91Ó°ÊÓ

When dealing with negative numbers, it's essential to understand how they interact with each other and with positive numbers during multiplication. A negative number is any number less than zero. Negative numbers are usually represented with a minus sign (-). A key rule to remember when multiplying is:

• A negative number times a positive number gives a negative product.
• If both numbers are negative, the product is positive.

This is important because the sign of the product is entirely determined by the signs of the numbers being multiplied, not the numbers' sizes.

Product calculation involves multiplying two numbers to get a result called the product. In our exercise, we're finding the product of -56 and 43. The important part of this calculation is to first multiply the absolute values, the numbers without considering their signs. This helps simplify the process, as you can focus purely on the multiplication aspect first without worrying about the signs until later. For instance, multiplying the absolute values 56 and 43 gives us the intermediate product before addressing the negative sign.

The column method is a traditional way of performing multiplication, useful especially for larger numbers. It involves writing the numbers in columns according to their place values and solving the multiplication bit by bit starting with the smallest value.

• Align the numbers by their rightmost digit.
• Multiply each digit of the bottom number by each digit of the top number.
• Write each resulting product beneath the line, shifted according to its place value.
• Add all these products to get the final result.

This method can be applied systematically to ensure that no crucial step is missed during calculation.

Absolute value refers to the magnitude of a number regardless of its sign, essentially how far a number is from zero on a number line. This concept is pivotal during multiplication involving negatives. It allows us to temporarily set aside the sign and deal solely with the size of the numbers. For instance, the absolute value of -56 is 56, and for 43 it remains 43. Multiplying these absolute values gives us the size of the product before we pay attention to the signs. In mathematical terms, the absolute value is denoted by vertical bars, such as \(|-56| = 56\). This step simplifies problems as it transforms negative numbers into positive ones, making arithmetic more straightforward.