Number line

The distance between two numbers on a number line is the absolute value of their difference. Thus, \(|0-(-10)|=|10|=10\) units. -10 shows a position or direction, not a distance. Exam tip: a distance is always zero or positive.

The midpoint of two numbers on a number line is their average: \(\frac{1+5}{2}=\frac{6}{2}=3\). Therefore, 3 is equally distant from 1 and 5. Option 2 is not the midpoint because it is 1 unit from 1 but 3 units from 5. Exam tip: add the two numbers and divide by 2 to find their midpoint.

In increasing order, numbers are written from smallest to greatest. On the number line, \(-2\) lies to the left of \(-1\), and \(3\) lies farthest to the right. Therefore, the correct order is \(-2, -1, 3\). In option C, \(-1\) is placed before \(-2\), which is incorrect. Exam tip: among negative numbers, the number with the greater negative value is smaller.

On a number line, the number to the right is greater. Since 0 lies to the right of -0.5, 0 is greater. -0.5 is a negative number, and every negative number is less than zero. Exam tip: Among negative numbers, the number closer to zero is greater.

The successor of an integer is obtained by adding 1. Thus, \(-1+1=0\), so 0 is the correct answer. \(-2\) is the predecessor of \(-1\), not its successor. Exam tip: on a number line, moving one step to the right increases the integer by 1.

On the number line, a number between -3 and 2 must be to the right of -3 and to the left of 2. Since
-3 < 0 < 2, 0 is the correct answer. -4 and -5 lie to the left of -3, while 3 lies to the right of 2. Exam tip: For a “between” question, compare the number with both endpoints.

On a number line, the reflection of a number about zero is its additive inverse. Since -6 is 6 units to the left of zero, its reflection is 6 units to the right of zero, i.e., 6. The option -6 is the original number, not its reflection. Exam tip: for reflection about zero, change the sign of the number.

The absolute value of a number is its distance from 0 on the number line. Since 0 is zero units away from itself, its absolute value is 0. The number 1 is one unit away from 0, so it is not correct. Exam tip: An absolute value is never negative.

On a number line, values increase as we move to the right.
-1 is greater than -2, so it lies to the right of -2. In contrast, -3 is less than -2 and lies to its left. Exam tip: Among negative numbers, the number closer to zero is greater.

On a number line, the number farther to the left is smaller. Among the given options, \(-2\) lies to the left of \(-1\), so \(-2\) is the smallest number. Both \(0\) and \(1\) are greater than negative numbers. Exam tip: among negative numbers, the one with the greater magnitude is smaller.

The distance between two numbers on a number line is the absolute value of their difference: \(|4-(-2)|=|6|=6\). Therefore, the correct answer is 6. The value 4 is the magnitude of one number, not the distance between the two numbers. Exam tip: always take the absolute value of the difference because distance cannot be negative.

1.15 is greater than 1.1 and less than 1.2, since \(1.1 < 1.15 < 1.2\). Therefore, it lies between the two numbers on the number line. 1.05 is a close distractor, but it is less than 1.1. Exam tip: Compare decimals by writing them to the same number of decimal places if needed.

\(-\frac{1}{2}=-0.5\), whereas \(-\frac{1}{3}\approx -0.333\). On the number line, \(-0.5\) lies to the left of \(-0.333\), so \(-\frac{1}{2}\) is smaller. They are not equal because their values are different. Exam tip: Among negative numbers, the number farther to the left on the number line is smaller.

Every point on the number line represents a real number, and every real number has a definite position on it. Real numbers include both rational and irrational numbers. Exam tip: real numbers = rational numbers + irrational numbers.

On the number line, the integers strictly between -2 and 3 are -1, 0, 1 and 2. Therefore, 2 is the correct option. -3 lies to the left of -2, while 3 and 4 are not less than 3. Exam tip: “Between” usually excludes the two endpoint numbers.

On a number line, the value of numbers increases as we move from left to right. For example, \(3\) and then \(4\) lie to the right of \(2\). Values decrease when we move left. Exam tip: numbers on the right are greater, while numbers on the left are smaller.

The successor of an integer is 1 greater than the number. Therefore, the successor of 9 is 9 + 1 = 10. Here, 8 is the predecessor of 9, while 11 is 2 greater than 9. Exam tip: add 1 to a number to find its successor.

The predecessor of a number is 1 less than that number. Thus, \(-15-1=-16\), so -16 is correct. -14 is the successor of -15 because it is 1 greater. Exam tip: subtract 1 for a predecessor and add 1 for a successor.

The midpoint of two numbers on a number line is their average: \(\frac{-8+6}{2}=\frac{-2}{2}=-1\). Therefore, the correct answer is \(-1\). The value \(-2\) is not the average of the two numbers. Exam tip: add the two numbers and divide by 2 to find their midpoint.

The distance between two numbers on a number line is the absolute value of their difference: \(|9-(-5)|=|14|=14\). Therefore, the correct answer is 14.
Although -14 may arise from subtracting in the opposite order, a distance can never be negative. Exam tip: always take the absolute value of the difference when finding distance.