Table of 312

Explanation

• Multiplication is an operation that involves combining a certain number (the multiplier) with another number (the multiplicand) a specified number of times. This can be thought of as repeated addition of the multiplicand, with the number of repetitions equal to the value of the multiplier. For example, 4 multiplied by 5 is the same as adding 4 five times, or expressing it as a sum: 4 + 4 + 4 + 4 + 4 = 20.

  This Story also Contains

  1. Explanation
  2. Facts
  3. Table Of 312
  4. Trick to learn
  5. Solved Examples

• When we multiply two numbers For example, 4\times 5=20

• When we perform multiplication, we use a specific symbol, such as "X", "*", or "." to represent the operation. The two numbers that we multiply together are referred to as the multiplier (the first number) and the multiplicand (the second number). When we multiply the two numbers, we get a new number called the product, which represents the total result of the multiplication. In the example given, the number 4 is the multiplier, 5 is the multiplicand, and 20 is the product.

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 still remains the same.

• Multiplication is distributive. ie 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 312

Addition form:

312 = 312

312 + 312 = 624

312 + 312 + 312 = 936

312 + 312 + 312 + 312 = 1248

312 + 312 + 312 +312 +312 = 1560

312 + 312 + 312 312 + 312 + 312 = 1872

312 + 312 + 312 + 312 + 312 + 312 + 312 = 2184

312 + 312 + 312 + 312 + 312 + 312 + 312 + 312 = 2496

312 + 312 + 312 + 312 + 312 + 312 + 312 + 312 + 312 = 2808

312 + 312 + 312 + 312 + 312 + 312 + 312 + 312 + 312 + 312 = 3120

Multiplication Form:

Trick to learn

For multiplication from 1 to 8 we write 3’s table on the left side (vertically). The second step is to write 12’s table on the right side (vertically). For 31X9 we do the same but we get an extra 1 which is added to 27 and forms 28.

Solved Examples

1. What do we get if we multiply 312, 60, and 45 by 1 ?

Solution: If we multiply any number by 1, we get the number itself. So, the answers are 312, 6,0, and 45.

2. If we have 1 eraser for $312, How much will 8 erasers cost?

Solution: The cost of a single eraser is $312.

So, for 8 erasers we have to multiply 312 X 8 =2496.

Therefore, 8 erasers cost $2496.

3. The shopkeeper sells single pencils at the cost of 312, how much do 5 pencils cost?

Solution: The cost of a single pencil is 312.

By tables, we can directly write the answer 1560.

Or, we can try the additive property. Adding 312 five times gives the same answer as above.

4. How do we find the cost of 50 phones, if 1 phone costs 50 rupees?

Solution: The cost of a single phone is 50 rupees.

To find 50 phones we multiply 50 by 50 which equals 2500.

Thus, we get an answer of 2500. If we use addition here, it becomes hectic.

So knowing tables makes it easier to calculate.

5. What will be the cost of 1,00,000 phones, if the price is $312 each?

Solution:

If we are talking about 10’s, 100’s and 1000’s or any such number. we write the number as it is and add the zeros preceded by 1. Hence, the cost will be 312 followed by five 0’s. Thus, the cost is 3,12,00,000.