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base 5,3,
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base 5,3,

by susan
(jackson,ohio)








































how do you subtract in base five?

Remember that base five is a system which is similar to the system we use for base 10:

For example, using base 5:

375(five) = 3*5³ + 0*5² + 0*5¹ + 0*5⁰

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Oct 01, 2010
Arithmetic Using Base 5
by: Staff

The question:

by Susan
(Jackson, Ohio)

How do you subtract in base five?

The answer:

Rather than begin with subtraction, I’m going to show you how to add numbers in base 5 because I think it will be easier to follow.

To subtract, just replace the + sign with a – sign.


Let’s start out with what you already know about numbers:

We generally use the number base 10.

This is convenient. Humans have exactly 10 fingers to count with.

That is where the expanded form of a number becomes useful.

How to write the expanded form of a number is routinely taught in grade school and middle school.

For example, you probably have been asked to complete this type of exercise many times in the past:

Write the number 375 in expanded form.

The answer is: 300 + 70 + 5

This is usually explained to students as:

300 means 3 times 100
70 means 7 times 10
5 means 5 times 1

But . . . the real point is, each of these numbers in the expanded format is a POWER OF 10 :

300 = 3 * 100 = 3*10^2
70 = 7 * 10 = 7*10^1
5 = 5 * 1 = 5*10^0 (remember that 10^0 = 1)

The expanded form can be written as:

375 = 300 + 70 + 5
375 = 3*10^2 + 7*10^1 + 5*10^0

How do you add two numbers in BASE 10? (I am going to apply the same idea to base 5 in a moment)

What is 375 + 110 ?

Using the expanded forms

1st number = 375(ten) = 300 + 70 + 5
375(ten) = 3*10^2 + 7*10^1 + 5*10^0

2nd number = 110(ten) = 100 + 10 + 0
110(ten) = 1*10^2 + 1*10^1 + 0*10^0

Now, combine every number with the same power of 10

375 + 110 = (300 + 70 + 5) + (100 + 10 + 0)

375 + 110 = (3*10^2 + 7*10^1 + 5*10^0) + (1*10^2 + 1*10^1 + 0*10^0)

375 + 110 = (3*10^2 + 1*10^2 ) + (7*10^1 + 1*10^1) + (5*10^0 + 0*10^0)

375 + 110 = 4*10^2 + 8*10^1 + 5*10^0 = 485

The final answer is (in the number base 10):

375 + 110 = 4*10^2 + 8*10^1 + 5*10^0 = 485

If we switch our number base to 5 instead of 10, we can apply the same idea. The only difference will be, EVERY DIGIT WILL BE A POWER OF 5.

1st number = 375(five) = 3*5^3 + 0*5^2 + 0*5^1 + 0*5^0
2nd number = 110(five) = 4*5^2 + 2*5^1 + 0*5^0


375(five) + 110(five) = (3*5^3 + 0*5^2 + 0*5^1 + 0*5^0) + (4*5^2 + 2*5^1 + 0*5^0)
375(five) + 110(five) = 3*5^3 + 4*5^2 + 2*5^1 + 0*5^0

375(five) + 110(five) = 3420

The final answer is

375(five) + 110(five) = 3420


As a practical matter, we use a shorthand method:

375 + 110 =

.……375
……+110
…------
.……485

If the base is 5

1st number = 375(five) = 3*5^3 + 0*5^2 + 0*5^1 + 0*5^0
2nd number = 110(five) = 4*5^2 + 2*5^1 + 0*5^0

1st number = 375(five) = 3000
2nd number = 110(five) = 420

……3000
……+420
……------
……3420

The final answer is

375(five) + 110(five) = 3420

One last thought.

You can check your answers (converting from base 10 to base 5) by going to the following web site:

http://www.unitconversion.org/numbers/base-5-to-base-10-conversion.html


Thanks for writing.


Staff
www.solving-math-problems.com


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