I would like to add the following fractions represented in base-8 as both fractions and decimals: (2/3)8+(5/7)8 Please somebody explain to me how to do this problem? Thanks!

badlife18va

badlife18va

Open question

2022-08-17

Adding fractions in base- 8 as fractions and decimals.
( 2 3 ) 8 + ( 5 7 ) 8
Please somebody explain to me how to do this problem? Thanks!

Answer & Explanation

Addison Herman

Addison Herman

Beginner2022-08-18Added 15 answers

Properties of fractions do not change when it comes to the base:
So if you have
2 8 3 8 + 5 8 7 8
Use the properties you already know. Get common denominators and add!
2 8 3 8 + 5 8 7 8 = 2 8 7 8 3 8 7 8 + 5 8 3 8 7 8 3 8 = 16 8 25 8 + 17 8 25 8 = 35 8 25 8 = 29 10 21 10
For decimals it is the same. Let's take 29 10 = 1.380952381 10 ... Using the recursive multiplication base method for decimals, first notice that 1.380952381 > 1. Mark that down, and subtract 1. Our number now is
1 8 + 0.380952381 10
Multiply .380952381 by our base, or 8. We get: 8 0.380952381 = 3.04739048 Notice that 3.04739048 > 1. Mark that down, and subtract 3. Our number now is
1.3 8 + 0.04739048 10
Multiply 0.04739048 by our base, or 8. We get: 8 0.04739048 = 0.37912384 Notice that 0.37912384 < 1. Mark that down. Our number now is
1.30 8 + 0.37912384 10
Keep repeating this on and on to your heart's content or until you reach a certian level of accuracy. After 7 iterations I got
35 8 25 8 = 1.30302071 8

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