**Larger Numbers**

The law of large numbers is a principle of probability according to which the frequencies of events with the same likelihood of occurrence even out, given enough trials or instances. As the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.Watch Larger Numbers to learn more.

**Addition of Large Numbers**

To add large numbers, list them in columns and then add only those digits that have the same place value.

Example 2

Find the sum of 5897, 78, 726 and 8569.

Solution:

###### Note:

- Write the numbers in columns with the thousands, hundreds, tens and units lined up.
- 7 + 8 + 6 + 9 = 30. Thus, the sum of the digits in the units column is 30. So, we place 0 in the units place and carry 3 to the tens place.
- The sum of the digits in the tens column after adding 3 is 27. So, we place 7 in the tens place and carry 2 to the hundreds place.
- The sum of the digits in the hundreds column after adding 2 is 22. So, we place 2 in the hundreds place and carry 2 to the thousdands place.

### Subtraction of Large Numbers

To subtract large numbers, list them in columns and then subtract only those digits that have the same place value.

#### Example

Find the difference between 7064 and 489.

##### Solution:

Note:

- Use the
**equals addition method**or the**decomposition method**. - Line up the thousands, hundreds, tens and units place values for the two numbers when placing the smaller number below the larger number as shown above.

**Multiplication of larger numbers**

#### Example

Calculate 765 × 9.

##### Solution:

Write the smaller number, 9, under the larger number, 765, and then calculate the multiplication.

###### Note:

- 9 × 5 = 45. So, place 5 units in the units column and carry the 4 (i.e. four tens) to the tens column.
- Calculate 9 × 6 and then add 4 to give 58 (i.e. 58 tens). Then place 8 in the tens column and carry 5 to the hundreds column.
- Finally multiply 7 by 9 and add 5 to give 68 (i.e. 68 hundreds).

Division of larger numbers

#### Example

##### Solution:

###### Note:

- As division is the inverse of multiplication, start by dividing 4 into the column furthest to the left.
- 6 ÷ 4 = 1 and 2 is the remainder.
- Clearly, the remainder 2 is 200 (i.e. 20 tens); and we can carry this into the tens column to make 29.
- Now, 29 ÷ 4 = 7 with a remainder of 1. Clearly, the remainder of 1 is 10 (i.e. 10 units) and we carry this into the units column to make 12.
- Finally, 12 ÷ 4 = 3.

**Larger Numbers **

Useful for CBSE, ICSE, NCERT & International Students

Grade : 6

Subject : Maths

Lesson : Numbers and Numbers

Topic: Larger Numbers

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