Number line

Correct answer: B. -2

Explanation: On a number line, the number farther to the right is greater. Since -2 lies to the right of -9 and is closer to zero, -2 is greater. The number -9 is smaller because it lies farther to the left. Exam tip: Among negative numbers, the number closer to zero is greater.

Correct answer: B. -7

Explanation: The successor of an integer is obtained by adding 1. Thus, \(-8+1=-7\), so -7 is correct. -9 is the predecessor of -8 because it lies one step to the left of -8 on the number line. Exam tip: Even for negative integers, moving right on the number line increases the number by 1.

Correct answer: A. 4

Explanation: The predecessor of a number is exactly one less than the number. Therefore, the predecessor of 5 is 5 - 1 = 4. The number 6 is the successor of 5 because it is one more than 5. Exam tip: subtract 1 to find a predecessor and add 1 to find a successor.

Correct answer: A. -1

Explanation: The midpoint of two numbers is their average: \(\frac{-6+4}{2}=\frac{-2}{2}=-1\). Therefore, \(-1\) is correct. Although \(0\) lies between the two numbers, it is not equally distant from -6 and 4. Exam tip: add the two numbers and divide by 2 to find their midpoint.

Correct answer: B. 10

Explanation: The distance between two numbers on a number line is the absolute value of their difference: \(|7-(-3)|=|10|=10\). Hence, the correct answer is 10.
-10 may arise from subtracting in the reverse order, but distance can never be negative. Exam tip: always take the absolute value of the difference when finding distance.

Correct answer: C. 0

Explanation: The correct answer is 0 because \(-\frac{1}{2}<0<\frac{1}{2}\). On the number line, 0 is to the right of \(-\frac{1}{2}\) and to the left of \(\frac{1}{2}\). The numbers \(-1\), 1, and 2 lie outside the given interval. Exam tip: Check whether a number lies between two values by writing it in an inequality chain.

Correct answer: B. 0.03

Explanation: Write 0.3 as 0.30. The numbers are then 0.30, 0.03, and 0.13. Comparing the first digits after the decimal point, 0.03 has 0, which is less than 1 in 0.13 and 3 in 0.30. Hence, 0.03 is the smallest. Although 0.13 is less than 0.30, it is greater than 0.03. Exam tip: Add zeros to the right of decimals when needed to compare place values easily.

Correct answer: B. 5

Explanation: The absolute value of a number is its distance from 0 on the number line. Since -5 is 5 units away from 0, \(|-5|=5\). Option -5 is the number itself, not its absolute value. Exam tip: An absolute value is never negative.

Correct answer: B. \(\sqrt{5}\)

Explanation: Since \(2^2=4\) and \(3^2=9\), the number 5 lies between 4 and 9. Therefore, \(\sqrt{5}\) lies between 2 and 3. In contrast, \(\sqrt{3}<2\) and \(\sqrt{10}>3\). Exam tip: compare nearby perfect squares to locate square roots.

Correct answer: A. Moving to the right

Explanation: On a number line, adding a positive number means moving that many units to the right. For example, to add 3 to 2, move 3 steps right from 2 to reach 5. Moving left represents subtraction or adding a negative number. Exam tip: while adding, count the required steps to the right for a positive addend.

Correct answer: A. Moving to the left

Explanation: On a number line, subtracting a positive number means moving to the left because the value decreases. For example, to find 5 - 2 = 3, move two steps left from 5. Moving to the right represents addition. Exam tip: in subtraction, count leftward from the starting number by the number being subtracted.

Correct answer: A. \(\frac{5}{2}\)

Explanation: \(\frac{5}{2}=2.5\), and \(2<2.5<3\). Therefore, \(\frac{5}{2}\) is the rational number between 2 and 3. \(\frac{7}{2}=3.5\) is greater than 3, while \(\frac{3}{2}=1.5\) is less than 2. Exam tip: Convert a fraction to a decimal, or compare it using inequalities, to check whether it lies between two integers.

