6th Grade Math Quiz: Position Rational Numbers On Diagrams

20 questions · exam conditions

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Position Rational Numbers On DiagramsQuestion 1 of 20

In the coordinate plane, point Q is located at $\left(-1\frac{1}{3}, 2\frac{2}{3}\right)$ and point R is located at $\left(\frac{5}{6}, -\frac{1}{6}\right)$ . If you plot point S such that it has the same x-coordinate as point Q and the same y-coordinate as point R, in which quadrant will point S be located?

Quadrant I, where both coordinates are positive numbers

Quadrant II, where x is negative and y is positive

Quadrant III, where both coordinates are negative numbers

Quadrant IV, where x is positive and y is negative

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6th Grade Math Quiz

6th Grade Math Quiz: Position Rational Numbers On Diagrams

Practice Position Rational Numbers On Diagrams in 6th Grade Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Position Rational Numbers On Diagrams, giving you a quick way to practice the rules, question types, and explanations that matter most for 6th Grade Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Quadrant I, where both coordinates are positive numbers
Quadrant II, where x is negative and y is positive
Quadrant III, where both coordinates are negative numbers (correct answer)
Quadrant IV, where x is positive and y is negative

Explanation: Point S has the same x-coordinate as Q, which is

-1\frac{1}{3}

(negative), and the same y-coordinate as R, which is

-\frac{1}{6}

(negative). Since both coordinates are negative, point S is in Quadrant III. Choice A would require both coordinates positive. Choice B would require negative x and positive y. Choice D would require positive x and negative y.

Question 2

A vertical number line has markings every $\frac{1}{4}$ unit. If the number $-1\frac{1}{2}$ is located 3 markings below the number $-\frac{3}{4}$ , and you move up 7 markings from $-1\frac{1}{2}$ , at which number will you be positioned?

$\frac{1}{4}$ , which is one marking above zero on the number line (correct answer)
$-\frac{3}{4}$ , which is three markings below zero on the number line
$\frac{3}{4}$ , which is three markings above zero on the number line
$1\frac{1}{4}$ , which is five markings above zero on the number line

Explanation: Moving up 7 markings from

-1\frac{1}{2}

means adding

7 \times \frac{1}{4} = \frac{7}{4} = 1\frac{3}{4}

. So:

-1\frac{1}{2} + 1\frac{3}{4} = -\frac{3}{2} + \frac{7}{4} = -\frac{6}{4} + \frac{7}{4} = \frac{1}{4}

. Choice B would be if you moved up 3 markings. Choice C results from incorrectly calculating

1\frac{1}{2} - \frac{3}{4}

. Choice D results from adding instead of accounting for the negative starting position.

Question 3

On a coordinate plane, you start at the origin and move $2\frac{1}{4}$ units right, then $1\frac{3}{4}$ units down, then $\frac{1}{2}$ unit left, and finally $\frac{3}{4}$ unit up. What are your final coordinates?

$\left(1\frac{3}{4}, -1\right)$ , after completing all horizontal then vertical movements (correct answer)
$\left(2\frac{3}{4}, -\frac{1}{2}\right)$ , after combining movements in the given sequence
$\left(1\frac{1}{2}, -1\frac{1}{4}\right)$ , after calculating net displacement in each direction
$\left(\frac{3}{4}, -1\frac{1}{2}\right)$ , after applying movements relative to previous positions

Explanation: Starting at (0,0): Move right

2\frac{1}{4}

: x =

2\frac{1}{4}

. Move down

1\frac{3}{4}

: y =

-1\frac{3}{4}

. Move left

\frac{1}{2}

: x =

2\frac{1}{4} - \frac{1}{2} = 1\frac{3}{4}

. Move up

\frac{3}{4}

: y =

-1\frac{3}{4} + \frac{3}{4} = -1

. Final coordinates:

(1\frac{3}{4}, -1)

. Choice B doesn't account for leftward movement. Choice C miscalculates horizontal net movement. Choice D makes errors in both coordinate calculations.

Question 4

A thermometer is shown as a vertical number line where each tick mark is $5^\circ\text{C}$ . The center tick is $0^\circ\text{C}$ , values increase upward, and decrease downward. Which placement is correct?

