1.5 Divide whole numbers  (Page 2/12)

Translate word phrases to math notation

Earlier in this section, we translated math notation for division into words. Now we’ll translate word phrases into math notation. Some of the words that indicate division are given in [link] .

Divide whole numbers in applications

We will use the same strategy we used in previous sections to solve applications. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We then translate the phrase into math notation and simplify it to get the answer. Finally, we write a sentence to answer the question.

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.