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# Multiplication Tables|Definition & Meaning

## Definition

A **multiplication table **represents the** multiplication **of two numbers in the form of a **table**. The first **row **and **column **both contain a sequence of numbers, indicating different choices for the first and second multiplicand, respectively. The **product **of any two numbers is the **entry **in the table where the respective multiplicands’ **row **and **column **meet.

A **table **that displays the results of multiplying two **integers **is a multiplication chart. It is **standard** to write one set of numbers in the left **column **and the other set in the top **row**. An array of **integers **in a rectangle shape is used to list the products. **Repeated addition **is known as **multiplication**.

## What Is Multiplication?

The most effective technique to explain **multiplication **is to use “**groups **of” rather than “**times.**” Multiplication is the process of **adding **sets of numbers together. Now suppose you have divided your students into 4 groups, and each group has 2 students. The total number of students would be:

Since there are s 4 groups of 2. So 2 times 4 make:

2 x 4 = 8

or

4 + 4 = 8

It is simpler to **multiply **groups of integers than to **add **them all together.

## How To Use a Multiplication Table?

First, take a glance at the **rows **and **columns **in the following illustration that are shaded in grey.

Although columns are viewed **vertically **from top to bottom, rows are interpreted **horizontally **from left to right. On the diagram, the **squares **of the numbers, such as 1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, etc., are represented by the green **diagonal**.

To comprehend how to analyze the **multiplication **chart, use the green diagonal. The value on the green diagonal is the **product **of the values in the grey-aligned **columns **and **rows**. For instance, the result of 4 and 4 is 16. 15 is obtained by multiplying 3 by 5, 5 by 3, etc.

To utilize the **multiplication** chart, select the two numbers you wish to **multiply** from the grey row and column, and then calculate the **point** at where an imaginary **horizontal** and **vertical** line—drawn from the grey **column** and **row**, respectively—would cross to yield the **product** of the two values.

## Analyzing a Multiplication Table

The following steps are required to analyze a multiplication table:

- The first step entails picking the
**top row’s**second number and the first number from the leftmost**column’s**list of numbers. - The second step involves moving the
**first**number down a**column**and the**second**number along a**row**. The result is found in the cell in which the two numbers**intersect**. - For instance,
**5**is along the row while**6**is in the column. Hence,**5 × 6 = 30**.

## Understanding Multiplication Table

There are **two **sections to a multiplication chart: the **lower **times table and the **higher **times table.

Because they have a pattern, the **multiplication **tables for 1, 2, 5, and 10 are simpler to memorize.

- The number itself is the
**product**of any**numbe**r and**1**. For example, 3 multiplied by 1 will still be 3. - Any
**integer**is**doubled**when it is**multiplied**by**2**. For instance, 4, when multiplied by 2 gets doubled, i.e., 8. - In the
**multiplication**table for**five**, the ones digit shift between 0 and 5. - The fact that
**zero**is always the digit in the ones spot makes it simple to memorize the table of**10**.

**Lower **time tables refer to those areas of the **multiplication **chart that are simple to remember. The **upper **time table refers to the remaining portion of the table.

The **upper **time table can also be memorized through exercise and repetitive **addition**.

The fact that the **product **is unaffected by the **sequence **in which any two numbers are multiplied is a crucial aspect of **multiplication**.

In a **multiplication **table, you may therefore obtain the same value for any **product **with the statement’s numbers reversed.

There are several **blocks **that are identical but in a transposed way.

## Memorizing the Multiplication Table

When learning **multiplication **for the first time, memorizing 100 facts could seem like a lot of information to retain, but by making use of specific multiplication **properties**, the quantity of information that must be retained can be minimized.

### Using Commutative Property To Memorize Multiplication Table

The order of **multiplication **is irrelevant, according to the **commutative **property of multiplication. Two numbers, a and b, are given. According to the **commutative **property of multiplication:

a x b = b x a

This is supported by the **multiplication **chart, which shows that the answer is always 15 whether we use the **multiplication** facts 3 x 5 = 15 or 5 x 3 = 15. For anything being multiplied, this is true. We only truly need to memorize the numbers below or above (and including) the **diagonal** line displayed in green on the chart because the sequence doesn’t matter. The number of **multiplication **facts we need to remember is practically reduced by half as a result of this property.

### Using Identity Property To Memorize Multiplication Table

According to the **identical **property of multiplication, any number a multiplied by 1 equals a:

1 × a = a

Since 1 multiplied by any number equals that number, it is not required to remember the **first row** or **column **of the multiplication table as long as we are aware of this **property**.

## Examples Using the Multiplication Table

### Example 1

Check the **multiplication** table to see if the results of 7 x 3 and 3 x 7 are the same.

### Solution

In order to determine **3 x 7**, first find the **row **containing all **multiples** of 3. Next, locate the **column **that has multiples of **7**. You can find out the value of the **product **of **3** and **7** is **21,** which is in the **cell** where they overlap.

Find the **row** containing all the multiples of **7** before attempting to find **7 x 3**. Next, look for the **column **that has multiples of **3**. You can determine the product of **7 **and **3 **to get **21 **by looking at the **cell **where they intersect.

Consequently, the results of **3 x 7 **and **7 x 3 **are the same.

### Example 2

How do you use a **multiplication **table to find 4 multiplied by 2?

### Solution

We must locate the **row **that displays the **4 **time tables and the **column **which displays the table of **2 **in order to determine **4 x 2**. The next step is to locate the region where they cross. They cross over at **8**.

Therefore, we can conclude by making use of the **multiplication **table that **4 x 2 = 8.**

*All images/mathematical drawings were created using GeoGebra.*