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SubjectsMathematics
संख्या रेखा
The Number Line topic in Class 9 Mathematics, within Number Systems, helps students visualise numbers as points on a continuous line. They learn to locate and compare integers, rational numbers, irrational numbers and real numbers, understand their order and relative position, and interpret distance using intervals. The topic also supports the geometric representation of irrational numbers such as √2, making the connection between numerical expressions and their positions on the real number line clear.
Correct answer: B. \(8\)
Explanation: The absolute value of a number is its distance from zero on the number line. Since \(-8\) is 8 units away from zero, \(|-8|=8\). \(-8\) is the original number, not its absolute value. Exam tip: the absolute value of a negative number is always positive.
Correct answer: B. \(-3\)
Explanation: On a number line, moving left means subtracting. Therefore, moving 7 steps left from 4 gives \(4-7=-3\). The value \(3\) would result from moving only 1 step left, while \(-11\) would require subtracting 15 from 4. Exam tip: subtract for leftward movement and add for rightward movement.
Correct answer: B. \(2\)
Explanation: On the number line, the integers to the right of \(-1\) and to the left of \(3\) are \(0, 1, 2\). Therefore, \(2\) lies between \(-1\) and \(3\). \(-2\) is less than \(-1\), while \(4\) is greater than \(3\). Exam tip: For a number to be between two limits, it must lie inside both bounds.
Correct answer: C. Positive numbers lie to the right of zero
Explanation: On a number line, positive numbers lie to the right of zero, while negative numbers lie to its left. Therefore, option C is correct. Options A and B reverse these directions, and zero is not at an end of the number line; it lies between negative and positive numbers. Exam tip: Values increase as you move to the right on a number line.
Correct answer: B. -9
Explanation: On a number line, the number to the right is greater. -9 lies to the right of -14 and is also closer to zero, so -9 is greater. “Both are equal” is incorrect because -14 and -9 are different integers. Exam tip: Among negative numbers, the number closer to zero is greater.
Correct answer: B. 13
Explanation: The successor of an integer is 1 greater than the given integer. Therefore, \(12+1=13\), so 13 is the successor of 12. Here, 11 is the predecessor of 12, while 14 is 2 greater than 12. Exam tip: add 1 to find a successor.
Correct answer: B. \(-19\)
Explanation: The predecessor of a number is 1 less than that number. Therefore, \(-18-1=-19\), so \(-19\) is correct. \(-17\) is the successor of \(-18\), not its predecessor. Exam tip: subtract 1 from a number to find its predecessor.
Correct answer: A. \(-3\)
Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-12+6}{2}=\frac{-6}{2}=-3\). Therefore, \(-3\) is correct. Although \(0\) lies between the two numbers, it is not equally distant from both. Exam tip: add the two numbers and divide by 2 to find their midpoint.
Correct answer: B. 16
Explanation: On a number line, the distance between two numbers is the absolute value of their difference: \(|11-(-5)|=|16|=16\). Therefore, 16 is correct. \(-16\) may arise as a signed difference, but distance can never be negative. Exam tip: always use the absolute value of the difference for distance questions.
Correct answer: C. ( 1 )
Explanation: On the number line,
(1) is to the right of
(-2) and to the left of
(3), so
-2 < 1 < 3. Therefore,
(1) is the correct answer.
(-3) is less than
-2, while
4 and
5 are greater than
3. Exam tip: A number lies between two numbers only if it is greater than the left number and less than the right number.
Correct answer: B. \(0.7\)
Explanation: The correct answer is \(0.7\). Write it as \(0.70\): it has 70 hundredths, whereas \(0.09\) has 9 hundredths. Since \(70 > 9\), \(0.70 > 0.09\). Therefore, 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: B. \(15\)
Explanation: The absolute value of a number is its distance from 0 on the number line. Since \(-15\) is 15 units from 0, \(|-15|=15\). \(-15\) is the number itself, not its absolute value. Exam tip: the absolute value of a negative number is positive.
