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 69/35)
Detailed Explanation:
Problem 3: -27.5 / 0.25
The final answer is -110.
To solve this division problem, we first determine the sign of the answer. A negative number divided by a positive number will always result in a negative number.
Next, we can solve the calculation 27.5 / 0.25. One of the simplest methods is to recognize that the decimal 0.25 is equivalent to the fraction 1/4. Dividing a number by 1/4 is the same as multiplying that number by 4. Therefore, the problem can be rewritten as 27.5 multiplied by 4.
27.5 * 4 = 110.
Combining this with our sign rule, the final answer is -110.
Alternatively, we can solve this by eliminating the decimals. To turn the divisor 0.25 into a whole number, we multiply it by 100, which gives us 25. To keep the equation balanced, we must also multiply the dividend, -27.5, by 100. This gives us -2750. The new problem is -2750 / 25, which equals -110.
Problem 4: -4 3/5 / -2 1/3
The final answer is 1 34/35.
First, let’s address the signs. When a negative number is divided by another negative number, the result is always positive. So, our final answer will be positive.
To divide mixed numbers, we must first convert them into improper fractions.
For 4 3/5, we multiply the whole number by the denominator and add the numerator: (4 * 5) + 3 = 23. The improper fraction is 23/5.
For 2 1/3, we do the same: (2 * 3) + 1 = 7. The improper fraction is 7/3.
The problem is now (23/5) / (7/3).
To divide fractions, we multiply the first fraction by the reciprocal of the second. This means we flip the second fraction upside down. The calculation becomes:
(23/5) * (3/7)
Now, we multiply the numerators together and the denominators together:
Numerator: 23 * 3 = 69
Denominator: 5 * 7 = 35
The result is the improper fraction 69/35. To express this as a mixed number, we divide 69 by 35. It goes in 1 time with a remainder of 34 (since 69 – 35 = 34). The final mixed number is 1 34/35.
