Word Problems: Dividing Multi-Digit Numbers in Grade 4

Real-world word problems to practice division of multi-digit numbers: long division, remainders, and problem-solving strategies.

Word Problems Introduction

Understanding Word Problems

Word problems require you to identify the dividend (total amount) and divisor (number of groups) from the story context.

Division word problems often involve sharing equally, organizing into groups, or finding how many times one number fits into another.

\( \text{Dividend} \div \text{Divisor} = \text{Quotient} \) remainder \( \text{Remainder} \)
Division Formula
Key Definitions:

Dividend: The total amount being divided (often found after words like "total," "altogether," "in all")

Divisor: The number of groups or the size of each group (often found after words like "each," "per," "groups of")

Quotient: The result of division (the answer to the problem)

Remainder: What's left over after division

Context: The real-world situation that gives meaning to the division

Types of Division Word Problems:

  • Sharing equally: Distributing items evenly among people or groups
  • Grouping: Organizing items into equal groups
  • Rate problems: Finding how many times one quantity fits into another
  • Area problems: Finding dimensions when area is known

Key Words for Division:

  • divide, split, share, distribute
  • equally, per, each, among
  • how many, how much each
  • groups of, sets of
Word Problems: 1 to 3
1 Sharing Equally
Word Problem 1: Sharing Cookies
Emma baked 246 cookies for her class. There are 6 students in her class. If she wants to give each student the same number of cookies, how many cookies will each student get?

Context Analysis:

Total cookies (dividend): 246

Number of students (divisor): 6

Question: How many cookies per student (quotient)?

Solution Process:

We need to divide 246 by 6 to find how many cookies each student gets.

1 Set up: 246 ÷ 6
2 Divide: How many times does 6 go into 24? Answer: 4
3 Multiply: 4 × 6 = 24
4 Subtract: 24 - 24 = 0
5 Bring Down: Bring down the 6 to make 06
6 Divide: How many times does 6 go into 6? Answer: 1
7 Multiply: 1 × 6 = 6
8 Subtract: 6 - 6 = 0
Each student gets 41 cookies
Check: 41 × 6 = 246 ✓
Each student will get 41 cookies.
2 Grouping Items
Word Problem 2: Packing Books
A library received 528 books. The librarian wants to place them equally on 4 shelves. How many books will go on each shelf?

Context Analysis:

Total books (dividend): 528

Number of shelves (divisor): 4

Question: How many books per shelf (quotient)?

Solution Process:

We need to divide 528 by 4 to find how many books go on each shelf.

1 Set up: 528 ÷ 4
2 Divide: How many times does 4 go into 5? Answer: 1
3 Multiply: 1 × 4 = 4
4 Subtract: 5 - 4 = 1
5 Bring Down: Bring down the 2 to make 12
6 Divide: How many times does 4 go into 12? Answer: 3
7 Multiply: 3 × 4 = 12
8 Subtract: 12 - 12 = 0
9 Bring Down: Bring down the 8
10 Divide: How many times does 4 go into 8? Answer: 2
11 Multiply: 2 × 4 = 8
12 Subtract: 8 - 8 = 0
Each shelf gets 132 books
Check: 132 × 4 = 528 ✓
Each shelf will have 132 books.
3 School Scenario
Word Problem 3: Students in Classrooms
A school has 728 students. They want to divide them equally among 7 classrooms. How many students will be in each classroom?

Context Analysis:

Total students (dividend): 728

Number of classrooms (divisor): 7

Question: How many students per classroom (quotient)?

Solution Process:

We need to divide 728 by 7 to find how many students go in each classroom.

1 Set up: 728 ÷ 7
2 Divide: How many times does 7 go into 7? Answer: 1
3 Multiply: 1 × 7 = 7
4 Subtract: 7 - 7 = 0
5 Bring Down: Bring down the 2
6 Divide: How many times does 7 go into 2? Answer: 0 (write 0, bring down 8 to make 28)
7 Divide: How many times does 7 go into 28? Answer: 4
8 Multiply: 4 × 7 = 28
9 Subtract: 28 - 28 = 0
Each classroom gets 104 students
Check: 104 × 7 = 728 ✓
Each classroom will have 104 students.
Word Problems: 4 to 5
4 Shopping Scenario
Word Problem 4: Candy Bags
A candy store received 945 pieces of candy. They want to put them equally into 9 bags. How many pieces of candy will go in each bag? Will there be any left over?

Context Analysis:

Total candy (dividend): 945

Number of bags (divisor): 9

Question: How many pieces per bag (quotient) and remainder?

Solution Process:

We need to divide 945 by 9 to find how many pieces go in each bag and any remainder.

