1. What is the product of (-6)^2?
C. 36***
2. Simplify the expression -84 ÷ 14.
A. -6***
3. Simplify the expression -8(12)
A. -96***
4. Find the quotient. 20 ÷ 1/4
D. 80***
5. You are given a problem in which positive and negative numbers are multiplied and then divided by a positive number.
D. A negative number would be most reasonable because a positive time a negative will wield a negative. Dividing that by a positive will result in a negative.
To solve these math problems:
1. To find the product of (-6)^2, you need to square the number -6. Squaring means multiplying a number by itself. So, (-6)^2 is (-6) x (-6), which equals 36. Therefore, the correct answer is C. 36.
2. To simplify the expression -84 ÷ 14, you need to divide -84 by 14. Division is the process of sharing or distributing a number into equal parts. So, -84 ÷ 14 is -6. Therefore, the correct answer is A. -6.
3. To simplify the expression -8(12), you need to multiply -8 by 12. Multiplication is the process of repeated addition. So, -8(12) is -8 x 12, which equals -96. Therefore, the correct answer is A. -96.
4. To find the quotient of 20 ÷ 1/4, you need to divide 20 by 1/4. When dividing by a fraction, you can invert the divisor and multiply. So, 20 ÷ 1/4 is the same as 20 x 4/1, which equals 80. Therefore, the correct answer is D. 80.
5. When multiplying positive and negative numbers together and then dividing by a positive number, the result depends on the number of negative factors involved. In this case, since there is at least one negative number being multiplied, the product will be negative. Dividing a negative number by a positive number will result in a negative answer. So, the correct answer is D. A negative number would be most reasonable because a positive times a negative will yield a negative. Dividing that by a positive will result in a negative.