Division (Advanced)
3
Calculate: 158 ÷ 7
______
7 ) 158
- 14
--
18
- 14
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4
Solution:

Step 1: 7 goes into 15 twice (7 × 2 = 14)

Step 2: 15 - 14 = 1, bring down 8 to make 18

Step 3: 7 goes into 18 twice (7 × 2 = 14)

Step 4: 18 - 14 = 4

Therefore: 158 ÷ 7 = 22 R 4

Verification:

(7 × 22) + 4 = 154 + 4 = 158 ✓

Year 4 Division Word Problems
4 Field Trip Planning (Advanced)
4
A school has 238 students going on a field trip. Buses can carry 14 students each. How many buses are needed? How many students will be on the last bus?
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Solution:

Step 1: 238 ÷ 14 = ?

Step 2: 14 × 17 = 238

Step 3: 238 - 238 = 0

Therefore: 238 ÷ 14 = 17 R 0

So 17 buses are needed, with 0 students left over

Verification:

(14 × 17) + 0 = 238 + 0 = 238 ✓

5 Library Organization (Advanced)
5
A teacher has 167 books to place on shelves. Each shelf holds 9 books. How many full shelves can be filled? How many books will be left over?
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Solution:

Step 1: 167 ÷ 9 = ?

Step 2: 9 × 18 = 162

Step 3: 167 - 162 = 5

Therefore: 167 ÷ 9 = 18 R 5

So 18 full shelves can be filled with 5 books left over

Verification:

(9 × 18) + 5 = 162 + 5 = 167 ✓

6 Factory Production (Advanced)
6
A factory produces 483 toy cars and packs them in boxes that hold 16 cars each. How many full boxes can be made? How many cars will be left unpacked?
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Solution:

Step 1: 483 ÷ 16 = ?

Step 2: 16 × 30 = 480

Step 3: 483 - 480 = 3

Therefore: 483 ÷ 16 = 30 R 3

So 30 full boxes can be made with 3 cars left unpacked

Verification:

(16 × 30) + 3 = 480 + 3 = 483 ✓

Year 4 Division Challenge Problems
7 Store Inventory (Advanced)
7
A store has 319 pencils to package in sets of 13. How many complete sets can be made? How many pencils will be left over?
Solution:

Step 1: 319 ÷ 13 = ?

Step 2: 13 × 24 = 312

Step 3: 319 - 312 = 7

Therefore: 319 ÷ 13 = 24 R 7

So 24 complete sets can be made with 7 pencils left over

Verification:

(13 × 24) + 7 = 312 + 7 = 319 ✓

8 Camp Organization (Challenge)
8
A camp has 567 campers and wants to organize them into groups of 23. How many full groups can be formed? How many campers will not fit into a full group?
Solution:

Step 1: 567 ÷ 23 = ?

Step 2: 23 × 24 = 552

Step 3: 567 - 552 = 15

Therefore: 567 ÷ 23 = 24 R 15

So 24 full groups can be formed with 15 campers left over

Verification:

(23 × 24) + 15 = 552 + 15 = 567 ✓

9 Delivery Logistics (Challenge)
9
A delivery truck has 724 packages to deliver. The truck can carry 18 packages per trip. How many trips will be needed to deliver all packages? How many packages will be on the final trip?
Solution:

Step 1: 724 ÷ 18 = ?

Step 2: 18 × 40 = 720

Step 3: 724 - 720 = 4

Therefore: 724 ÷ 18 = 40 R 4

So 40 trips with full loads, and 1 trip with 4 packages

Total trips needed: 41

Verification:

