Number line

On a number line, the number farther to the right is greater. Here, 2 lies to the right of 0, whereas -3 lies to the left of 0; therefore, 2 > -3. “Both are equal” is incorrect because the two numbers have different values. Exam tip: Every positive integer is greater than every negative integer.

The successor of an integer is obtained by adding 1. Thus, \(-5+1=-4\), so -4 is correct. -6 is the predecessor of -5 because it lies one step to the left on the number line. Exam tip: Numbers increase as you move right on a number line.

The predecessor of an integer is 1 less than the number and lies immediately to its left on the number line. Therefore, the predecessor of -2 is \(-2-1=-3\). The number -1 is the successor of -2, not its predecessor. Exam tip: subtract 1 for a predecessor and add 1 for a successor.

On the number line, moving from 0 to -7 covers 7 units. Hence the distance is \(|-7-0|=|-7|=7\). The option -7 shows the location of the number, not its distance, because distance cannot be negative. Exam tip: Find the distance between two numbers by taking the absolute value of their difference.

Distance on a number line is found using the absolute difference. The distance of 1 from 0 is \(|1-0|=1\), while the distance of \(-3\) from 0 is \(|-3-0|=3\). Therefore, 1 is closer to 0. Exam tip: Compare absolute values when finding which number is closer to zero.

The midpoint of two numbers on a number line is their average: \(\frac{-4+3}{2}=\frac{-1}{2}\). Therefore, \(-\frac{1}{2}\) is correct. Although \(-1\) lies between -4 and 3, it is not equally distant from both numbers. Exam tip: add the two numbers and divide by 2 to find their midpoint.

For \(\frac{1}{2}=0.5\), we have \(-1 < \frac{1}{2} < 2\), so it is a rational number between -1 and 2. \(-\frac{3}{2}\) is less than -1, while \(\frac{5}{2}\) is greater than 2. Exam tip: To check whether a number lies between two values, compare it with both endpoints.

3.5 is greater than 3 and less than 4: \(3 < 3.5 < 4\). Therefore, it lies between 3 and 4 on the number line. In contrast, 2.9 is less than 3, so it does not lie between them. Exam tip: To check whether a number lies between two values, compare it with both boundary numbers.

The number -2.5 lies between -3 and -2. Since -2.5 = -3 + 0.5, it is half a unit to the right of -3, exactly midway between -3 and -2. The point between -2 and -1 is -1.5, so it is not correct. Exam tip: among negative numbers, values increase as you move to the right on the number line.

If a - b is positive, then a - b > 0. Adding b to both sides gives a > b. Therefore, a is greater than b. “Both are equal” would be true only if a - b = 0. Exam tip: A positive difference means that the first quantity is greater than the second quantity.

In increasing order, numbers are written from smallest to greatest. Among negative numbers, the number with the greater magnitude is smaller; therefore, \(-3 < -2 < -1\). Hence the correct order is \(-3, -2, -1\). Option A is in decreasing order. Exam tip: on a number line, the number farther to the left is always smaller.

0.2 can be written as 0.20. Comparing 0.20 and 0.15, 20 hundredths is greater than 15 hundredths, so 0.2 is greater. Thus, 0.15 is smaller and the two numbers are not equal. Exam tip: Add zeros to the right of a decimal, when needed, to compare the same decimal places.

\(-\frac{1}{2}=-0.5\), 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. \(-\frac{1}{3}\) is closer to zero and is therefore greater. Exam tip: among negative numbers, the number farther from zero is smaller.

On a number line, the distance between two numbers is the absolute value of their difference: \(|5-(-3)|=|8|=8\). Therefore, the correct answer is 8. \(-8\) may represent a directed difference, but distance can never be negative. Exam tip: always use absolute value when finding distance.

On a number line, values increase as we move from left to right. For example, \, -1, 0, and 1 lie to the right of -2, and each is greater than -2. Negative numbers are not represented by the right direction; they lie to the left of zero. Exam tip: right means greater values, while left means smaller values on a number line.

\(-3\) is an integer because integers include negative whole numbers, zero, and positive whole numbers. \(2.5\), \(\frac{1}{2}\), and \(0.3\) have fractional parts, so they are not integers. Exam tip: A number written as a non-zero decimal or a non-whole fraction is not an integer.

On the number line, the integers to the right of -2 and to the left of 1 are -1 and 0. Among the given options, only 0 lies in this interval, so option C is correct. -3 and -4 are less than -2, while 2 is greater than 1. Exam tip: For “between,” check that the number is greater than the smaller endpoint and less than the larger endpoint.

\(\frac{2}{5}=0.4\), so it is greater than 0 and less than 1, placing it between them on the number line. \(\sqrt{2}\approx1.41\), so it lies to the right of 1. Exam tip: convert a fraction to a decimal to identify its position quickly.

Among negative integers, the number closer to zero is greater. Of -1, -2, -5 and -10, -1 is closest to zero, so it is the greatest negative integer. -2 is the closest distractor, but it lies to the left of -1 on the number line; hence -2 < -1. Exam tip: On a number line, the number to the right is always greater.

Values increase as we move right on a number line. Hence, every number to the right of a rational number is greater than it; numbers on the left are smaller. Exam tip: remember right means greater and left means smaller.