Learn on PengienVision, Mathematics, Grade 6Chapter 5: Understand and Use Ratio and Rate

Lesson 10: Relate Customary and Metric Units

In this Grade 6 lesson from Chapter 5 of enVision Mathematics, students learn how to convert between customary and metric units of length, weight/mass, and capacity using conversion factors and dimensional analysis. They practice both single-step and two-step conversions, such as changing meters to inches or liters to cups, using approximate equivalents like 1 m ≈ 39.37 in. and 1 kg ≈ 2.20 lb. The lesson builds on students' understanding of ratios and rates to set up and simplify unit conversions accurately.

Section 1

Convert Between Customary and Metric Lengths

Property

To convert between customary and metric units of length, multiply by a conversion factor. Key conversion factors include:

  • 1 m≈3.28 ft1 \text{ m} \approx 3.28 \text{ ft}
  • 1 m≈39.37 in1 \text{ m} \approx 39.37 \text{ in}
  • 1 in=2.54 cm1 \text{ in} = 2.54 \text{ cm}
  • 1 mi≈1.61 km1 \text{ mi} \approx 1.61 \text{ km}

Examples

  • Convert 12 inches to centimeters:
12 in×2.54 cm1 in=30.48 cmor1 in2.54 cm×1212=12 in30.48 cm12 \text{ in} \times \frac{2.54 \text{ cm}}{1 \text{ in}} = 30.48 \text{ cm} \quad \text{or} \quad \frac{1 \text{ in}}{2.54 \text{ cm}} \times \frac{12}{12} = \frac{12 \text{ in}}{30.48 \text{ cm}}
  • Convert 8 kilometers to miles:
8 km×1 mi1.61 km≈4.97 mior1.61 km1 mi×88≈8 km4.97 mi8 \text{ km} \times \frac{1 \text{ mi}}{1.61 \text{ km}} \approx 4.97 \text{ mi} \quad \text{or} \quad \frac{1.61 \text{ km}}{1 \text{ mi}} \times \frac{8}{8} \approx \frac{8 \text{ km}}{4.97 \text{ mi}}

Section 2

Convert Between Customary and Metric Weight/Mass

Property

To convert between customary and metric units of weight and mass, use the following approximate conversion factors:

  • 1 ounce (oz) ≈\approx 28.35 grams (g)
  • 1 kilogram (kg) ≈\approx 2.205 pounds (lb)
  • 1 metric ton (t) ≈\approx 1.102 short tons (T)

Examples

  • Convert 5 ounces to grams:
5 oz×28.35 g1 oz=141.75 gor141.75 g×1 oz28.35 g=5 oz5 \text{ oz} \times \frac{28.35 \text{ g}}{1 \text{ oz}} = 141.75 \text{ g} \quad \text{or} \quad 141.75 \text{ g} \times \frac{1 \text{ oz}}{28.35 \text{ g}} = 5 \text{ oz}
  • Convert 3 kilograms to pounds:
3 kg×2.205 lb1 kg≈6.615 lbor6.615 lb×1 kg2.205 lb≈3 kg3 \text{ kg} \times \frac{2.205 \text{ lb}}{1 \text{ kg}} \approx 6.615 \text{ lb} \quad \text{or} \quad 6.615 \text{ lb} \times \frac{1 \text{ kg}}{2.205 \text{ lb}} \approx 3 \text{ kg}

Section 3

Convert Between Customary and Metric Capacity

Property

Key approximate conversion factors for capacity are:

  • 1 gallon (gal) ≈\approx 3.79 liters (L)
  • 1 liter (L) ≈\approx 0.264 gallon (gal)
  • 1 quart (qt) ≈\approx 0.946 liter (L)
  • 1 liter (L) ≈\approx 1.06 quart (qt)

Examples

  • Convert 2 gallons to liters:
2 gal×3.79 L1 gal≈7.58 Lor7.58 L×1 gal3.79 L≈2 gal2 \text{ gal} \times \frac{3.79 \text{ L}}{1 \text{ gal}} \approx 7.58 \text{ L} \quad \text{or} \quad 7.58 \text{ L} \times \frac{1 \text{ gal}}{3.79 \text{ L}} \approx 2 \text{ gal}
  • Convert 5 liters to gallons:
5 L×1 gal3.79 L≈1.32 galor1.32 gal×3.79 L1 gal≈5 L5 \text{ L} \times \frac{1 \text{ gal}}{3.79 \text{ L}} \approx 1.32 \text{ gal} \quad \text{or} \quad 1.32 \text{ gal} \times \frac{3.79 \text{ L}}{1 \text{ gal}} \approx 5 \text{ L}

Section 4

Multi-Step Rate Conversions

Property

For multi-step rate problems, chain conversion factors to cancel intermediate units:

Starting quantity×unit1unit2×unit3unit1×unit4unit3=Final quantity in unit4\text{Starting quantity} \times \frac{\text{unit}_1}{\text{unit}_2} \times \frac{\text{unit}_3}{\text{unit}_1} \times \frac{\text{unit}_4}{\text{unit}_3} = \text{Final quantity in unit}_4

Examples

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Chapter 5: Understand and Use Ratio and Rate

  1. Lesson 1

    Lesson 1: Understand Ratios

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  2. Lesson 2

    Lesson 2: Generate Equivalent Ratios

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  3. Lesson 3

    Lesson 3: Compare Ratios

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  4. Lesson 4

    Lesson 4: Represent and Graph Ratios

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  5. Lesson 5

    Lesson 5: Understand Rates and Unit Rates

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  6. Lesson 6

    Lesson 6: Compare Unit Rates

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  7. Lesson 7

    Lesson 7: Solve Unit Rate Problems

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  8. Lesson 8

    Lesson 8: Ratio Reasoning: Convert Customary Units

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  9. Lesson 9

    Lesson 9: Ratio Reasoning: Convert Metric Units

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  10. Lesson 10Current

    Lesson 10: Relate Customary and Metric Units

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Section 1

Convert Between Customary and Metric Lengths

Property

To convert between customary and metric units of length, multiply by a conversion factor. Key conversion factors include:

