Mental Division Strategies - Orchids The International School
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Mental Math

Mental Division Strategies

Mental Math refers to a group of skills that allows students to do arithmetical calculations in their head without the use of calculators or other resources.
It helps the students to understand the basic and higher-level math concepts in a better way.
We can use the mental math in division, numbesr can be easily divided mentally using some tricks.

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Advantages of Mental Math:

  1. It helps students to understand the basic and higher-level math concepts in a better way.
  2. It helps students solve higher-level problems at a better speed.
  3. It has a lot of practical applications.
  4. It stimulates the brain and makes it sharper. It makes a student good with imagination, visualization, and creativity.

For division, we use four terms that are divisor, dividend, quotient and remainder.

Example:
If we divide 135 by 5, then we get 27 as quotient and 0 as reminder.

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Divisor smaller and closer to the power of 10

Step1: Identify how much short the divisor is to the power of 10.

Step2: Split the dividend into two parts – Quotient and Remainder. The number of digits considered as the remainder is the same as the number of digits in the divisor.

Step3:Multiply the first digit of the quotient with the number obtained from step 1. Add this to the tens digit of the quotient part (from step 2). Continue the same process for the digit at unit place for the remainder.

Step4:Multiply the number obtained from the step 3 with the number from step 1. Add this number to the Remainder part (from step 2).

Step5:Now, we check if the remainder is greater than or equal to the divisor. If yes, divide it again and add the new quotient part to the quotient (from step 2). The remainder obtained now is the final remainder.
Here, it is explained with an example.

Example 1: Divide 2341 by 9

Step1: 9 is 1 short of 10.

Step2: Split 2341 as 234(quotient) and 1 (remainder)

Step3:

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Step4:But here the remainder 10 is greater than 9
So, we subtract 9 from 10 and add the value with the quotient.

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So, the quotient is 260 and remainder is 1.

Division by 10, 100, 1000 …

While dividing any number with 10, 100, 1000, …, we can do it in two ways.

  1. If the number has zero or zeros in its right end, then we can cancel out the common zeros from the divisor and the dividend both.
  2. If the number has no zero or zeros in the right end, then we have to decimal point on the dividend. We have to move the decimal point starting from the right to the left as many places as there are zeros in the divisor.

Example :

Divide:
(i) 123400 ÷ 10     (ii) 56000 ÷ 1000     (iii) 97000 ÷ 100

Answer:

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Example :

Divide:
345635 ÷ 1000

Answer:

If we divide 345635 by 10000, then we find the remainder and quotient.
Here, we can write 345635 as 345635.00

Then,345635.00÷10000 =
345635.00 / 10000
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So, the quotient is 34 and remainder is 5635.

Division trick for numbers 25 and 125 in place of divisor

  • To divide a number by 25, we turn the number 25 in 100, then divide the number.
  • To divide a number by 125, we turn the number 125 in 1000, then divide.

Here, it is explained with some examples.

Example:

3466÷25=?

Answer:

Here we can write 3466÷25 as
3466 / 25

Now to make 25 as 100, we have to multiply the number by 4

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Thus, we get, 3466÷25=138.64

Example:

23565÷125=?

Answer:

Here we can write 23565÷125 as
23565 / 125

Now to make 125 as 1000, we need to multiply the number by 8.

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Division by using factor method

If both the dividend and divisor are large numbers, then we can express the numbers (dividend and divisor) as the product of their factors and then perform the division by cancelling out the common factors.

Example: Divide 2040 by 24.

Here we can write 2040÷24=
2040 / 24

Now,

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So, the final answer is 85.

Division trick for number 9

If the sum of digits of a number is divisible by 9, then the number itself is divisible by 9.

Example 1:

Let us check if the number 49689 is divisible by 9 or not.
We 1st take the sum of the digits of the given number
4 + 9 + 6 + 8 + 9 = 36
36 is divisible by 9, so the given number is divisible by 9.

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