Number line

On a number line, zero is the origin. Negative numbers lie to its left and positive numbers lie to its right, so zero is between them. A number line has no actual endpoints because it extends infinitely in both directions. Exam tip: numbers become smaller to the left and greater to the right.

On a number line, the reflection of a number about zero is its additive inverse. Since -4 is 4 units to the left of zero, its reflection is 4 units to the right of zero, i.e. 4. The option -4 represents the original point, not its reflection. Exam tip: the reflection of x about zero is -x.

On a number line, adding a positive number means moving to the right from the starting number. For example, adding 3 to 2 means moving 3 steps right from 2 to reach 5. Moving left represents subtraction or adding a negative number. Exam tip: numbers increase to the right and decrease to the left.

On a number line, subtracting a positive number means moving to the left. For example, \(5-3=2\): starting at 5 and moving 3 steps left reaches 2. Moving right represents addition. Exam tip: for subtraction, count the required number of steps to the left from the starting number.

Absolute value represents a number’s distance from 0 on the number line. The distance of \(-6\) from 0 is 6 units, so \(|-6|=6\). \(-6\) is the original number, not its absolute value. Exam tip: the absolute value of a negative number is positive.

Rational numbers are dense on the number line. Between any two distinct rational numbers, there are infinitely many rational numbers; for example, their average is also a rational number lying between them. Hence, “finite” is incorrect. Exam tip: When asked for a rational number between two rationals, use their average.

\(-5/2=-2.5\). On the number line, \(-2.5\) is greater than \(-3\) and less than \(-2\), so it lies between \(-2\) and \(-3\). The interval between \(-4\) and \(-5\) contains numbers that are more negative. Exam tip: for negative numbers, the more negative value lies farther to the left on the number line.

The absolute value of -3 is 3, while the absolute value of 2 is 2. Since 3 is greater than 2, -3 has the greater absolute value. “Both are equal” is incorrect because the two numbers are not at the same distance from zero. Exam tip: remove the negative sign when finding absolute value, then compare the distances from zero.

In increasing order, numbers are arranged from the smallest to the largest. On the number line,
-1 lies to the left of 0, so it is the smallest, followed by 0, 2, and 3. Therefore, the correct order is
-1, 0, 2, 3. In option B, 0 is placed before -1, so it is not an increasing order. Exam tip: A number farther left on the number line is smaller.

In decreasing order, numbers are arranged from the largest to the smallest. For example, 3, 2, 1, 0 is in decreasing order. Option A goes from the smallest to the largest, so it represents increasing order. Exam tip: Compare the first and last terms to identify the order quickly.

On a number line, a number placed to the right has a greater value than a number placed to its left. For example, \,3\, is to the right of \,−2\,, so \,3 > −2\,. Option A reverses this direction. Exam tip: moving right on a number line always means moving to a greater value.

Numbers to the right of 0 are positive. Hence a point \(\sqrt{5}\) units to the right of 0 represents \(\sqrt{5}\), not \(-\sqrt{5}\). Exam tip: distance is always positive; use direction to decide the sign.

\(-\frac{5}{2}=-2.5\). The gap from \(-3\) to \(-2\) is 1 unit, so \(-2.5\) is 0.5 unit from each endpoint. In exams, remember that more negative numbers lie further left.

0 is greater than -2 and less than 3, so \(-2 < 0 < 3\). Hence, 0 lies strictly between the two numbers. Although 3 is an endpoint, it is not between -2 and 3. Exam tip: on a number line, values increase from left to right.

On a number line, numbers to the left of 0 are negative. Therefore, -1 represents the point one unit to the left of 0. One unit to the right of 0 is +1, so that option is incorrect. Exam tip: Values increase as you move right on a number line and decrease as you move left.

On a number line, the number to the right is greater. Since -5 lies to the right of -8 and is closer to zero, -5 is greater. -8 is smaller because it lies further to the left. Exam tip: Among negative numbers, the number closer to zero is greater.

The successor of an integer is obtained by adding 1 to it. Therefore, the successor of 7 is 7 + 1 = 8. Here, 6 is the predecessor of 7, while 9 is the successor of 8. Exam tip: add 1 for a successor and subtract 1 for a predecessor.

The predecessor of an integer is the number exactly 1 less than it. Therefore, the predecessor of 0 is \(0-1=-1\). \(1\) is the successor of 0, while \(-2\) is the predecessor of \(-1\). Exam tip: subtract 1 to find a predecessor and add 1 to find a successor.

The midpoint of two numbers is their average: \(\frac{-6+2}{2}=\frac{-4}{2}=-2\). Therefore, \(-2\) is the correct answer. \(-3\) is not equally distant from \(-6\) and \(2\). Exam tip: To find a midpoint on a number line, add the two numbers and divide by 2.

On the number line, -2 lies to the right of -4 and to the left of -1. Since \(-4 < -2 < -1\), the correct answer is -2. Note that -5 is smaller than -4, while 0 and 2 are greater than -1. Exam tip: Write the numbers as an inequality to check whether a number lies between them.