$-10^\circ\text{C}$ is 4 ticks below $0^\circ\text{C}$ and $20^\circ\text{C}$ is 2 ticks above $0^\circ\text{C}$ .
$-10^\circ\text{C}$ is 1 tick below $0^\circ\text{C}$ and $20^\circ\text{C}$ is 2 ticks above $0^\circ\text{C}$ .
$-10^\circ\text{C}$ is 2 ticks below $0^\circ\text{C}$ and $20^\circ\text{C}$ is 4 ticks above $0^\circ\text{C}$ . (correct answer)
$-10^\circ\text{C}$ is 2 ticks above $0^\circ\text{C}$ and $20^\circ\text{C}$ is 4 ticks below $0^\circ\text{C}$ .

Explanation: This question tests positioning integers, fractions, and decimals (positive/negative) on number lines (horizontal/vertical) and coordinate planes, understanding signs indicate direction from zero/axes. On a number line, negative numbers are left of 0 (horizontal) or below 0 (vertical), positive numbers right/above, fractions/decimals between integers (1/2 between 0 and 1 at 0.5, -1.5 between -1 and -2). For example, position -3, 0, 1/2, 2.5 on horizontal number line: -3 is 3 units left of 0, 0 at center, 1/2 halfway between 0 and 1, 2.5 halfway between 2 and 3. The correct placement is -10°C at 2 ticks below 0°C (since each tick is 5°C, -10 is two ticks down) and 20°C at 4 ticks above 0°C (20 divided by 5 is 4 ticks up). A common error is confusing directions on vertical lines, like placing negatives above 0 as in A, or miscalculating ticks like in C and D by halving or doubling the count. For number line positioning: (1) identify if horizontal or vertical, (2) locate zero (center/origin), (3) determine direction from sign (negative→left/down, positive→right/up), (4) measure distance (|number| from zero: |-3|=3 units, |2.5|=2.5 units), (5) mark position (3 units left for -3, 2.5 units right for 2.5). Fractions/decimals: estimate position (1/2=0.5 midway between 0 and 1, 3/4=0.75 three-quarters to 1); mistakes include direction from sign wrong, vertical number line direction reversed, or scale not respected.

Question 5

On a coordinate plane, point $P$ is plotted at $(-2,\,3)$ . Which description correctly tells how to get to $P$ from the origin?

Move 2 units left, then 3 units up. (correct answer)
Move 3 units left, then 2 units up.
Move 2 units right, then 3 units up.
Move 2 units left, then 3 units down.

Explanation: This question tests positioning integers, fractions, and decimals (positive/negative) on number lines (horizontal/vertical) and coordinate planes, understanding signs indicate direction from zero/axes. Coordinate plane: ordered pair (x,y) plotted by moving x units horizontally from origin (negative→left, positive→right), then y units vertically (negative→down, positive→up), signs determine quadrant (I: both +, II: x- y+, III: both -, IV: x+ y-). For example, plot (2,3), (-4,1), (-2,-3), (3,-2): (2,3) is 2 right, 3 up (Quadrant I), (-4,1) is 4 left, 1 up (Quadrant II), (-2,-3) is 2 left, 3 down (Quadrant III), (3,-2) is 3 right, 2 down (Quadrant IV). For (-2,3), move 2 left then 3 up, matching choice C. A common error is swapping distances like 3 left and 2 up (B) or wrong directions like down instead of up (D). To position on coordinate plane: (1) start at origin (0,0), (2) move x (right if +, left if -), (3) move y (up if +, down if -), (4) mark point. Mistakes include direction from sign wrong, coordinates reversed, or mixing horizontal/vertical moves.

Question 6

A horizontal number line is marked in tenths (0.1). Which decimal is located exactly one tick mark to the left of $0$ ?

$-0.01$
$-0.1$ (correct answer)
$0.1$
$-1.0$

Explanation: This question tests positioning integers, fractions, and decimals (positive/negative) on number lines (horizontal/vertical) and coordinate planes, understanding signs indicate direction from zero/axes. On a number line, negative numbers are left of 0 (horizontal) or below 0 (vertical), positive numbers right/above, fractions/decimals between integers (1/2 between 0 and 1 at 0.5, -1.5 between -1 and -2). For example, position -3, 0, 1/2, 2.5 on horizontal number line: -3 is 3 units left of 0, 0 at center, 1/2 halfway between 0 and 1, 2.5 halfway between 2 and 3. One tick mark (0.1) left of 0 is -0.1, matching choice B. A common error is picking positives like 0.1 (C) or wrong decimals like -0.01 (A) or -1.0 (D), or ignoring tenths scale. To position on a number line: (1) identify if horizontal or vertical, (2) locate zero, (3) determine direction from sign (negative→left/down, positive→right/up), (4) measure distance from zero, (5) mark position. For fractions/decimals, estimate position ( -0.1 one tenth left); mistakes include wrong direction, scale not respected, or placing at integers.

