Integer Operations with Absolute Value

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a non-negative value.

Front

How do you calculate the absolute value of a negative number?

Back

To calculate the absolute value of a negative number, you remove the negative sign. For example, |-5| = 5.

Front

What is the result of the expression \( \frac{\left|-20\right|}{2} \)?

Back

The result is 10, since |-20| = 20 and 20 divided by 2 equals 10.

Front

What does the expression \( -\left|3 \cdot 3\right| \) evaluate to?

Back

The expression evaluates to -9, since |3 \cdot 3| = 9.

Front

How do you evaluate the expression \( \left|3 \cdot (-4)\right| \)?

Back

First, calculate 3 \cdot (-4) = -12, then take the absolute value: |-12| = 12.

Front

What is the result of the expression \( -6 - (-5) \)?

Back

The result is -1, since subtracting a negative is the same as adding: -6 + 5 = -1.

Front

What is the property of absolute value that states \( |a| = |-a| \)?

Back

This property states that the absolute value of a number is equal to the absolute value of its negative.

Front

How do you simplify the expression \( |x| + |y| \) when both x and y are negative?

Back

When both x and y are negative, you simplify it as follows: |x| + |y| = -x + -y.

Front

What is the absolute value of zero?

Back

The absolute value of zero is 0, since it is at the origin on the number line.

Front

How do you interpret the absolute value in a real-world context?

Back

In real-world contexts, absolute value can represent quantities like distance, which cannot be negative.