1 Set up: 945 ÷ 9
2 Divide: How many times does 9 go into 9? Answer: 1
3 Multiply: 1 × 9 = 9
4 Subtract: 9 - 9 = 0
5 Bring Down: Bring down the 4
6 Divide: How many times does 9 go into 4? Answer: 0 (write 0, bring down 5 to make 45)
7 Divide: How many times does 9 go into 45? Answer: 5
8 Multiply: 5 × 9 = 45
9 Subtract: 45 - 45 = 0
Each bag gets 105 pieces, no remainder
Check: 105 × 9 = 945 ✓
Each bag will have 105 pieces of candy, with none left over.
5 Home Scenario
Word Problem 5: Stickers for Friends
Maya has 672 stickers. She wants to give the same number of stickers to each of her 6 friends. How many stickers will each friend get? How many stickers will Maya have left?

Context Analysis:

Total stickers (dividend): 672

Number of friends (divisor): 6

Question: How many stickers per friend (quotient) and remainder?

Solution Process:

We need to divide 672 by 6 to find how many stickers each friend gets and any remainder.

1 Set up: 672 ÷ 6
2 Divide: How many times does 6 go into 6? Answer: 1
3 Multiply: 1 × 6 = 6
4 Subtract: 6 - 6 = 0
5 Bring Down: Bring down the 7
6 Divide: How many times does 6 go into 7? Answer: 1
7 Multiply: 1 × 6 = 6
8 Subtract: 7 - 6 = 1
9 Bring Down: Bring down the 2 to make 12
10 Divide: How many times does 6 go into 12? Answer: 2
11 Multiply: 2 × 6 = 12
12 Subtract: 12 - 12 = 0
Each friend gets 112 stickers, no remainder
Check: 112 × 6 = 672 ✓
Each friend will get 112 stickers, and Maya will have 0 stickers left.
Word Problems Complete Summary
\( \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \)
Division Verification

Problem-Solving Strategy

Follow these steps when solving division word problems:

Key definitions:

Division: Splitting a number into equal groups

Long Division: Methodical approach to divide multi-digit numbers

Remainder: Amount left over after division

Place Value: Position of digits determines their value

Context: Real-world situation giving meaning to the problem

Key Words: Words that indicate mathematical operations

Word problem methodology:
  1. Read carefully: Understand the situation described
  2. Identify key information: Find the total amount and number of groups
  3. Determine operation: Decide if you need division
  4. Set up equation: Write the division problem
  5. Solve: Use long division to find the answer
  6. Interpret result: Make sure the answer makes sense in context
  7. Check: Verify your answer using multiplication

Key Words for Division:

  • share, divide, distribute equally
  • each, per, among, between
  • how many each, how many in each group
  • split into, groups of, sets of
Tip 1: Underline the question to focus on what you need to find.
Tip 2: Circle key numbers in the problem.
Tip 3: Always check if your answer makes sense in the context of the problem.
Tip 4: Don't forget to consider remainders in real-world contexts.
Tip 5: Verify your answer by multiplying quotient by divisor and adding remainder.
Common errors: Misidentifying dividend and divisor, forgetting to check work, misinterpreting remainders.
Success strategies: Read carefully, identify key information, draw diagrams when helpful.

Real-World Applications:

  • Sharing resources equally
  • Organizing items into containers
  • Calculating rates and ratios
  • Distributing supplies
  • Planning events and seating

Questions & Answers

Question: How do I know when a word problem requires division?

Answer: Look for key words and phrases that indicate division:

  • Sharing equally: "shared among," "divided equally," "given to each"
  • Grouping: "put into groups of," "packed in sets of," "organized into"
  • Rate problems: "per," "each," "for every"
  • How many times: "how many times does," "fits into," "goes into"

Also, if the problem asks "how many in each group" or "how many groups," it's likely a division problem.

Question: How can I help my child identify the dividend and divisor in word problems?

Answer: Teach your child to look for specific clues:

  • Dividend (total amount): Look for phrases like "total," "altogether," "in all," "number of items"
  • Divisor (number of groups): Look for phrases like "each," "per," "groups of," "shared among"
  • Draw pictures: Visual representations help clarify the problem
  • Act it out: Use manipulatives to physically demonstrate the problem

Practice with many examples to build pattern recognition skills.

Question: What should I do if I get a remainder in a word problem?

Answer: When you get a remainder in a word problem:

  • Include it in your answer: State both the quotient and the remainder
  • Interpret the meaning: Consider what the remainder represents in the context
  • Think about the situation: Sometimes you might need to round up (like needing extra buses)
  • Check your work: Verify using the formula: Dividend = (Divisor × Quotient) + Remainder

For example, if dividing 25 candies among 4 children gives 6 remainder 1, each child gets 6 candies and there's 1 left over.