Multiplication

Multiplication is "the process or skill of multiplying" and "the process of combining matrices, vectors, or other quantities under specific rules to obtain their product." To multiply, you "obtain from (a number) another that contains the first number a specified number of times."

— Oxford Languages & Dictionary

Quick Overview of Multiplication:

There are four parts of multiplication: the factors, the multiplication symbol, the equal sign, and the product

Example problem/equation: $32 * 11 = 352$

Terminology:

• Factors - these are the two numbers being multiplied together. These two numbers make up the left-hand side (LHS) of the equation. In the problem above, the factors are 32 and 11

• Multiplication symbol ( $*$or $✕$ ) - this is how you know what operation the problem is. If the problem has one of those symbols, then you need to multiply. In the problem above, the 32 and 11 have the $*$symbol, so they're to be multiplied

• Equal Sign - the symbol (=) in the middle of the equation. This symbol sets the left-hand side (LHS) EQUAL to the right-hand side (RHS)

• Product - this is the number on the far right-hand side (RHS) of the equation. This is the result, or equals, the two factors being multiplied together. In the problem above, the product is 352

Properties of Multiplication:

• Commutative Property of Multiplication - this property states; it does not matter what order the factors are multiplied in. For instance, $3 * 5 = 15$and $5 * 3 = 15$. As we can see here, the order in which they're multiplied does not matter

• Distributive Property of Multiplication - this property states; if there is a number being multiplied by a statement in parentheses, $2(5 + 3)$or $2 * (5 + 3)$, then it is equal to $(2 * 5) + (2 * 3)$. Either way, they all equal 16

• Associative Property of Multiplication - this property states; switching the order that you multiply the numbers in won't have an effect on the final result. For instance, $2 * (5 * 6)$ is the same as $(2 * 5) * 6$, they both equal $60$

• Identity Property of Multiplication - this property states; multiplying any number by 1, will result in the same number that you started with. For instance, $2 * 1 = 2$just like $10,000 * 1 = 10,000$

• Zero Property of Multiplication - this property states; multiplying any number by 0, will result in 0. For instance, $2 * 0 = 0$and $10,000 * 0 = 0$

Application of Multiplication:

• Normally, multiplication is a substitute for addition, which means that instead of doing long addition problems, you can use multiplication to do it faster! For example, the distance of 6 tables, if each table is 3 feet long? Instead of doing, $3 + 3 + 3 + 3 + 3 + 3$, you can just do the easier way, which is $3 * 6$

• Multiplication can be used to quickly calculate distances, prices, weights, and many things you would need to know in real-life!

• For example, Sara needs to bring 10 bags of candy to school tomorrow, but her backpack can oly hold 10 pounds. If each bag of candy weighs 2 pounds, can she bring all of the 10 bags to school together the next day?

Complex Multiplication:

• Complex multiplication can mean many different things! It can mean decimal or fractional multiplication, multiplication involving larger numbers, and/or word problems

• Luckily, the concept of multiplication will never change even while doing complex problems. So, if you're able to get good fundamentals, you can do any multiplication problem!

• Some example problems are:

  • $1/2 * 3/8$

  • $0.54 * 1.62$

  • And many more you will see later on!

Links to resources, videos, and worksheets:

• The Story Of Mathematics (Website)

• Math Is Fun (Website)

• Math Is Fun (Worksheets)

Multiplication Tables up to 10!

Lesson Complete!