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Develop fluency in division facts and algorithms for various types of numbers.

Sharing Equally: Division

Division is the operation of splitting a quantity into equal parts or determining how many times one number fits into another. It covers dividing whole numbers, decimals, and fractions, using long division, mental strategies, and reciprocal methods that are essential for measurement, distribution, and rate calculations.

Components of Division

This section breaks down the core aspects of performing division across different number types:

  • Whole Numbers: Dividing integers using long division, focusing on quotients and remainders.
  • Decimals: Dividing numbers with decimal points, including moving the decimal in the divisor.
  • Fractions: Dividing fractions by multiplying by the reciprocal (flip and multiply).
  • Applications of Division: Practical uses such as sharing equally, finding unit rates, and converting units.

Examples of Division

Whole Numbers Examples

  • Dividing 84 ÷ 7: Ask how many times 7 fits into 84. 7 × 12 = 84, so the answer is 12.
  • Dividing 155 ÷ 6: 6 × 25 = 150 with remainder 5, so the answer is 25 remainder 5, or 25 R5.
  • A teacher splits 96 stickers among 8 students, dividing 96 ÷ 8 to find each student gets 12 stickers.

Decimals Examples

  • Dividing 7.5 ÷ 2.5: Move the decimal one place in both numbers to get 75 ÷ 25 = 3.
  • Dividing 9.36 ÷ 4: Divide step by step: 9 ÷ 4 = 2 remainder 1, bring down 3 to get 13 ÷ 4 = 3 remainder 1, bring down 6 to get 16 ÷ 4 = 4, giving 2.34.
  • A 6.4-kilometer trail is split into 4 equal sections, dividing 6.4 ÷ 4 to find each section is 1.6 kilometers.

Fractions Examples

  • Dividing 3/4 ÷ 1/2: Multiply by the reciprocal, 3/4 × 2/1 = 6/4, which simplifies to 3/2 or 1 1/2.
  • Dividing 2/5 ÷ 3/10: Multiply by the reciprocal, 2/5 × 10/3 = 20/15, which simplifies to 4/3 or 1 1/3.
  • A rope 3/4 meter long is cut into pieces of 1/8 meter each, dividing 3/4 ÷ 1/8 = 3/4 × 8/1 = 6 pieces.

Applications Examples

  • A pizza with 8 slices is shared among 3 friends, dividing 8 ÷ 3 to find each person gets 2 slices with 2 remaining.
  • A car uses 12.6 gallons of gas over 3 trips, dividing 12.6 ÷ 3 to find an average of 4.2 gallons per trip.
  • A factory produces 450 items in 9 hours, dividing 450 ÷ 9 to calculate a rate of 50 items per hour.