Question 7

On a horizontal number line from $-10$ to $10$ with tick marks every 1 unit, which value is farther from $0$ ?

They are the same distance from $0$
Not enough information (need a different scale)
$-6$ (correct answer)
$\frac{3}{2}$

Explanation: This question tests positioning integers, fractions, and decimals (positive and negative) on number lines (horizontal or vertical) and coordinate planes, understanding that signs indicate direction from zero or the axes. On a number line, negative numbers are to the left of 0 on horizontal lines or below 0 on vertical lines, positive numbers to the right or above, and fractions or decimals are placed between integers, such as 1/2 between 0 and 1 at 0.5, or -1.5 between -2 and -1. On a coordinate plane, an ordered pair (x,y) is plotted by moving x units horizontally from the origin (negative to left, positive to right), then y units vertically (negative down, positive up), with signs determining the quadrant (I: both positive, II: x negative y positive, III: both negative, IV: x positive y negative). For example, position -3, 0, 1/2, 2.5 on horizontal number line: -3 3 left of 0, 0 at center, 1/2 halfway between 0 and 1, 2.5 halfway between 2 and 3; or plot (2,3) 2 right 3 up (QI), (-4,1) 4 left 1 up (QII), (-2,-3) 2 left 3 down (QIII), (3,-2) 3 right 2 down (QIV). The value farther from 0 is -6 (distance 6) compared to 3/2 (distance 1.5), matching choice A on the 1-unit scale. A common error is thinking they are the same (choice C), or selecting 3/2 (choice B), or claiming not enough info (choice D), miscalculating absolute distances. To position on a number line: (1) identify horizontal or vertical, (2) locate zero, (3) determine direction from sign (negative left/down, positive right/up), (4) measure distance (|number| from zero), (5) mark position; for fractions/decimals estimate; mistakes include ignoring absolute value for distance.

Question 8

On a horizontal number line with tick marks every $0.5$ , a student needs to place the numbers $-2.5$ , $-1$ , $0$ , $\frac{1}{2}$ , and $3$ .

Which number is exactly halfway between $0$ and $1$ on this number line?

$3$
$\frac{1}{2}$ (correct answer)
$-1$
$-2.5$

Explanation: This question tests positioning integers, fractions, and decimals (positive and negative) on number lines (horizontal or vertical) and coordinate planes, understanding that signs indicate direction from zero or the axes. On a number line, negative numbers are to the left of 0 on horizontal lines or below 0 on vertical lines, positive numbers to the right or above, and fractions or decimals are placed between integers, such as 1/2 between 0 and 1 at 0.5, or -1.5 between -2 and -1. On a coordinate plane, an ordered pair (x,y) is plotted by moving x units horizontally from the origin (negative to left, positive to right), then y units vertically (negative down, positive up), with signs determining the quadrant (I: both positive, II: x negative y positive, III: both negative, IV: x positive y negative). For example, position -3, 0, 1/2, 2.5 on horizontal number line: -3 3 left of 0, 0 at center, 1/2 halfway between 0 and 1, 2.5 halfway between 2 and 3; or plot (2,3) 2 right 3 up (QI), (-4,1) 4 left 1 up (QII), (-2,-3) 2 left 3 down (QIII), (3,-2) 3 right 2 down (QIV). The number exactly halfway between 0 and 1 is 1/2 (at 0.5), matching choice B on the 0.5 increment line. A common error is selecting negatives like -1 or -2.5 (choices A, C) or 3 (choice D) as halfway, ignoring the specified interval between 0 and 1. To position on a number line: (1) identify horizontal or vertical, (2) locate zero, (3) determine direction from sign (negative left/down, positive right/up), (4) measure distance (|number| from zero), (5) mark position; for fractions/decimals estimate like 1/2=0.5 midway; mistakes include wrong positions for fractions, ignoring scale.

Question 9

On a horizontal number line marked in increments of $0.5$ from $-5$ to $5$ , which list shows the numbers in the correct order from left to right?