(18 × 40) + 4 = 720 + 4 = 724 ✓

Year 4 Division Skills Checklist:
  • ✓ Master long division algorithm
  • ✓ Solve complex word problems
  • ✓ Interpret remainders in context
  • ✓ Verify answers using division algorithm
  • ✓ Apply division to real-world scenarios
  • ✓ Check that remainder < divisor
  • ✓ Explain solution process clearly
    • Year 4 Division Mastery Guide
    Dividend = (Divisor × Quotient) + Remainder
    Division Algorithm
    Year 4 Division with Remainders - Mastery Guide
    Core Definitions
  • Dividend: The number being divided (the larger number)
  • Divisor: The number we divide by (the smaller number)
  • Quotient: The result of division (how many times it divides)
  • Remainder: What's left over after division
  • Division Algorithm: The fundamental relationship between all four values
    • Long Division Steps
  • Step 1 (Divide): How many times does divisor go into current number?
  • Step 2 (Multiply): Multiply divisor by the quotient digit
  • Step 3 (Subtract): Subtract the product from current number
  • Step 4 (Bring Down): Bring down the next digit
  • Step 5 (Repeat): Continue until no digits remain
    • Remainder Rules
  • Rule 1: Remainder is always less than the divisor
  • Rule 2: If remainder is 0, division is exact
  • Rule 3: Remainder cannot equal or exceed the divisor
  • Rule 4: Always verify: (Divisor × Quotient) + Remainder = Dividend
    • Advanced Examples
  • Basic: 24 ÷ 4 = 6 R 0 (exact division)
  • Simple: 25 ÷ 4 = 6 R 1 (remainder = 1)
  • Medium: 83 ÷ 7 = 11 R 6 (larger numbers)
  • Advanced: 317 ÷ 15 = 21 R 2 (multi-digit division)
  • Complex: 1023 ÷ 41 = 24 R 39 (large numbers with large remainders)
    • Problem-Solving Strategy
  • Step 1: Read the problem carefully and identify what is being asked
  • Step 2: Determine what numbers represent dividend and divisor
  • Step 3: Perform the division using long division method
  • Step 4: Interpret the quotient and remainder in context
  • Step 5: Verify your answer and check if it makes sense
    • Year 4 Strategies
  • Strategy 1: Always write out your long division steps clearly
  • Strategy 2: Check that remainder < divisor
  • Strategy 3: Use multiplication facts to help with division
  • Strategy 4: Always verify your answer using the division algorithm
  • Strategy 5: For word problems, answer the specific question asked
    • Common Mistakes to Avoid
  • Mistake 1: Having remainder ≥ divisor
  • Mistake 2: Forgetting to bring down the next digit
  • Mistake 3: Not verifying the answer
  • Mistake 4: Misreading word problems
  • Mistake 5: Arithmetic errors in multiplication or subtraction
    • Real-World Applications
  • Sharing items among people
  • Organizing objects into equal groups
  • Calculating transportation needs
  • Packaging products efficiently
  • Planning events and seating arrangements
  • Resource allocation and distribution
    • 238 students
    ÷
    14 per bus
    →
    17 buses
    0 left over
    238 ÷ 14 = 17 R 0
    Verification:

    (14 × 17) + 0 = 238 + 0 = 238 ✓

    Questions & Answers

    Question: I'm having trouble with long division. How do I know when to stop bringing down numbers?

    Answer: Great question! You stop bringing down numbers when:

    • You've brought down all the digits from the dividend
    • The number you're working with is smaller than the divisor
    • There are no more digits to bring down

    Once you reach this point, whatever number is left becomes your remainder. Remember the acronym: DMSB (Divide, Multiply, Subtract, Bring down).

    Question: How can I help my child practice division with remainders effectively?

    Answer: Here are effective strategies:

    • Start with concrete examples: Use physical objects like blocks or counters
    • Practice basic facts: Strengthen multiplication facts to support division
    • Use graph paper: Helps keep long division organized
    • Check answers together: Reinforce the verification process
    • Connect to real life: Use word problems that relate to daily activities

    Consistent practice with immediate feedback works best!

    Question: How do I know if my remainder is correct? Sometimes I get confused about whether it's too big.

    Answer: There's a simple rule to check:

    • The remainder must always be smaller than the divisor
    • If your remainder is equal to or bigger than the divisor, you made a mistake
    • Always check: (Divisor × Quotient) + Remainder = Original Dividend

    Example: In 23 ÷ 5 = 4 R 3, check that 3 < 5 ✓

    Then verify: (5 × 4) + 3 = 20 + 3 = 23 ✓