To solve the division of -86 by 9 and express it as a mixed number, follow these steps:
1. Perform the Division:
- Divide the absolute value of -86 by 9, which yields [tex]\( 86 \div 9 = 9 \text{ remainder } 5 \)[/tex].
2. Adjust the Quotient for Negativity:
- Since we are dividing a negative number by a positive number, the quotient should also be negative. So the initial quotient [tex]\( 9 \)[/tex] becomes [tex]\( -10 \)[/tex], because [tex]\( -10 \)[/tex] is the integer that, when multiplied by 9, comes closest to -86 without exceeding it.
3. Calculate the Correct Remainder:
- The remainder of this division should retain the positive value calculated for the absolute remainder minus any additional steps. Thus, the remainder remains 5. To have the proper fraction, we compensate [tex]\( -10 \)[/tex] by having [tex]\( -86 - (-90) = 4 \)[/tex].
4. Construct the Mixed Number:
- Combining the quotient and the remainder:
[tex]\( -10 \text{ remainder } 4 \)[/tex]
As a mixed number, this is [tex]\( -10 \frac{4}{9} \)[/tex].
However, this needs adjusting to proper choices available.
Reattempting: Perform the proper calculation,
[tex]\( -86 \div 9 = -10 \text{ remainder } 4 \)[/tex]
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The closest answer among options, The correct is:
Answer:
(b) \( -9\frac{5}{9} \)[/tex].
