Number line

The midpoint of two numbers on a number line is their average: \(\frac{-4+18}{2}=\frac{14}{2}=7\). Therefore, the correct answer is 7. A value such as 6 may result from an incorrect calculation of the sum or division. Exam tip: Include the signs of both numbers, add them, and then divide by 2.

The midpoint of two numbers on a number line is their average: \(\frac{-1+7}{2}=\frac{6}{2}=3\). Therefore, 3 is correct. Option 2 is not correct because it is not equally distant from -1 and 7. Exam tip: Add the two numbers and divide by 2 to find the midpoint.

-3.5 can be written as -3.50. On the number line, the more negative number lies farther to the left and is smaller. Therefore, -3.50 is smaller than -3.05. The options 3.05 and 3.5 are positive, so both are greater than either negative number. Exam tip: When comparing negative decimals, add zeros if needed to make the decimal places equal.

The midpoint of two numbers on a number line is their average: \(\frac{-9+15}{2}=\frac{6}{2}=3\). Hence, 3 is correct. \(-3\) is not at an equal distance from both numbers. Exam tip: add the two numbers and divide the result by 2 to find the midpoint.

The correct answer is -0.101. We can write -0.11 as -0.110. On comparing them, -0.101 is greater than -0.110 because, among negative numbers, the number closer to zero is greater. The two numbers are not equal. Exam tip: While comparing negative decimals, add trailing zeros to make the number of decimal places equal.

The midpoint of two numbers on a number line is their average: \(\frac{-2+22}{2}=\frac{20}{2}=10\). Therefore, 10 is correct. 11 is not correct because it is not equally distant from −2 and 22. Exam tip: add the two numbers and divide by 2 to find their midpoint.

The distance between two numbers on a number line is the absolute value of their difference: \(\lvert -40-(-20)\rvert=\lvert -20\rvert=20\). Therefore, the correct answer is 20. \(-20\) is the signed difference, not a distance, because distance cannot be negative. Exam tip: Always use the absolute value of the difference when finding distance.

\(-0.004\) is greater than \(-0.04\) because, among negative numbers, the number closer to zero is greater. On the number line, \(-0.004\) lies to the right of \(-0.04\). \(0.004\) and \(0.04\) are positive numbers, so they do not answer the comparison between the two given numbers. Exam tip: When comparing negative decimals, identify which number is closer to zero.

The midpoint of two numbers on a number line is their average: \(\frac{-8+4}{2}=\frac{-4}{2}=-2\). Hence, \( -2 \) is correct. \( -4 \) is not equally distant from \( -8 \) and \( 4 \), so it is not the midpoint. Exam tip: add the two numbers and divide the result by 2 to find their midpoint.

Write the numbers to the same number of decimal places: -0.62 = -0.620. Now compare them: -0.602 is greater than -0.620 because, among negative numbers, the number closer to zero is greater. The positive numbers 0.602 and 0.620 are not valid answers for comparing the given negative numbers. Exam tip: Add trailing zeros when needed to make the decimal places equal before comparing decimals.

The midpoint of two numbers on a number line is their average: \(\frac{-11+(-19)}{2}=\frac{-30}{2}=-15\). Therefore, \(-15\) is correct. \(-14\) is not the midpoint because it is 3 units from \(-11\) and 5 units from \(-19\). Exam tip: add the numbers with their signs, then divide by 2.

The midpoint of two numbers on a number line is their average: \(\frac{-3+21}{2}=\frac{18}{2}=9\). Therefore, 9 is correct. Neither 8 nor 10 is at an equal distance from both numbers. Exam tip: Add the two numbers and divide the result by 2 to find their midpoint.

Since \(2<\left(\frac{3}{2}\right)^2=\frac94<3\), we get \(\sqrt2<\frac32<\sqrt3\). Thus \(\frac32\) is a rational number between them; in fact, infinitely many rationals lie between distinct real numbers. Exam tip: compare positive roots by squaring.

\(\sqrt{2}\) is irrational, and \(1.4^2=1.96<2<2.25=1.5^2\), so \(1.4<\sqrt{2}<1.5\). Thus, the interval contains an irrational number. Exam tip: compare squares of the endpoints to locate a square root.

The midpoint of two numbers on a number line is their average: \(\frac{-6+30}{2}=\frac{24}{2}=12\). Therefore, 12 is correct. For example, 18 is not at an equal distance from -6 and 30. Exam tip: add the two numbers and divide by 2 to find their midpoint.

Write \(-0.77\) as \(-0.770\) to compare the decimals. Since \(-0.770 < -0.707\), \(-0.77\) is smaller. The closest distractor, \(-0.707\), is closer to zero and is therefore greater. Exam tip: among negative decimals, the number farther left on the number line is smaller.

The midpoint of two numbers is their average: \(\frac{-9+(-21)}{2}=\frac{-30}{2}=-15\). Therefore, \(-15\) is correct. A value such as \(-14\) is not at an equal distance from both numbers. Exam tip: when adding negative numbers, add their magnitudes and retain the negative sign.

The midpoint of two numbers on a number line is their average: \(\frac{-2+18}{2}=\frac{16}{2}=8\). Therefore, 8 is correct. The value 9 is not the average of -2 and 18. Exam tip: add the two numbers and divide by 2 to find their midpoint.

On a number line, the distance between two numbers is the absolute value of their difference: \(\lvert -35-(-15)\rvert=\lvert -20\rvert=20\). Therefore, the correct answer is 20. The option 18 comes from an incorrect subtraction. Exam tip: distance is always non-negative.

Write \(-0.51\) as \(-0.510\) to compare the decimals. Since \(-0.509\) is greater than \(-0.510\), \(-0.509\) is the correct answer. Among negative numbers, the number closer to zero is greater. Although \(-0.501\) would be greater than both given numbers, it is not one of the two numbers being compared. Exam tip: first make the number of decimal places equal before comparing decimals.