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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.
TOPIC PRACTICE
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Easy · Level 12 · number line,integers,negative numbers,comparisonView options
-12
-6
Equal
Cannot be determined
Easy · Level 12 · number line,number comparison,integers,place valueView options
5
11
Equal
Cannot be determined
Easy · Level 12 · number line,integers,negative numbers,number comparisonView options
-8
-3
Equal
Cannot be determined
Easy · Level 12 · number systems,number line,comparison of numbers,positive numbers,zeroView options
2
0
Both are equal
Cannot be determined
Easy · Level 12 · number line,integers,negative numbers,number comparisonView options
-15
-11
Equal
Cannot be determined
Easy · Level 12 · number systems,number line,integer comparison,positive and negative numbersView options
9
-7
Equal
Cannot be determined
Easy · Level 12 · number line,integers,negative numbers,comparison of numbersView options
-2
-6
Equal
Cannot be determined
Easy · Level 12 · number line,number comparison,integers,place on number lineView options
3
7
Equal
Cannot be determined
Easy · Level 12 · number systems,number line,integer comparison,positive and negative numbersView options
Easy · Level 12 · number line,orderingView options
-5
-1
0
2
Easy · Level 12 · number systems,number line,integers,direction on number lineView options
5
1
-1
3
Medium · Level 7 · number line,integers,absolute value,distance,number systemsView options
6
7
8
9
Medium · Level 7 · number line,integers,whole numbers,direction on number line,subtractionView options
0
10
-5
1
Medium · Level 7 · number systems,number line,integer operations,addition of integersView options
-10
4
-4
10
Medium · Level 7 · number line, midpoint, average, rational numbersView options
2
3
4
5
Question 1EasyLevel 12
Which is greater: -12 or -6?
Correct answer: B
On a number line, the number farther to the right is greater.
-6 is closer to zero and lies to the right of -12, so -6 is greater. Therefore, option B is correct. Exam tip: among negative numbers, the one with the smaller absolute value is greater; hence -12 is not the correct answer.
On a number line, the number to the right is greater. Since 11 lies to the right of 5, 11 is greater. Therefore, 5 is smaller and the two numbers are not equal. Exam tip: Moving to the right on a number line means the value increases.
On a number line, the number farther to the right is greater. Since -3 lies to the right of -8 and is closer to zero, -3 is greater. Exam tip: among negative numbers, the one closer to zero has the greater value.
On a number line, the number farther to the right is greater. Since 2 lies to the right of 0, 2 is greater. Option B is incorrect because 0 is less than 2. Exam tip: Every positive number is greater than 0.
On a number line, the number farther to the right is greater. Since -11 is closer to zero and lies to the right of -15, -11 is greater. -15 is smaller because it is more negative. Exam tip: Among negative numbers, the one with the smaller absolute value is greater.
On a number line, the number farther to the right is greater. Since 9 lies to the right of -7, 9 is greater. Also, every positive number is greater than every negative number, so -7 cannot be the larger number. Exam tip: compare the positions of the numbers on the number line; the rightmost number is greater.
On a number line, the number farther to the right is greater. Since -2 lies to the right of -6 and is closer to zero, -2 is greater. Remember that among negative numbers, the one closer to zero is greater; therefore, -6 is not greater even though its magnitude is 6.
On a number line, the number farther to the right is greater. Since 7 lies to the right of 3, 7 is greater. Therefore, 3 is smaller and the two numbers are not equal. Exam tip: when comparing numbers on a number line, choose the one farther to the right.
On a number line, the number farther to the right is greater. Since 2 lies to the right of -5, we have 2 > -5, so option B is correct. A common mistake is to choose -5 because 5 is larger than 2, but the negative sign changes the comparison. Exam tip: every positive number is greater than every negative number.
On a number line, the number farther to the right is greater. Since -9 lies to the right of -10 and is closer to zero, -9 is greater. A common mistake is to choose -10 because 10 is larger than 9, but among negative numbers, the number closer to zero is greater. Exam tip: For negative numbers, select the number positioned farther to the right on the number line.
On the number line, 6 lies to the right of 0, so 6 is greater. It is neither equal to nor smaller than 0. Exam tip: on a number line, the number farther to the right is greater.
On a number line, the number farther to the right is greater. Among -1, 2, and -3, 2 lies farthest to the right, so it is the greatest. The distractor -1 is greater than -3, but it is still less than the positive number 2. Exam tip: Among negative numbers, the number closer to zero is greater.
What is the distance between -4 and 3 on the number line?
Correct answer: C
The distance between two numbers on a number line is their absolute difference: \(|3-(-4)|=|7|=7\). Hence, the correct answer is 7. Subtracting a negative number means adding it, so 6 is not correct. Exam tip: a distance is always non-negative.
On a number line, moving to the left means decreasing the number. Therefore, moving 3 units left from 2 gives 2 - 3 = -1. The number 1 would result from moving only 1 unit left. Exam tip: add when moving right and subtract when moving left.
What is the distance from -6 to 2 on the number line?
Correct answer: C
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.
Which number is 5 units left of 5 on the number line?
Correct answer: A
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.
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.
What is the midpoint of -2 and 6 on the number line?
Correct answer: A
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.
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