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

Scaling Up: Multiplication

Multiplication is the operation of repeated addition, used to find the total when combining equal groups. It covers multiplying whole numbers, decimals, and fractions, building fluency with facts, multi-digit algorithms, and mental math strategies that are essential for more advanced mathematics and real-world problem solving.

Components of Multiplication

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

  • Whole Numbers: Multiplying integers using the standard algorithm, focusing on place value and partial products.
  • Decimals: Multiplying numbers with decimal points, then placing the decimal in the product correctly.
  • Fractions: Multiplying numerators together and denominators together, simplifying when possible.
  • Applications of Multiplication: Practical uses such as calculating areas, total costs, and scaling recipes.

Examples of Multiplication

Whole Numbers Examples

  • Multiplying 12 Γ— 7: Break it into 10 Γ— 7 = 70 and 2 Γ— 7 = 14, then add 70 + 14 to get 84.
  • Multiplying 23 Γ— 15: Calculate 23 Γ— 5 = 115 and 23 Γ— 10 = 230, then add 115 + 230 to get 345.
  • A teacher orders 8 packs of 24 pencils, multiplying 8 Γ— 24 to find a total of 192 pencils.

Decimals Examples

  • Multiplying 2.5 Γ— 4: Multiply 25 Γ— 4 = 100, then place the decimal one position from the right, giving 10.0.
  • Multiplying 1.2 Γ— 3.5: Multiply 12 Γ— 35 = 420, then place the decimal two positions from the right, giving 4.20.
  • A fabric store sells ribbon at 3.75 dollars per meter, and a customer buys 2 meters, multiplying 3.75 Γ— 2 to get 7.50 dollars.

Fractions Examples

  • Multiplying 2/3 Γ— 3/4: Multiply numerators 2 Γ— 3 = 6, denominators 3 Γ— 4 = 12, giving 6/12, which simplifies to 1/2.
  • Multiplying 5 Γ— 1/3: Rewrite 5 as 5/1, then multiply 5 Γ— 1 = 5 and 1 Γ— 3 = 3, giving 5/3 or 1 2/3.
  • A recipe calls for 3/4 cup of sugar but you want to make half the recipe, multiplying 3/4 Γ— 1/2 to get 3/8 cup.

Applications Examples

  • A rectangular garden is 6 meters by 4.5 meters, multiplying 6 Γ— 4.5 to find an area of 27 square meters.
  • A store sells 15 shirts at 12 dollars each, multiplying 15 Γ— 12 to find total revenue of 180 dollars.
  • A car travels at 55 miles per hour for 3 hours, multiplying 55 Γ— 3 to calculate a distance of 165 miles.