Learn on PengiPengi Math (Grade 4)Chapter 4: Multiplication & Division Strategies

Lesson 5: Word Problems with Division and Remainders

In this Grade 4 Pengi Math lesson from Chapter 4, students learn how to interpret remainders in real-world contexts by deciding whether to round up, drop, or share them depending on the situation. They use tape diagrams to solve multiplicative comparison problems and tackle multi-step word problems involving all four operations. Students also practice deconstructing word problems to uncover hidden questions and determine the correct sequence of operations.

Section 1

Understanding Multiplication in Word Problems

Property

To solve a word problem using multiplication, identify the number of equal groups and the size of each group.
The total amount can be found using the equation:

Total=(Number of groups)×(Size of each group)Total = (\text{Number of groups}) \times (\text{Size of each group})

Examples

Section 2

Interpreting Remainders in Division Word Problems

Property

When solving a division word problem, the quotient is the number of equal groups, and the remainder is the amount left over. The final answer depends on how the question asks you to interpret this remainder: either ignore it, use it to round up the quotient, or use the remainder itself as the answer.

Examples

  • A bakery has 1,250 eggs. If each cake requires 6 eggs, how many full cakes can the bakery make?
1250÷6=208 R 21250 \div 6 = 208 \text{ R } 2

The bakery can make 208 full cakes. The remainder of 2 eggs is ignored.

  • A school needs to transport 2,415 students to a museum. Each bus can hold 8 students. How many buses are needed to transport all the students?
2415÷8=301 R 72415 \div 8 = 301 \text{ R } 7

302 buses are needed. 301 buses will be full, and one extra bus is needed for the remaining 7 students.

  • A farmer collected 3,147 apples and wants to pack them into bags of 5. After making as many full bags as possible, how many apples will be left over?
3147÷5=629 R 23147 \div 5 = 629 \text{ R } 2

There will be 2 apples left over. The remainder is the answer.

Explanation

This skill involves solving division word problems where the dividend is a four-digit number and the divisor is a one-digit number. After performing the long division, you must carefully read the question to understand what to do with the remainder. Sometimes the answer is the quotient, sometimes you need to add one to the quotient, and other times the remainder itself is the answer. The context of the story problem is the key to finding the correct solution.

Book overview

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Continue this chapter

Chapter 4: Multiplication & Division Strategies

  1. Lesson 1

    Lesson 1: Mental Math and Estimation Strategies

  2. Lesson 2

    Lesson 2: Multiplying by One-Digit Numbers

  3. Lesson 3

    Lesson 3: Multiplying Two-Digit Numbers

  4. Lesson 4

    Lesson 4: Long Division Algorithms

  5. Lesson 5Current

    Lesson 5: Word Problems with Division and Remainders

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Understanding Multiplication in Word Problems

Property

To solve a word problem using multiplication, identify the number of equal groups and the size of each group.
The total amount can be found using the equation:

Total=(Number of groups)×(Size of each group)Total = (\text{Number of groups}) \times (\text{Size of each group})

Examples

Section 2

Interpreting Remainders in Division Word Problems

Property

When solving a division word problem, the quotient is the number of equal groups, and the remainder is the amount left over. The final answer depends on how the question asks you to interpret this remainder: either ignore it, use it to round up the quotient, or use the remainder itself as the answer.

Examples

  • A bakery has 1,250 eggs. If each cake requires 6 eggs, how many full cakes can the bakery make?
1250÷6=208 R 21250 \div 6 = 208 \text{ R } 2

The bakery can make 208 full cakes. The remainder of 2 eggs is ignored.

  • A school needs to transport 2,415 students to a museum. Each bus can hold 8 students. How many buses are needed to transport all the students?
2415÷8=301 R 72415 \div 8 = 301 \text{ R } 7

302 buses are needed. 301 buses will be full, and one extra bus is needed for the remaining 7 students.

  • A farmer collected 3,147 apples and wants to pack them into bags of 5. After making as many full bags as possible, how many apples will be left over?
3147÷5=629 R 23147 \div 5 = 629 \text{ R } 2

There will be 2 apples left over. The remainder is the answer.

Explanation

This skill involves solving division word problems where the dividend is a four-digit number and the divisor is a one-digit number. After performing the long division, you must carefully read the question to understand what to do with the remainder. Sometimes the answer is the quotient, sometimes you need to add one to the quotient, and other times the remainder itself is the answer. The context of the story problem is the key to finding the correct solution.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 4: Multiplication & Division Strategies

  1. Lesson 1

    Lesson 1: Mental Math and Estimation Strategies

  2. Lesson 2

    Lesson 2: Multiplying by One-Digit Numbers

  3. Lesson 3

    Lesson 3: Multiplying Two-Digit Numbers

  4. Lesson 4

    Lesson 4: Long Division Algorithms

  5. Lesson 5Current

    Lesson 5: Word Problems with Division and Remainders