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Difficulty: EasyDivisibility Rules and Remainder Theorem

Evaluate the arithmetic expression 17−5×617 - 5 \times 6. What is the positive remainder when the result of this expression is divided by 88?

  1. A
    0
  2. 3Answer
  3. C
    5
  4. D
    7

Answer

The positive remainder is 3.
Following the correct order of operations, multiplication must be performed before subtraction. The expression becomes 17 - 30, which equals -13. To find the positive remainder when a negative number is divided by 8, we add the smallest multiple of 8 that is greater than 13 (which is 16) to the negative number. Thus, -13 + 16 = 3. The correct remainder is 3.

Step-by-Step Solution

1
Apply the correct order of operations to evaluate the multiplication first.
17−(5×6)=17−3017 - (5 \times 6) = 17 - 30
According to mathematical order of operations, multiplication takes precedence over subtraction.
2
Complete the subtraction to find the final integer value.
17−30=−1317 - 30 = -13
Subtracting a larger positive number from a smaller one results in a negative integer.
3
Determine the positive remainder when −13-13 is divided by 88.
−13=8×(−2)+3-13 = 8 \times (-2) + 3
To find a valid positive remainder for a negative number, add the divisor until the result is positive: −13+8=−5-13 + 8 = -5, and −5+8=3-5 + 8 = 3.

Key Concept

Order of Operations and Negative Remainders
Estimated Time:45s
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Topics

Divisibility Rules and Remainder Theorem

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