Multiplication

Multiplication is a basic arithmetic operation that involves repeated addition of the same number. It is represented using the symbol "x" or "•". When you multiply two numbers, you are finding the total of adding one number to itself the other number of times.

Understanding Multiplication

Here's an example to help you understand multiplication: If you have 3 groups of 4 apples, you can find the total number of apples by adding 4 + 4 + 4, or by multiplying 3 by 4 (3 x 4 = 12). So, 3 groups of 4 is the same as 3 times 4, which equals 12.

Basic Multiplication Terms

Here are some key terms to understand when learning about multiplication:

Multiplicand: The number to be multiplied.
Multiplier: The number by which the multiplicand is multiplied.
Product: The result of multiplying two or more numbers.

Multiplication Properties

There are several important properties of multiplication:

Commutative Property: The order of the numbers does not change the result. For example, 2 x 3 is the same as 3 x 2.
Associative Property: The grouping of the numbers does not change the result. For example, (2 x 3) x 4 is the same as 2 x (3 x 4).
Identity Property: Any number multiplied by 1 is the number itself. For example, 5 x 1 = 5.
Zero Property: Any number multiplied by 0 is 0. For example, 6 x 0 = 0.

Multiplication Tables

Memorizing multiplication tables can help you quickly solve multiplication problems. Here is a basic multiplication table:

x	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100

Multiplying Larger Numbers

When multiplying larger numbers, use the long multiplication method to find the product. Here's an example:

Find the product of 23 and 15:

    23
x   15
------
   115  (23 x 5)
+ 345  (23 x 10, shifted one place to the left)
------
  345  (Partial products added together to get the final product)

Practice Questions

Here are some practice questions to test your multiplication skills:

What is the product of 8 and 7? (Answer: 56)
Find the value of 5 multiplied by 6. (Answer: 30)
Calculate the product of 9 and 4. (Answer: 36)

Remember to practice regularly to improve your multiplication skills!

◂Math Worksheets and Study Guides Sixth Grade. Commutative/Associative Properties

Study Guide

Commutative/Associative Properties

Worksheet/Answer key

Commutative/Associative Properties

Worksheet/Answer key

Commutative/Associative Properties

Worksheet/Answer key

Commutative/Associative Properties

Worksheet/Answer key

Commutative/Associative Properties

The resources above cover the following skills:

Number and Operations (NCTM)

Understand meanings of operations and how they relate to one another.

Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.

Connections to the Grade 6 Focal Points (NCTM)

Algebra: Students use the commutative, associative, and distributive properties to show that two expressions are equivalent. They also illustrate properties of operations by showing that two expressions are equivalent in a given context (e.g., determining the area in two different ways for a rectangle whose dimensions are x + 3 by 5). Sequences, including those that arise in the context of finding possible rules for patterns of figures or stacks of objects, provide opportunities for students to develop formulas.