Table of 31

Introduction

Multiplication is a crucial aspect of the four foundational mathematical operations taught in the early stages of education. It is believed that what is learned during these formative years remains ingrained for a lifetime. By studying multiplication tables, students gain an understanding of the multiples of specific numbers and can perform rapid, accurate calculations in everyday life.

Not only does this improve mental agility and computational speed, but it also aids in grasping complex mathematical concepts. The history of multiplication tables dates back to ancient Babylon, where they were first used as early as 2500 B.C. This rich legacy highlights the significance of mastering multiplication and its continued relevance in shaping future mathematicians.

Explanation

• Multiplication is a fundamental mathematical concept that is widely used in everyday life. The technique of repeated addition is one of the simplest ways to understand multiplication. For instance, 4 multiplied by 5 can be represented as 4 added to itself 5 times, which results in the product 20.

• The symbol used to denote multiplication is "x", "*", or ".". The first number in a multiplication equation is known as the "multiplier", and the second number is referred to as the "multiplicand". The result of multiplying two numbers is called the "product". In the example, 4 is the multiplier, 5 is the multiplicand, and 20 is the product.

• Learning multiplication tables at an early stage of education is crucial for building a strong foundation in mathematics. The ability to multiply numbers quickly and accurately can save time and increase efficiency in various real-life situations. The ancient Babylonians were the first known civilization to use multiplication tables and their use can be traced back to around 2500 B.C.

Facts

• When we multiply any number by zero, the answer will always be zero.

6\times 0 = 0

• When any number is multiplied by 1, we get the number itself.

6\times 1 = 6

• The order of multiplier and multiplicand doesn't matter. This shows multiplication is associative.

6\times 1 = 6 \\1\times 6 = 6

• It is also Commutative.If there are three or more integers and we rotate the numbers, the product remains the same.

• Multiplication is distributive. If there are three integers A, B and C then

Ax(B+C)= AxB+AxC.

• The obtained products are the divisibles of a given number. For example, 6 and 9 are divisible by 3.

Table Of 31

Addition form:

31 = 31

31 + 31 = 62

31 + 31 + 31 = 93

31 + 31 + 31 + 31 = 124

31 + 31 + 31 + 31 + 31 = 155

31 + 31 + 31 + 31 + 31 + 31 = 186

31 + 31 + 31 + 31 + 31 + 31 + 31 = 217

31 + 31 + 31 + 31 + 31 + 31 + 31 + 31 = 248

31 + 31 + 31 + 31 + 31 + 31 + 31 + 31 + 31 = 279

31 + 31 + 31 + 31 + 31 + 31 + 31 + 31 + 31 + 31 = 310

Multiplication Form:

Trick To Learn

Almost every children remembers 3’s table, So we write 3’s table up to multiplicand 9 (vertically). Further, we write From 1 to 9 vertically on the right side (vertically). Thus, we get the required table.

Solved Examples

1. What do we get if we multiply 31 by 4 ?

Solution:

There are two ways to find solutions . First, if we know tables we can directly write answers . Second is repetitive addition.

31\times4=124\\31+31+31+31=124

2. If we have 1 lipstick for $31, How much will 8 lipsticks cost?

Solution:

The cost of a single lipstick is $31.

So, for 8 lipsticks we have to multiply 31 X 8 =248.

Therefore, 8 lipsticks cost $248.

3. The shopkeeper sells a single bag for $31, What will be the cost of 6 bags?

Solution:

The cost of a single bag is $31, we can triple the 31 we get 93. This will be the cost of three bags. For calculating six bags we will double again. Now, we get 93 +93. So, the cost of six bags is 186.

4. How do we find the cost of 30 chocolates, if we get them for free?

Solution:

We didn't pay anything for a single chocolate. As we already know, any number multiplied by 0 is 0. The cost of chocolates will also be zero.

5. What will be the cost of 100 threads, if the price is $31 each?

Solution:

If we are talking about 10’s, 100’s and 1000’s we write the number as it is and add the zeros preceded by 1. Hence, the cost will be 31 followed by 0. Thus, the cost is 3100.