Divide 578 by -17. A) -24 B) -34 C) 27 D) 42
The correct answer and explanation is:
Let’s start with the division:
578 ÷ (-17)
First, divide 578 by 17 (ignoring the negative sign):
578 ÷ 17 = ?
To do this, we can perform long division or use multiplication to find the quotient:
- 17 × 30 = 510
- 17 × 33 = 561
- 17 × 34 = 578
So, 17 × 34 = 578 exactly.
Since the divisor is negative, the quotient will be negative:
578 ÷ (-17) = -34
Correct answer: B) -34
Explanation (around 300 words):
Division is one of the four basic arithmetic operations, which involves splitting a number (the dividend) into equal parts based on another number (the divisor). When dividing a positive number by a negative number, the result is always negative because the signs differ.
In this problem, we divide 578 by -17. To simplify, first ignore the sign and divide the absolute values:
- Divide 578 by 17. You can check multiples of 17 to find the exact quotient:
- 17 × 30 = 510, which is less than 578.
- 17 × 33 = 561, closer but still less than 578.
- 17 × 34 = 578, exactly the dividend.
So, 578 divided by 17 equals 34 exactly, with no remainder.
Next, consider the sign of the divisor:
- Dividend (578) is positive.
- Divisor (-17) is negative.
The rule for signs in division (and multiplication) is:
- Positive ÷ Positive = Positive
- Negative ÷ Negative = Positive
- Positive ÷ Negative = Negative
- Negative ÷ Positive = Negative
Since a positive number divided by a negative number is negative, the quotient must be negative.
Therefore:
578 ÷ (-17) = -34
Among the options given:
- A) -24 (incorrect)
- B) -34 (correct)
- C) 27 (incorrect)
- D) 42 (incorrect)
The correct answer is B) -34.
Understanding this problem reinforces both the arithmetic process of division and the rules governing the signs of numbers when multiplied or divided. This is fundamental in algebra and helps build confidence in working with positive and negative numbers across many areas of math.