Correct answer: A. \(2^2<5<3^2\), so \(\sqrt{5}\) is between 2 and 3 and \(\sqrt{5}\approx2.24\)

Explanation: Since \(2^2=4\) and \(3^2=9\), \(4<5<9\) gives \(2<\sqrt{5}<3\). Also, \(\sqrt{5}\approx2.24\), so it is closer to 2, not 2.5. Exam tip: compare with nearby perfect squares first.

Correct answer: A. \(\frac{1}{3}\)

Explanation: \(\frac{1}{3}=0.333\ldots\), whereas \(0.25=\frac{1}{4}\). Since \(0.333\ldots > 0.25\), \(\frac{1}{3}\) is greater. The “both are equal” option is incorrect because their decimal values are different. Exam tip: compare fractions by converting them to decimals or by using a common denominator.

Correct answer: B. 10

Explanation: The distance between two numbers on a number line is the absolute value of their difference. Thus, \(|0-(-10)|=|10|=10\) units. -10 shows a position or direction, not a distance. Exam tip: a distance is always zero or positive.

Correct answer: B. 3

Explanation: The midpoint of two numbers on a number line is their average: \(\frac{1+5}{2}=\frac{6}{2}=3\). Therefore, 3 is equally distant from 1 and 5. Option 2 is not the midpoint because it is 1 unit from 1 but 3 units from 5. Exam tip: add the two numbers and divide by 2 to find their midpoint.

Correct answer: B. \(-2, -1, 3\)

Explanation: In increasing order, numbers are written from smallest to greatest. On the number line, \(-2\) lies to the left of \(-1\), and \(3\) lies farthest to the right. Therefore, the correct order is \(-2, -1, 3\). In option C, \(-1\) is placed before \(-2\), which is incorrect. Exam tip: among negative numbers, the number with the greater negative value is smaller.

Correct answer: A. 0

Explanation: On a number line, the number to the right is greater. Since 0 lies to the right of -0.5, 0 is greater. -0.5 is a negative number, and every negative number is less than zero. Exam tip: Among negative numbers, the number closer to zero is greater.

Correct answer: B. 0

Explanation: The successor of an integer is obtained by adding 1. Thus, \(-1+1=0\), so 0 is the correct answer. \(-2\) is the predecessor of \(-1\), not its successor. Exam tip: on a number line, moving one step to the right increases the integer by 1.

Correct answer: B. 0

Explanation: On the number line, a number between -3 and 2 must be to the right of -3 and to the left of 2. Since
-3 < 0 < 2, 0 is the correct answer. -4 and -5 lie to the left of -3, while 3 lies to the right of 2. Exam tip: For a “between” question, compare the number with both endpoints.

Correct answer: B. 6

Explanation: On a number line, the reflection of a number about zero is its additive inverse. Since -6 is 6 units to the left of zero, its reflection is 6 units to the right of zero, i.e., 6. The option -6 is the original number, not its reflection. Exam tip: for reflection about zero, change the sign of the number.

Correct answer: A. 0

Explanation: The absolute value of a number is its distance from 0 on the number line. Since 0 is zero units away from itself, its absolute value is 0. The number 1 is one unit away from 0, so it is not correct. Exam tip: An absolute value is never negative.

Correct answer: C. -1

Explanation: On a number line, values increase as we move to the right.
-1 is greater than -2, so it lies to the right of -2. In contrast, -3 is less than -2 and lies to its left. Exam tip: Among negative numbers, the number closer to zero is greater.

Correct answer: D. -2

Explanation: On a number line, the number farther to the left is smaller. Among the given options, \(-2\) lies to the left of \(-1\), so \(-2\) is the smallest number. Both \(0\) and \(1\) are greater than negative numbers. Exam tip: among negative numbers, the one with the greater magnitude is smaller.

Correct answer: C. 6

Explanation: The distance between two numbers on a number line is the absolute value of their difference: \(|4-(-2)|=|6|=6\). Therefore, the correct answer is 6. The value 4 is the magnitude of one number, not the distance between the two numbers. Exam tip: always take the absolute value of the difference because distance cannot be negative.