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Multiplication Notation

Would you count the pennies individually? Or would you count the number of pennies in each row and add that number 3 times. Multiplication is a way to represent repeated addition. So instead of adding 8 three times, we could write a multiplication expression.

By the end of this lesson and the next few, you should be able to:

  • Use multiplication notation
  • Model multiplication of whole numbers
  • Multiply whole numbers
  • Translate word phrases to math notation
  • Multiply whole numbers in applications

multiplication

Use Multiplication Notation

Suppose you were asked to count all these pennies shown the figure below.

An image of 3 horizontal rows of pennies, each row containing 8 pennies.

Would you count the pennies individually? Or would you count the number of pennies in each row and add that number \(3\) times.

\(8+8+8\)

Multiplication is a way to represent repeated addition. So instead of adding \(8\) three times, we could write a multiplication expression.

\(3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}8\)

We call each number being multiplied a factor and the result the product. We read \(3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}8\) as three times eight, and the result as the product of three and eight.

There are several symbols that represent multiplication. These include the symbol \(×\) as well as the dot, \(·\), and parentheses \(\left( \right ).\)

Operation Symbols for Multiplication:

To describe multiplication, we can use symbols and words.

Operation Notation Expression Read as Result
\(\text{Multiplication}\) \(×\)
\(·\)
\(\left( \right)\)		 \(3×8\)
\(3·8\)
\(3\left(8\right)\)		 \(\text{three times eight}\) \(\text{the product of 3 and 8}\)

Example

Translate from math notation to words:

  1. \(7\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}6\)
  2. \(12·14\)
  3. \(6\left(13\right)\)

Solution

  1. We read this as seven times six and the result is the product of seven and six.
  2. We read this as twelve times fourteen and the result is the product of twelve and fourteen.
  3. We read this as six times thirteen and the result is the product of six and thirteen.

Extra:

Translate from math notation to words:

  1. \(8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}7\)
  2. \(18·11\)

Solution

  1. eight times seven; the product of eight and seven
  2. eighteen times eleven; the product of eighteen and eleven

Extra:

Translate from math notation to words:

  1. \(\left(13\right)\left(7\right)\)
  2. \(5\left(16\right)\)

Solution

  1. thirteen times seven; the product of thirteen and seven
  2. five times sixteen; the product of five and sixteen

This lesson is part of:

Introducing Numbers

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