Numbers: $-3$ , $-1.5$ , $0$ , $\frac{2}{3}$ , $5$

$-3,\,0,\,-1.5,\,\frac{2}{3},\,5$
$-3,\,-1.5,\,0,\,\frac{2}{3},\,5$ (correct answer)
$-3,\,-1.5,\,\frac{2}{3},\,0,\,5$
$-1.5,\,-3,\,0,\,\frac{2}{3},\,5$

Explanation: This question tests positioning integers, fractions, and decimals (positive and negative) on number lines (horizontal or vertical) and coordinate planes, understanding that signs indicate direction from zero or the axes. On a number line, negative numbers are to the left of 0 on horizontal lines or below 0 on vertical lines, positive numbers to the right or above, and fractions or decimals are placed between integers, such as 1/2 between 0 and 1 at 0.5, or -1.5 between -2 and -1. On a coordinate plane, an ordered pair (x,y) is plotted by moving x units horizontally from the origin (negative to left, positive to right), then y units vertically (negative down, positive up), with signs determining the quadrant (I: both positive, II: x negative y positive, III: both negative, IV: x positive y negative). For example, to position -3, -1.5, 0, 2/3, 5 on a horizontal number line: -3 is 3 units left of 0, -1.5 is 1.5 units left of 0 (between -2 and -1), 0 at center, 2/3 (about 0.67) between 0 and 1, 5 is 5 units right of 0. The correct positioning is the order from left to right as -3, -1.5, 0, 2/3, 5, matching choice A on the number line with 0.5 increments. A common error is misordering negatives like putting -1.5 before -3 (more negative is further left), or placing 0 before -1.5, or 2/3 before 0, ignoring signs and values. To position on a number line: (1) identify horizontal or vertical, (2) locate zero, (3) determine direction from sign (negative left/down, positive right/up), (4) measure distance (|number| from zero), (5) mark position; for fractions/decimals estimate like 2/3 ≈0.67 between 0.5 and 1; mistakes include wrong direction, reversed order, ignoring scale.

Question 10

A horizontal number line is labeled at every integer from $-5$ to $5$ , with one tick mark halfway between each pair of integers. Which number should be placed at the tick mark halfway between $1$ and $2$ ?

$\tfrac{2}{3}$
$\tfrac{3}{2}$ (correct answer)
$\tfrac{5}{2}$
$\tfrac{1}{2}$

Explanation: This question tests positioning integers, fractions, and decimals (positive/negative) on number lines (horizontal/vertical) and coordinate planes, understanding signs indicate direction from zero/axes. On a number line, negative numbers are left of 0 (horizontal) or below 0 (vertical), positive numbers right/above, fractions/decimals between integers (1/2 between 0 and 1 at 0.5, -1.5 between -1 and -2). For example, position -3, 0, 1/2, 2.5 on horizontal number line: -3 is 3 units left of 0, 0 at center, 1/2 halfway between 0 and 1, 2.5 halfway between 2 and 3. The tick mark halfway between 1 and 2 is 1.5 or 3/2, matching choice A. A common error is picking wrong fractions like 1/2 (B) or 5/2=2.5 (C), or unrelated 2/3 (D). To position on a number line: (1) identify if horizontal or vertical, (2) locate zero, (3) determine direction from sign (negative→left/down, positive→right/up), (4) measure distance from zero, (5) mark position. For fractions/decimals, estimate position (3/2=1.5 midway between 1 and 2); mistakes include fractions at wrong positions, scale not respected, or confusing with other intervals.

Question 11

On a horizontal number line with tick marks every $\tfrac{1}{2}$ unit from $-5$ to $5$ , a student needs to plot the numbers $-3$ , $-1.5$ , $0$ , $\tfrac{2}{3}$ , and $5$ . Which list shows the correct order from left to right?