  • 1 m≈3.28 ft1 \text{ m} \approx 3.28 \text{ ft}
  • 1 m≈39.37 in1 \text{ m} \approx 39.37 \text{ in}
  • 1 in=2.54 cm1 \text{ in} = 2.54 \text{ cm}
  • 1 mi≈1.61 km1 \text{ mi} \approx 1.61 \text{ km}

Examples

  • Convert 12 inches to centimeters:
12 in×2.54 cm1 in=30.48 cmor1 in2.54 cm×1212=12 in30.48 cm12 \text{ in} \times \frac{2.54 \text{ cm}}{1 \text{ in}} = 30.48 \text{ cm} \quad \text{or} \quad \frac{1 \text{ in}}{2.54 \text{ cm}} \times \frac{12}{12} = \frac{12 \text{ in}}{30.48 \text{ cm}}
  • Convert 8 kilometers to miles:
8 km×1 mi1.61 km≈4.97 mior1.61 km1 mi×88≈8 km4.97 mi8 \text{ km} \times \frac{1 \text{ mi}}{1.61 \text{ km}} \approx 4.97 \text{ mi} \quad \text{or} \quad \frac{1.61 \text{ km}}{1 \text{ mi}} \times \frac{8}{8} \approx \frac{8 \text{ km}}{4.97 \text{ mi}}

Section 2

Convert Between Customary and Metric Weight/Mass

Property

To convert between customary and metric units of weight and mass, use the following approximate conversion factors:

  • 1 ounce (oz) ≈\approx 28.35 grams (g)
  • 1 kilogram (kg) ≈\approx 2.205 pounds (lb)
  • 1 metric ton (t) ≈\approx 1.102 short tons (T)

Examples

  • Convert 5 ounces to grams:
5 oz×28.35 g1 oz=141.75 gor141.75 g×1 oz28.35 g=5 oz5 \text{ oz} \times \frac{28.35 \text{ g}}{1 \text{ oz}} = 141.75 \text{ g} \quad \text{or} \quad 141.75 \text{ g} \times \frac{1 \text{ oz}}{28.35 \text{ g}} = 5 \text{ oz}
  • Convert 3 kilograms to pounds:
3 kg×2.205 lb1 kg≈6.615 lbor6.615 lb×1 kg2.205 lb≈3 kg3 \text{ kg} \times \frac{2.205 \text{ lb}}{1 \text{ kg}} \approx 6.615 \text{ lb} \quad \text{or} \quad 6.615 \text{ lb} \times \frac{1 \text{ kg}}{2.205 \text{ lb}} \approx 3 \text{ kg}

Section 3

Convert Between Customary and Metric Capacity

Property

Key approximate conversion factors for capacity are:

  • 1 gallon (gal) ≈\approx 3.79 liters (L)
  • 1 liter (L) ≈\approx 0.264 gallon (gal)
  • 1 quart (qt) ≈\approx 0.946 liter (L)
  • 1 liter (L) ≈\approx 1.06 quart (qt)

Examples

  • Convert 2 gallons to liters:
2 gal×3.79 L1 gal≈7.58 Lor7.58 L×1 gal3.79 L≈2 gal2 \text{ gal} \times \frac{3.79 \text{ L}}{1 \text{ gal}} \approx 7.58 \text{ L} \quad \text{or} \quad 7.58 \text{ L} \times \frac{1 \text{ gal}}{3.79 \text{ L}} \approx 2 \text{ gal}
  • Convert 5 liters to gallons:
5 L×1 gal3.79 L≈1.32 galor1.32 gal×3.79 L1 gal≈5 L5 \text{ L} \times \frac{1 \text{ gal}}{3.79 \text{ L}} \approx 1.32 \text{ gal} \quad \text{or} \quad 1.32 \text{ gal} \times \frac{3.79 \text{ L}}{1 \text{ gal}} \approx 5 \text{ L}

Section 4

Multi-Step Rate Conversions

Property

For multi-step rate problems, chain conversion factors to cancel intermediate units:

Starting quantity×unit1unit2×unit3unit1×unit4unit3=Final quantity in unit4\text{Starting quantity} \times \frac{\text{unit}_1}{\text{unit}_2} \times \frac{\text{unit}_3}{\text{unit}_1} \times \frac{\text{unit}_4}{\text{unit}_3} = \text{Final quantity in unit}_4

Examples

Book overview

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Chapter 5: Understand and Use Ratio and Rate

  1. Lesson 1

    Lesson 1: Understand Ratios

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  2. Lesson 2

    Lesson 2: Generate Equivalent Ratios

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  3. Lesson 3

    Lesson 3: Compare Ratios

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  4. Lesson 4

    Lesson 4: Represent and Graph Ratios

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  5. Lesson 5

    Lesson 5: Understand Rates and Unit Rates

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  6. Lesson 6

    Lesson 6: Compare Unit Rates

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  7. Lesson 7

    Lesson 7: Solve Unit Rate Problems

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  8. Lesson 8

    Lesson 8: Ratio Reasoning: Convert Customary Units

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  9. Lesson 9

    Lesson 9: Ratio Reasoning: Convert Metric Units

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  10. Lesson 10Current

    Lesson 10: Relate Customary and Metric Units

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