Write the rules for determining the sign of the product when multiplying integers. Then, write the rules for determining the sign of the quotient when dividing integers. Use your own words and use complete sentences. Make sure you answer both questions presented in this problem.

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When multiplying integers, the sign of the product can be determined using the following rules:

1. If the two integers have the same sign (both positive or both negative), the product will be positive.
For example: (+4) multiplied by (+2) equals (+8), and (-5) multiplied by (-3) equals (+15).

2. If the two integers have different signs (one positive and one negative), the product will be negative.
For example: (-7) multiplied by (+5) equals (-35), and (+6) multiplied by (-2) equals (-12).

When dividing integers, the sign of the quotient can be determined using the following rules:

1. If the divisor (the number we divide by) and the dividend (the number we divide) have the same sign (both positive or both negative), the quotient will be positive.
For example: (+10) divided by (+2) equals (+5), and (-15) divided by (-3) equals (+5).

2. If the divisor and the dividend have different signs (one positive and one negative), the quotient will be negative.
For example: (-12) divided by (+3) equals (-4), and (+8) divided by (-2) equals (-4).

These rules can help determine the sign of the product when multiplying integers, as well as the sign of the quotient when dividing integers. Remember to consider the signs of the numbers involved to accurately determine the sign of the result.

To determine the sign of the product when multiplying integers, you can use the following rules:

1. If both numbers have the same sign (either positive or negative), the product will be positive.
2. If one number is positive and the other is negative, the product will be negative.

For example, if you multiply -3 and -4, both numbers are negative, so the product will be positive: -3 x -4 = 12. On the other hand, if you multiply 2 and -5, one number is positive and the other is negative, so the product will be negative: 2 x -5 = -10.

To determine the sign of the quotient when dividing integers, follow these rules:

1. If both numbers have the same sign, the quotient will be positive.
2. If one number is positive and the other is negative, the quotient will be negative.

For instance, if you divide -12 by -3, both numbers are negative, so the quotient will be positive: -12 ÷ -3 = 4. Conversely, if you divide 10 by -2, one number is positive and the other is negative, so the quotient will be negative: 10 ÷ -2 = -5.

Remember, it's essential to consider the signs of the numbers being multiplied or divided to determine the sign of the result accurately.

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