By using your calculator, or otherwise, compute the...

By using your calculator, or otherwise, compute the following:
a $(-343) \times 343$
b $(-343) \times(-343)$
c $(-729) \div 81$
d $\frac{(-729)}{81}$
e $(-666)-(-1945)$
f $(-2) \times(-5) \times(-7) \times(-10)$

Key Concepts

Subtraction and Addition of Negative Numbers

This concept deals with the arithmetic operations involving negative numbers. Subtracting a negative number is equivalent to adding its positive counterpart. Conversely, adding or subtracting negative numbers requires careful handling of the signs to arrive at the correct result. Mastery of these rules is crucial for simplifying expressions and solving problems that mix multiple arithmetic operations with negative integers.

Multiplication of Integers and Sign Rules

This concept involves multiplying integers and understanding how the signs (positive or negative) affect the result. When multiplying two numbers, if both numbers have the same sign (both positive or both negative), the product is positive. If the numbers have opposite signs, the product is negative. Additionally, when multiplying more than two numbers, the overall sign is determined by whether there is an even (resulting in a positive product) or odd (resulting in a negative product) number of negative factors.

Division of Integers and Sign Rules

Division of integers follows similar sign rules as multiplication. When dividing two numbers, if both the dividend and divisor have the same sign, the quotient is positive; if they have opposite signs, the quotient is negative. Understanding this rule is essential when handling problems that involve the division of negative numbers, ensuring that the proper sign is applied in the final result.

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