Correct answer: B. Move to the right
Explanation: On a number line, adding a positive number means moving to the right. Adding 5 to 7 moves 5 units right from 7 and gives 12. Moving left is used for subtraction or for adding a negative number. Exam tip: remember that addition moves right and subtraction moves left on a number line.
Correct answer: B. -5
Explanation: Here, 9 is subtracted from 4. On the number line, moving 9 steps left from 4 lands at -5, so the correct value is -5. The value 5 would result from subtracting 4 from 9. Exam tip: subtracting a larger integer from a smaller integer gives a negative result.
Correct answer: B. \( -\frac{3}{4} \)
Explanation: \( -\frac{3}{4} \) lies to the left of \( -\frac{1}{4} \) on the number line, so it is the smaller number. For negative fractions with the same denominator, the fraction with the larger numerator magnitude is more negative and hence smaller. \( -\frac{1}{4} \) is closer to zero, so it is greater. Exam tip: On a number line, the number farther left is always smaller.
Correct answer: B. \(\frac{2}{3}\)
Explanation: \(\frac{2}{3}=0.6666\ldots\), whereas \(0.6=0.6000\ldots\). Therefore, \(\frac{2}{3}\) lies to the right of 0.6 on the number line and is greater. Option A is incorrect because it represents the smaller number, 0.6. Exam tip: To compare a fraction and a decimal, convert them to the same form or use a common denominator.
Correct answer: A. To the left of zero
Explanation: Negative numbers lie to the left of zero on a number line. Values decrease as we move left from zero, while positive numbers lie to the right. Exam tip: remember that left means smaller and right means greater.
Correct answer: B. 5
Explanation: The midpoint of two numbers on a number line is their average: \(\frac{1+9}{2}=\frac{10}{2}=5\). Therefore, 5 is correct. Numbers 4 and 6 are not equally distant from 1 and 9. Exam tip: add the two numbers and divide by 2 to find their midpoint.
Correct answer: C. \(14\)
Explanation: The distance between two numbers on a number line is the absolute value of their difference: \(|10-(-4)|=|14|=14\). Therefore, the correct answer is \(14\). \(6\) can result from an incorrect subtraction. Exam tip: when subtracting a negative number, remember that it becomes addition.
Correct answer: B. \(-13\)
Explanation: On a number line, the number farther to the right is greater. \(-13\) lies to the right of \(-20\) and is also closer to zero, so \(-13 > -20\). “Both are equal” is incorrect because the two numbers are different. Exam tip: among negative numbers, the number closer to zero is greater.
Correct answer: B. ( -24 )
Explanation: The successor of an integer is found by adding 1. Thus, \( -25 + 1 = -24 \), so \( -24 \) is correct. \( -26 \) is the predecessor because it lies to the left of \( -25 \) on the number line. Exam tip: for negative integers, numbers increase as you move to the right.
Correct answer: A. \(2\)
Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-8+12}{2}=\frac{4}{2}=2\). Hence, \(2\) is correct. Although \(0\) lies between the two numbers, it is not at equal distance from both. Exam tip: Add the two numbers and divide by 2 to find their midpoint.
Correct answer: C. 11
Explanation: The distance between two numbers on a number line is the absolute value of their difference: \(|9-(-2)|=|11|=11\). Therefore, the correct answer is 11. Choosing 10 usually results from an error while subtracting a negative number. Exam tip: Always take the absolute value of the difference, so distance is never negative.
Correct answer: A. Between 2 and 3
Explanation: Since \(2^2=4\) and \(3^2=9\), we have \(4<5<9\). Therefore, \(2<\sqrt{5}<3\), so option A is correct. Exam tip: compare the number with nearby perfect squares to locate a square root.
Correct answer: C. -6
Explanation: On a number line, the number farther to the right is greater.
-6 is closer to zero and lies to the right of -6.5, so -6 is greater. Although -6.25 is greater than -6.5, it is still less than -6. Exam tip: among negative numbers, the number closer to zero is greater.
