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Negative numbers are values less than zero, and they often represent a deficit or a decrease. When you deal with negative numbers, it's essential to visualize them on a number line. The further left a number is on the number line, the smaller it is. For example:

• -1 is smaller than 0,
• -20 is much further to the left than -1, so -20 is smaller than -1.

Negative numbers can feel tricky when performing operations like subtraction. But with practice, they become more intuitive!Try to always keep a mental picture of where numbers lie on the number line. This helps in understanding their relative sizes, especially during subtraction. When we say subtract from another, like in \(-20 - (-11)\), we're really thinking about their positions and knowing that removing the negative is akin to moving in the opposite direction.

Absolute value refers to the distance of a number from zero on the number line, regardless of its direction.It is always a non-negative number, and for any positive number or zero, the absolute value of that number is the same as the original number.For example:

• The absolute value of 4 is 4, written as \(|4| = 4\).
• The absolute value of -11 is 11, written as \(|-11| = 11\).

Understanding absolute value is crucial when subtracting negative numbers. In our exercise, subtracting a negative essentially means adding its absolute value: \(-20 - (-11)\) becomes \(-20 + 11\).This conversion is what changes a subtraction into an addition problem, making it straightforward to solve.

Addition with negative numbers and negatives involved can sometimes be counterintuitive.When you're adding a negative number, you're essentially subtracting its absolute value, moving towards the left of the number line.However, adding a positive number can cancel out some or all of the negative impact:

• With the equation \(-20 + 11\), what we're doing is offsetting the negative influence of 20 by moving 11 steps towards zero.
• This action results in a less negative number, calculated as \(-9\).
• By visualizing the number line movement, we begin at -20 and add 11, reaching -9.

Addition of negatives is a fundamental concept when calculating real-world problems involving debt or temperature changes. Mastering this reassures confidence in tackling more advanced scenarios in mathematics.