The Correct Answer and Explanation is:
Of course. Here are the correct answers and a detailed explanation for each problem.
Correct Answers:
3. -110
4. 1 34/35 (or as an improper fraction, 69/35)
Explanation of Problem 3: -27.5 / 0.25
The goal is to divide a negative decimal by a positive decimal. The first rule to remember is that a negative number divided by a positive number will always result in a negative answer.
To make the division easier, we can eliminate the decimal in the divisor (0.25). We do this by multiplying both numbers by a power of 10 that turns 0.25 into a whole number. Since 0.25 has two decimal places, we multiply both parts of the problem by 100.
-27.5 * 100 = -2750
0.25 * 100 = 25
The problem is now transformed into a simpler one: -2750 / 25.
We can solve this using division. We know that 100 divided by 25 is 4. Therefore, 2700 divided by 25 would be (27 * 4), which is 108. With 50 remaining (2750 – 2700), we divide 50 by 25, which gives us 2. Adding these results, 108 + 2 = 110. Since our original problem involved a negative number, the final answer is -110.
Explanation of Problem 4: -4 3/5 / -2 1/3
This problem involves dividing two negative mixed numbers. The first rule here is that a negative number divided by another negative number results in a positive answer. So, we know our final result will be positive.
To divide mixed numbers, you must first convert them into improper fractions.
- Convert -4 3/5: Multiply the whole number (4) by the denominator (5) and add the numerator (3). This gives 20 + 3 = 23. Keep the same denominator. So, -4 3/5 becomes -23/5.
- Convert -2 1/3: Multiply the whole number (2) by the denominator (3) and add the numerator (1). This gives 6 + 1 = 7. Keep the same denominator. So, -2 1/3 becomes -7/3.
Our new problem is (-23/5) / (-7/3).
To divide fractions, we multiply the first fraction by the reciprocal (the flipped version) of the second fraction.
(-23/5) * (-3/7)
Now, multiply the numerators together and the denominators together.
Numerators: -23 * -3 = 69 (a negative times a negative is a positive).
Denominators: 5 * 7 = 35.
The result is the improper fraction 69/35. To convert this back to a mixed number, divide 69 by 35. It goes in 1 time with a remainder of 34 (69 – 35 = 34). Thus, the answer is 1 34/35.
