Number line

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.

The midpoint of two numbers on a number line is found by taking their average: \((11+11)÷2=11\). Therefore, the correct answer is 11. When both endpoints are the same, the midpoint remains that same number. Exam tip: The midpoint of any two endpoints equals their average.

On a number line, numbers to the right of 7 are greater than 7. Among the given options, 9 lies to the right of 7, so it is the correct answer. The numbers 6, 5 and 4 are all less than 7. 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. Since 2 lies to the right of -3, 2 is the greater number. A positive number such as 2 is greater than the negative number -3. In the exam, remember that numbers increase from left to right on the number line.

To find the midpoint, take the average of the two endpoints: \((0+10)\div 2=5\). Therefore, the midpoint between 0 and 10 on the number line is 5. The numbers 4 and 6 are not midpoints because they are not equally distant from both endpoints. Exam tip: Remember the midpoint formula \((a+b)\div 2\).

On a number line, the number farther to the right is greater. Since 8 lies to the right of -5, 8 is greater. A positive number such as 8 is greater than a negative number such as -5. In an exam, choose the number positioned farther to the right on the number line.

Numbers located to the left of 0 on the number line are less than 0, so they are negative numbers. Positive numbers lie to the right of 0, while 0 itself lies at the origin. Exam tip: moving left on the number line means the value decreases.

On a number line, the number farther to the right is greater. Since -6 lies to the right of -9 and is closer to zero, -6 is the greater number. The distractor -9 is smaller because it lies farther to the left. Exam tip: Among two negative numbers, the one closer to zero is greater.

On a number line, the number farther to the right is greater. Since 4 lies to the right of -7, 4 is the greater number. Also, 4 is positive and -7 is negative, and every positive number is greater than every negative number. Exam tip: For numbers on a number line, choose the number positioned farther to the right.

On a number line, the distance between two numbers is the absolute value of their difference. Here, the distance is \(|5-0|=5\) units, so 5 is correct. Although 4 is a close distractor, there are five unit intervals from 0 to 5. In an exam, use \(|a-b|\) to find the distance between two numbers.

On the number line, -3 lies to the left of -2, so -3 is less than -2. The numbers 0, 1, and 2 all lie to the right of -2 and are greater than it. Exam tip: when comparing numbers, the number farther to the left on the number line is smaller.

9 is a positive number. On the number line, all positive numbers are located to the right of zero, so 9 lies to the right of zero. Negative numbers lie to the left of zero. Exam tip: The values of numbers increase as we move to the right on the number line.