$-3,\ -1.5,\ 0,\ \tfrac{2}{3},\ 5$ (correct answer)
$-1.5,\ -3,\ 0,\ \tfrac{2}{3},\ 5$
$-3,\ 0,\ -1.5,\ \tfrac{2}{3},\ 5$
$5,\ \tfrac{2}{3},\ 0,\ -1.5,\ -3$

Explanation: This question tests positioning integers, fractions, and decimals (positive/negative) on number lines (horizontal/vertical) and coordinate planes, understanding signs indicate direction from zero/axes. On a number line, negative numbers are left of 0 (horizontal) or below 0 (vertical), positive numbers right/above, fractions/decimals between integers (1/2 between 0 and 1 at 0.5, -1.5 between -1 and -2). For example, position -3, 0, 1/2, 2.5 on horizontal number line: -3 is 3 units left of 0, 0 at center, 1/2 halfway between 0 and 1, 2.5 halfway between 2 and 3. The correct order from left to right is -3, -1.5, 0, 2/3, 5, as -3 is smallest, followed by -1.5, then 0, then 2/3 (about 0.666), and 5 largest. A common error is reversing the order like in choice D, placing positives left and negatives right, or misordering negatives like in B and C by swapping -3 and -1.5. For number line positioning: (1) identify if horizontal or vertical, (2) locate zero (center/origin), (3) determine direction from sign (negative→left/down, positive→right/up), (4) measure distance (|number| from zero: |-3|=3 units, |2.5|=2.5 units), (5) mark position (3 units left for -3, 2.5 units right for 2.5). Fractions/decimals: estimate position (1/2=0.5 midway between 0 and 1, 3/4=0.75 three-quarters to 1); mistakes include direction from sign wrong, fractions/decimals at wrong positions, or scale not respected.

Question 12

A horizontal number line is marked in tenths (0.1). Which decimal is located exactly one tick mark to the left of $0$ ?

$-0.1$ (correct answer)
$0.1$
$-1.0$
$-0.01$

Explanation: This question tests positioning integers, fractions, and decimals (positive/negative) on number lines (horizontal/vertical) and coordinate planes, understanding signs indicate direction from zero/axes. On a number line, negative numbers are left of 0 (horizontal) or below 0 (vertical), positive numbers right/above, fractions/decimals between integers (1/2 between 0 and 1 at 0.5, -1.5 between -1 and -2). For example, position -3, 0, 1/2, 2.5 on horizontal number line: -3 is 3 units left of 0, 0 at center, 1/2 halfway between 0 and 1, 2.5 halfway between 2 and 3. One tick mark (0.1) left of 0 is -0.1, matching choice B. A common error is picking positives like 0.1 (C) or wrong decimals like -0.01 (A) or -1.0 (D), or ignoring tenths scale. To position on a number line: (1) identify if horizontal or vertical, (2) locate zero, (3) determine direction from sign (negative→left/down, positive→right/up), (4) measure distance from zero, (5) mark position. For fractions/decimals, estimate position ( -0.1 one tenth left); mistakes include wrong direction, scale not respected, or placing at integers.

Question 13

On a number line, point $A$ is located at $-\frac{3}{4}$ and point $B$ is located at $\frac{5}{8}$ . If point $C$ is positioned exactly halfway between points $A$ and $B$ , what is the coordinate of point $C$ ?

$-\frac{1}{16}$ (correct answer)
$\frac{1}{16}$
$-\frac{7}{32}$
$\frac{7}{32}$

Explanation: To find the midpoint, use the formula:

\frac{a + b}{2}

. First convert to common denominators:

-\frac{3}{4} = -\frac{6}{8}

. Then:

\frac{-\frac{6}{8} + \frac{5}{8}}{2} = \frac{-\frac{1}{8}}{2} = -\frac{1}{16}

. Choice B incorrectly uses positive sign. Choice C results from using

\frac{-3 + 5}{4 + 8} = \frac{2}{12}

incorrectly. Choice D combines the error in C with wrong sign.

Question 14

On a vertical number line representing elevation (in meters), $0$ is sea level. Positive numbers are above sea level and negative numbers are below sea level. Which elevation is farthest from sea level?

$-2.5$
$-3.25$ (correct answer)
$3.1$
$2.9$

Explanation: This question tests positioning integers, fractions, and decimals (positive/negative) on number lines (horizontal/vertical) and coordinate planes, understanding signs indicate direction from zero/axes. On a number line, negative numbers are left of 0 (horizontal) or below 0 (vertical), positive numbers right/above, fractions/decimals between integers (1/2 between 0 and 1 at 0.5, -1.5 between -1 and -2). For example, position -3, 0, 1/2, 2.5 on horizontal number line: -3 is 3 units left of 0, 0 at center, 1/2 halfway between 0 and 1, 2.5 halfway between 2 and 3. The elevation farthest from 0 is -3.25, as its absolute value 3.25 is largest compared to 2.9, 2.5, and 3.1. A common error is choosing the largest positive like 3.1 in D, ignoring that distance considers absolute value on the vertical line. For number line positioning: (1) identify if horizontal or vertical, (2) locate zero (center/origin), (3) determine direction from sign (negative→left/down, positive→right/up), (4) measure distance (|number| from zero: |-3|=3 units, |2.5|=2.5 units), (5) mark position (3 units left for -3, 2.5 units right for 2.5). Fractions/decimals: estimate position (1/2=0.5 midway between 0 and 1, 3/4=0.75 three-quarters to 1); mistakes include vertical number line direction reversed or scale not respected.

