Learn on PengiEureka Math, Grade 4Chapter 7: Metric Unit Conversions

Lesson 2: Express metric mass measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric mass.

Grade 4 students learn to express metric mass measurements in terms of smaller units, converting between kilograms and grams, as part of Eureka Math Chapter 7 on Metric Unit Conversions. The lesson builds on place value understanding to convert mixed units and apply those skills to solve addition and subtraction word problems involving metric mass. Students use number bonds, tape diagrams, and algorithms to model and solve real-world mass problems.

Section 1

Convert Mixed Mass Units to a Smaller Unit

Property

To convert a mixed unit of mass to a single, smaller unit (grams), use the relationship 1 kg=1,000 g1 \text{ kg} = 1,000 \text{ g}. Convert the kilograms to grams and add the remaining grams.

X kg Y g=(X×1,000) g+Y gX \text{ kg } Y \text{ g} = (X \times 1,000) \text{ g} + Y \text{ g}

Examples

Section 2

Add and Subtract Mixed Mass Units

Property

To add or subtract mixed units of mass, combine the kilograms and grams separately. If the grams total 1,0001,000 or more, or if you need to subtract a larger number of grams from a smaller one, you must regroup.

  • 1,000 g=1 kg1,000 \text{ g} = 1 \text{ kg}

Examples

  • Addition: 5 kg 200 g+2 kg 300 g=7 kg 500 g5 \text{ kg } 200 \text{ g} + 2 \text{ kg } 300 \text{ g} = 7 \text{ kg } 500 \text{ g}
  • Addition with Regrouping: 3 kg 700 g+4 kg 500 g=7 kg 1200 g=8 kg 200 g3 \text{ kg } 700 \text{ g} + 4 \text{ kg } 500 \text{ g} = 7 \text{ kg } 1200 \text{ g} = 8 \text{ kg } 200 \text{ g}
  • Subtraction with Regrouping: 8 kg 150 g−2 kg 400 g=7 kg 1150 g−2 kg 400 g=5 kg 750 g8 \text{ kg } 150 \text{ g} - 2 \text{ kg } 400 \text{ g} = 7 \text{ kg } 1150 \text{ g} - 2 \text{ kg } 400 \text{ g} = 5 \text{ kg } 750 \text{ g}

Explanation

This skill involves performing addition and subtraction with measurements that have both kilograms and grams. You can treat the kilograms and grams as separate place values, similar to how you work with whole numbers. Add or subtract the like units, then regroup between kilograms and grams if necessary. This simplifying strategy is often faster than converting everything to grams first.

Book overview

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Chapter 7: Metric Unit Conversions

  1. Lesson 1

    Lesson 1: Express metric length measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric length.

    LearnPractice
  2. Lesson 2Current

    Lesson 2: Express metric mass measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric mass.

    LearnPractice
  3. Lesson 3

    Lesson 3: Express metric capacity measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric capacity.

    LearnPractice

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Convert Mixed Mass Units to a Smaller Unit

Property

To convert a mixed unit of mass to a single, smaller unit (grams), use the relationship 1 kg=1,000 g1 \text{ kg} = 1,000 \text{ g}. Convert the kilograms to grams and add the remaining grams.

X kg Y g=(X×1,000) g+Y gX \text{ kg } Y \text{ g} = (X \times 1,000) \text{ g} + Y \text{ g}

Examples

Section 2

Add and Subtract Mixed Mass Units

Property

To add or subtract mixed units of mass, combine the kilograms and grams separately. If the grams total 1,0001,000 or more, or if you need to subtract a larger number of grams from a smaller one, you must regroup.

  • 1,000 g=1 kg1,000 \text{ g} = 1 \text{ kg}

Examples

  • Addition: 5 kg 200 g+2 kg 300 g=7 kg 500 g5 \text{ kg } 200 \text{ g} + 2 \text{ kg } 300 \text{ g} = 7 \text{ kg } 500 \text{ g}
  • Addition with Regrouping: 3 kg 700 g+4 kg 500 g=7 kg 1200 g=8 kg 200 g3 \text{ kg } 700 \text{ g} + 4 \text{ kg } 500 \text{ g} = 7 \text{ kg } 1200 \text{ g} = 8 \text{ kg } 200 \text{ g}
  • Subtraction with Regrouping: 8 kg 150 g−2 kg 400 g=7 kg 1150 g−2 kg 400 g=5 kg 750 g8 \text{ kg } 150 \text{ g} - 2 \text{ kg } 400 \text{ g} = 7 \text{ kg } 1150 \text{ g} - 2 \text{ kg } 400 \text{ g} = 5 \text{ kg } 750 \text{ g}

Explanation

This skill involves performing addition and subtraction with measurements that have both kilograms and grams. You can treat the kilograms and grams as separate place values, similar to how you work with whole numbers. Add or subtract the like units, then regroup between kilograms and grams if necessary. This simplifying strategy is often faster than converting everything to grams first.

Book overview

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

Continue this chapter

Chapter 7: Metric Unit Conversions

  1. Lesson 1

    Lesson 1: Express metric length measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric length.

    LearnPractice
  2. Lesson 2Current

    Lesson 2: Express metric mass measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric mass.

    LearnPractice
  3. Lesson 3

    Lesson 3: Express metric capacity measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric capacity.

    LearnPractice