Number line

Correct answer: C. 8

Explanation: The distance between two numbers on a number line is the absolute value of their difference: \(|2-(-6)|=|8|=8\). Therefore, the correct answer is 8. The value 6 is only the magnitude of -6, not the distance between the two points. In exams, use absolute value because distance is always positive.

Correct answer: A. 0

Explanation: Moving left on the number line means subtracting. Starting at 5 and moving 5 units left gives 5 - 5 = 0, so 0 is correct. The number 10 would be reached by moving 5 units to the right. In exams, remember: left means subtraction and right means addition.

Correct answer: B. 4

Explanation: Given x=-3, we get x+7=-3+7=4. On the number line, moving 7 units to the right from -3 reaches 4. Choosing -4 results from subtracting 7 instead of adding it. Exam tip: when a positive number is added to a negative number, move to the right on the number line.

Correct answer: A. 2

Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-2+6}{2}=\frac{4}{2}=2\). Therefore, the correct answer is 2. Although 3 may seem plausible, it is not at an equal distance from -2 and 6. Exam tip: add the two numbers and divide by 2 to find their midpoint.

Correct answer: B. 2

Explanation: 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.

Correct answer: B. -4

Explanation: 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.

Correct answer: B. -3

Explanation: 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.

Correct answer: A. 7

Explanation: 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.

Correct answer: A. 1

Explanation: 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.

Correct answer: A. \(-\frac{1}{2}\)

Explanation: 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.

Correct answer: B. \(\frac{1}{2}\)

Explanation: 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.

Correct answer: B. 3.5

Explanation: 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.

Correct answer: A. -2 और -3 के ठीक बीच में

Explanation: 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.

Correct answer: A. a

Explanation: 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.

Correct answer: B. -3, -2, -1

Explanation: 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.

Correct answer: B. 0.2

Explanation: 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.

Correct answer: A. -1/2

Explanation: \(-\frac{1}{2}=-0.5\), 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.

Correct answer: B. 8

Explanation: 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.

Correct answer: B. Increasing numbers

Explanation: 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.

Correct answer: B. -3

Explanation: \(-3\) 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.

Correct answer: C. 0

Explanation: 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.

Correct answer: C. \(\frac{2}{5}\)

Explanation: \(\frac{2}{5}=0.4\), 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.

Correct answer: A. -1

Explanation: 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.

Correct answer: A. Numbers greater than that number

Explanation: 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.

Correct answer: C. At the origin, between negative and positive numbers

Explanation: 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.