Number line

1.45 is greater than 1.4 and less than 1.5, since 1.40 < 1.45 < 1.50. Therefore, it lies between 1.4 and 1.5 on the number line. 1.6 is greater than 1.5, while 1.3 and 1.2 are less than 1.4. Exam tip: Add zeros at the end of decimals when needed to compare the same number of decimal places.

The correct answer is \(7/8\), because \(3/4=6/8\) and \(1=8/8\). Thus, \(6/8 < 7/8 < 8/8\), so \(7/8\) lies between \(3/4\) and 1. While \(2/3\) is less than \(3/4\), \(5/4\) is greater than 1. Exam tip: Convert fractions to a common denominator to compare them quickly.

For any two distinct rational numbers, their average \(\frac{a+b}{2}\) is rational and lies between them. Hence B is correct. A whole number need not lie between them. Exam tip: use the average to identify a rational number between two rationals.

The absolute value of a number is its distance from 0 on the number line. Since -11 is 11 units away from 0, \(|-11|=11\). Option -11 is the original number, not its absolute value. Exam tip: the absolute value of a negative number is its positive counterpart.

All numbers to the right of 0 on a number line are positive, such as 1, 2, and \(\frac{1}{2}\). Negative numbers lie to the left of 0. Exam tip: values increase as you move to the right on a number line.

On a number line, subtraction means moving to the left. Starting at 5 and moving 3 steps left gives 4, then 3, and finally 2. Therefore, the correct answer is 2. Option 8 would be obtained by adding 3 to 5, not subtracting it. Exam tip: move right for addition and left for subtraction on a number line.

On a number line, subtracting 7 from 4 means moving 7 steps to the left from 4. This lands at -3, so the correct answer is -3. The value 3 would be obtained from 7 minus 4, not from 4 minus 7. Exam tip: in subtraction, move left by the number being subtracted.

\(-\frac{3}{5}\) is negative but greater than \(-1\), so it lies between \(-1\) and \(0\). In contrast, \(-\frac{5}{3}<-1\). Exam tip: among negative numbers, the one closer to 0 is greater.

Among negative integers, the number farther to the right on the number line is greater. Here,

displaystyle -1 > -4 > -6 > -8

Therefore, -1 is the greatest integer. The numbers -4, -6 and -8 lie to the left of -1 on the number line, so they are smaller. Exam tip: among negative numbers, the number closest to zero is greater.

On a number line, the number farther to the left is smaller.

-10 lies to the left of -9.5 because it is more negative, so -10 is smaller. Although -9.5 is negative, it is closer to zero and hence greater than -10. Exam tip: Among negative numbers, the number with the greater magnitude is smaller.

The midpoint of two numbers on a number line is their average: \(\frac{2+(-6)}{2}=\frac{-4}{2}=-2\). Therefore, \(-2\) is correct. \(-3\) is not the average of the two numbers. Exam tip: include the negative sign while adding the numbers, then divide by 2.

The distance between two numbers on a number line is the absolute value of their difference. Thus, \(\left|\frac{1}{2}-\left(-\frac{3}{2}\right)\right|=\left|\frac{4}{2}\right|=2\). Therefore, the correct answer is 2. While \(-2\) may arise as a signed displacement in some order, distance can never be negative. Exam tip: always use absolute value when finding distance on a number line.

On a number line, the reflection of a number about zero is its additive inverse. Since 8 is 8 units to the right of zero, its reflection is 8 units to the left of zero, i.e., -8. The number 8 is not its own reflection; only 0 reflects to itself. Exam tip: for reflection about zero, change the sign of the number.

The distance of a number from 0 is its absolute value.

\(|6|=6\) and \(|-5|=5\). Since 5 is less than 6, -5 is closer to 0. “Both are equally distant” would be correct only for opposite numbers such as 5 and -5. Exam tip: compare absolute values to decide which number is closer to zero.

The successor of an integer is obtained by adding 1 to it. Therefore, 100 + 1 = 101. While 99 is the predecessor of 100, 102 is two integers after 100. Exam tip: add 1 to find a successor.

The midpoint of two numbers \(a\) and \(b\) is \(\frac{a+b}{2}\). Therefore, the midpoint of \(-1\) and \(0\) is \(\frac{-1+0}{2}=-\frac{1}{2}\). \(\frac{1}{2}\) is the midpoint between 0 and 1, so it is not correct here. Exam tip: on a number line, a midpoint is equally distant from both numbers.

On a number line, the number to the right is greater. \( -3 \) lies to the right of \( -7 \) and is closer to zero, so \( -3 \) is greater. \( -7 \) is smaller because it lies further to the left. Exam tip: Among negative numbers, the number closer to zero is greater.

The successor of an integer is obtained by adding 1 to it. Thus, 6 + 1 = 7, so 7 is the correct answer. The number 6 is the given integer itself, not its successor. Exam tip: on a number line, the successor is the integer immediately to the right.

The predecessor of a number is exactly 1 less than the number. Thus, \(-4-1=-5\), so the correct answer is \(-5\). The number \(-3\) is the successor of \(-4\) because it is 1 greater. Exam tip: subtract 1 for a predecessor and add 1 for a successor.

The distance between two numbers on a number line is the absolute value of their difference: \(|3-(-8)|=|11|=11\). Therefore, 11 is correct. \(-11\) may arise as a signed difference, but distance can never be negative. Exam tip: always take the absolute value when finding distance.