1.4 Multiply whole numbers

If we want to know the size of a wall that needs to be painted or a floor that needs to be carpeted, we will need to find its area . The area is a measure of the amount of surface that is covered by the shape. Area is measured in square units. We often use square inches, square feet, square centimeters, or square miles to measure area. A square centimeter is a square that is one centimeter (cm.) on a side. A square inch is a square that is one inch on each side, and so on.

For a rectangular figure, the area is the product of the length and the width. [link] shows a rectangular rug with a length of $2$ feet and a width of $3$ feet. Each square is $1$ foot wide by $1$ foot long, or $1$ square foot. The rug is made of $6$ squares. The area of the rug is $6$ square feet.

Key concepts

• Multiplication Property of Zero
  • The product of any number and 0 is 0.
    $a\cdot 0=0$
    $0\cdot a=0$
• Identity Property of Multiplication
  • The product of any number and 1 is the number.
    $1\cdot a=a$
    $a\cdot 1=a$
• Commutative Property of Multiplication
  • Changing the order of the factors does not change their product.
    $a\cdot b=b\cdot a$
• Multiply two whole numbers to find the product.
  1. Write the numbers so each place value lines up vertically.
  2. Multiply the digits in each place value.
  3. Work from right to left, starting with the ones place in the bottom number.
  4. Multiply the bottom number by the ones digit in the top number, then by the tens digit, and so on.
  5. If a product in a place value is more than 9, carry to the next place value.
  6. Write the partial products, lining up the digits in the place values with the numbers above. Repeat for the tens place in the bottom number, the hundreds place, and so on.
  7. Insert a zero as a placeholder with each additional partial product.
  8. Add the partial products.