Number line

On a number line, the number located farther to the right is greater. Since 6 lies to the right of 2, 6 is the greater number. Exam tip: among positive numbers, moving right on the number line means the value increases.

A number line extends infinitely in both directions, so it has no rightmost or greatest number. A number located to the right of a given number is greater than it. Exam tip: moving right on the number line increases the value, but there is no final right endpoint.

On a number line, the number located farther to the right is greater. Since 1 lies to the right of −1, 1 is greater. Also, 1 is positive and −1 is negative, and every positive number is greater than every negative number. In an exam, choose the number placed farther to the right on the number line.

10 is a positive number. On a number line, positive numbers are located to the right of 0, so 10 will be on the right. Exam tip: negative numbers lie to the left of 0.

\(\frac{7}{11}\) 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.