Number line

\(\frac{7}{11}\) is written as a ratio of two integers, 7 and 11, with a non-zero denominator. Therefore, it is a rational number and has a definite position on the number line. \(\sqrt{2}\), \(\pi\), and \(\sqrt{5}\) are irrational because they cannot be expressed as a ratio of two integers. Exam tip: A number is rational if it can be written in the form \(p/q\), where \(p\) and \(q\) are integers and \(q\ne0\).

On a number line, the number farther to the right is greater. Since −2 lies to the right of −5, −2 is greater. Among negative numbers, the number closer to zero is greater, so −5 is not correct. Exam tip: When comparing negative numbers, the one with the smaller absolute value is greater.

Every point on the number line corresponds to a real number, and every real number has one definite position on it. This includes both rational and irrational numbers. Therefore, option A is correct. Options B and D are incorrect because an irrational number such as
√2 can also be represented on the number line. Exam tip: When you see “real numbers,” remember that they include both rational and irrational numbers.

4 is a positive number. On the number line, positive numbers are located to the right of 0, so 4 lies to the right of 0. Negative numbers lie to the left of 0. Exam tip: identify the sign of the number—positive numbers are on the right and negative numbers are on the left.

On a number line, the number farthest to the left is the smallest. Among the given options, \(-2\) lies to the left of 0, 1, and 3, so \(-2\) is the smallest number. Exam tip: Among negative numbers, the one farther to the left of zero is smaller.

On a number line, the number farther to the right is greater. Since −3 lies to the right of −6, −3 is the greater number. Among negative numbers, the number closer to zero is greater, so −6 is not correct. Exam tip: Compare negative numbers by locating them on a number line or checking which is closer to zero.

The midpoint of two numbers is their average: \((2+8)÷2=5\). On the number line, 5 is 3 units away from both 2 and 8, so it is the correct midpoint. Choosing 4 is incorrect because its distances from 2 and 8 are 2 and 4 units, not equal. Exam tip: Add the two endpoints and divide the sum by 2 to find the midpoint.

Every number less than 0 is negative. Among the given options, −4 is the only number located to the left of 0 on the number line, so option C is correct. On a number line, negative numbers lie to the left of 0 and positive numbers lie to its right. Exam tip: A number with a minus sign and a non-zero magnitude is less than 0.

On a number line, the number farther to the right is greater. Since 9 lies to the right of 1, 9 is the greater number. Option A, 1, is smaller. In exams, remember that the number on the right is greater when comparing numbers on a number line.

All numbers to the right of 0 on the number line are positive, such as 1, 2, and 3. Zero is neither positive nor negative, while negative numbers lie to the left of 0. Exam tip: on a number line, the right side represents positive numbers and the left side represents negative numbers.

On a number line, numbers to the left of 7 are less than 7. Among the given options, 6 lies to the left of 7, so it is the correct answer. The numbers 8, 9, and 10 lie to the right of 7 and are greater than 7. For exams, remember that the number farther to the left on a number line is smaller.

On a number line, negative numbers are located to the left of 0. Therefore, −8 is 8 units to the left of 0. Option A is incorrect because positive numbers lie to the right of 0. Exam tip: place any number with a minus sign to the left of zero.

On the number line, 0 lies to the right of −3. The number farther to the right is greater, so 0 > −3. Option C is incorrect because the two numbers are not equal. Exam tip: Zero is always greater than any negative number.

The two numbers are equal, so their difference is \(5-5=0\). On the number line, the distance from 5 to 5 is also 0. Therefore, 0 is correct. Exam tip: The difference between any number and itself is always zero.

On the number line, 5 lies to the right of both 1 and 3. A number farther to the right on the number line is greater, so 5 is the greatest number. Exam tip: while comparing positive integers, the number on the right is the larger one.

The midpoint of two numbers is found by taking their average: \((0+6)/2=3\). Therefore, the point exactly halfway between 0 and 6 on the number line is 3. Option 4 is not correct because it is closer to 6. Exam tip: Add the two numbers and divide the sum by 2 to find their midpoint.

On a number line, numbers greater than 2 lie to the right of 2. Among the given options, 3 is to the right of 2, so it is the correct answer. The numbers 1, 0, and -1 are all less than 2. Exam tip: Moving to the right on a number line increases the value of numbers.

On a number line, the number farther to the right is greater. Since 12 lies to the right of 9, 12 is the greater number. The numbers 0 and -1 are also less than 12. Exam tip: on a number line, choose the number on the right as the greater number.

On the number line, -8 lies to the right of -10. Among negative numbers, the number closer to zero is greater, so -8 is greater than -10. The numbers -12, -15, and -20 all lie to the left of -10 and are therefore smaller. Exam tip: When comparing negative numbers, the one with the smaller absolute value is greater.

Every real number has exactly one position on the number line, so option A is correct. This includes both rational and irrational numbers. Option C is incorrect because an irrational number such as √2 can also be represented by a point on the number line. Exam tip: A number line represents real numbers, not only natural numbers.

On a number line, the number farther to the right is greater. Since -4 lies to the right of -9, -4 is the greater number. Among negative numbers, the one closer to zero is greater, so -9 is not correct. Exam tip: Compare negative numbers by checking their positions on the number line.

12 is less than 15 because it lies to the left of 15 on the number line. The numbers 18, 20, and 25 are all greater than 15. Exam tip: on a number line, numbers to the left are smaller and numbers to the right are greater.

On a number line, positive numbers lie to the right of 0 and negative numbers lie to the left. Therefore, \(-3\) must be placed three equal units to the left of 0. Option B confuses the magnitude 3 with the direction; the negative sign determines the direction. Exam tip: When you see a negative sign, locate the number to the left of 0.

20 is a positive number. On the number line, all positive numbers are located to the right of 0, so 20 lies to the right of zero. Negative numbers lie to the left of 0. Exam tip: Moving right on the number line means the numerical value increases.

On the number line, 0 lies to the right of -7, so 0 is greater than -7. Among negative numbers, the number closer to zero is greater; therefore, -7 is not correct, and 5 is not one of the numbers being compared. Exam tip: On a number line, the number farther to the right is always greater.