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## Division of Number Bases

This post will treat in detail what you need to know about** number bases**. A number base is a system of counting in which certain units make up a “bundle”. Evaluate 2115 base seven Divided by 12 base seven

Generally, counting is done in base ten. Base ten can also be called Decimal or Denary. It is pertinent to note that the highest digit of any number base is always one less than the base. For instance, a number in base y will have the highest digit y-1.

This article will focus on Division of number bases. Relax and follow the steps outlined below in order to evaluate division of a number in other bases to a number in base ten.

**Question 1**

Evaluate 2115 base seven divided 12 base seven

There are two methods of solving this problem, namely

- Long Division Method
- Conversion to base ten Method

I will take the methods simultaneously

**Long Division Method**

In this method, you are expected to have a little knowledge of long division but if you don’t, do not panic. Simple steps you need to follow in order to solve the above problem are vividly listed and explained hereunder:

- Get the multiples of 12 in base seven from 1 to 6
- carry out the long division using the multiples

**Step 1**

Multiples of 12 from 1 to 6

12×1 = 12

12×2 = 24

12×3 = 36

12×4 = 51

This is gotten by using the normal multiplication method 4×2 = 8, remember the multiplication is in base seven. Divide 8 by 7 you will get 7 remainder 1, that is to say, there is one seven in 8 remainder 1.

Write the remainder at the right-hand side and call the seven 1 and add it to 4×1 = 4+1 = 5 as shown below:

12 × 4 = 51

12×5 = 63

This is also gotten by carrying out normal multiplication. 5×2 = 10, there is one 7 in 10 remainder 3, write the remainder 3 and call the seven one and add to 5 × 1 = 5+1 = 6 yielding 12 × 5 = 63.

Follow the same step to get 12 × 6 = 105

**Step 2**

Carry out the long division using the multiples

21 divided by 12 = 1

12 × 1 = 12

21-12 = 6

This is gotten by carrying out the subtraction in base seven. set up 21 -12 in the form of tens and unit you use to do your normal subtraction.

Borrow 1 from 2 and call it 7 and add it to 1 which gives 8 and subtract the 2 from it to get 6.

Bring down 1 and place in front of 6 to get 61. Repeat the division steps as in above till you get to zero. Evaluate 2115 base seven divided by 12 base seven = 146 base seven. See the division below for a clear understanding.

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**Method 2** to Evaluate 2115 base seven Divided by 12 base seven

**Conversion to base ten**

Evaluate 2115 base seven Divided by 12 base seven

Convert both numbers to a number in base ten. Do your division in base ten and bring your quotient (answer gotten after division) back to base seven.

To get the power, subtract 1 from the total number of digits.

2115 base seven= 4 digits, power = 4 -1 = 3

2115 base seven = 2×7^3+1×7^2+1× 7^1 +5 × 7^0

= 2 × 243+1 × 49+1 × 7+5 × 1

= 686+49+7+5 = 747 base ten

12 base seven = 1× 7^1 +2× 7^0 = 7+2 = 9 base ten

Do the division in base ten to get 83 base ten. Then, convert 83 base ten to base seven to get 146 base seven. That’s it. If you have any question, feel free to use the comment box below.

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That is it on the division of number bases

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