Question 15

In the coordinate plane, quadrilateral DEFG has vertices plotted. If you rotate the quadrilateral 90° counterclockwise about the origin, what will be the new coordinates of vertex F?

$\left(-1, 2\frac{1}{2}\right)$ , applying the rotation rule for 90° counterclockwise (correct answer)
$\left(1, -2\frac{1}{2}\right)$ , applying the rotation rule for 90° clockwise instead
$\left(2\frac{1}{2}, 1\right)$ , switching coordinates without proper rotation transformation
$\left(-2\frac{1}{2}, -1\right)$ , applying 180° rotation rule by mistake

Explanation: For 90° counterclockwise rotation about origin, the rule is (x,y) → (-y,x). Point F is at

(2\frac{1}{2}, 1)

, so F' =

(-1, 2\frac{1}{2})

. Choice B applies clockwise rotation rule (x,y) → (y,-x). Choice C simply switches coordinates without rotation. Choice D applies 180° rotation rule (x,y) → (-x,-y).

Question 16

Looking at the number line shown, what is the total distance between point J and point L if you travel through point K?

$2.7$ units, calculated by adding the individual segment lengths (correct answer)
$2.7$ units, calculated by finding the direct distance between endpoints
$3.1$ units, calculated by adding absolute values of all coordinates
$1.9$ units, calculated by subtracting the smaller coordinate from larger

Explanation: Point J is at -1.2, K is at 0.3, and L is at 1.5. Distance from J to K is |0.3 - (-1.2)| = 1.5. Distance from K to L is |1.5 - 0.3| = 1.2. Total distance through K is 1.5 + 1.2 = 2.7. Choice B gives the same numerical result but represents direct distance. Choice C incorrectly adds coordinate values. Choice D uses incorrect subtraction method.

Question 17

On the coordinate plane, triangle ABC has vertices at $A(-2, 3)$ , $B(1, -2)$ , and $C(-3, -1)$ . If the triangle is reflected across the y-axis to create triangle A'B'C', what are the coordinates of vertex B'?

$(1, 2)$
$(-1, -2)$ (correct answer)
$(-1, 2)$
$(2, -1)$

Explanation: When reflecting across the y-axis, the x-coordinate changes sign while the y-coordinate stays the same. Point B(1, -2) becomes B'(-1, -2). Choice A incorrectly reflects across x-axis. Choice C incorrectly reflects across both axes. Choice D incorrectly applies coordinate switching instead of reflection.

Question 18

A game score change is shown on a horizontal number line where each tick mark is 1 point. Which value is farther from $0$ on the number line?

$-\tfrac{3}{2}$ (correct answer)
They are the same distance from $0$ .
$1.4$
Not enough information to tell.

Explanation: This question tests positioning integers, fractions, and decimals (positive/negative) on number lines (horizontal/vertical) and coordinate planes, understanding signs indicate direction from zero/axes. On a number line, negative numbers are left of 0 (horizontal) or below 0 (vertical), positive numbers right/above, fractions/decimals between integers (1/2 between 0 and 1 at 0.5, -1.5 between -1 and -2). For example, position -3, 0, 1/2, 2.5 on horizontal number line: -3 is 3 units left of 0, 0 at center, 1/2 halfway between 0 and 1, 2.5 halfway between 2 and 3. Comparing distances, |-3/2|=1.5 > |1.4|=1.4, so -3/2 is farther from 0, matching choice A. A common error is thinking they are the same (C) or picking the positive (B), or claiming not enough info (D) without calculating absolute values. To position on a number line: (1) identify if horizontal or vertical, (2) locate zero, (3) determine direction from sign (negative→left/down, positive→right/up), (4) measure distance from zero, (5) mark position. For fractions/decimals, estimate position; mistakes include ignoring absolute value for distance, wrong positions, or scale not respected (each tick 1 point).

Question 19

A diver's elevation is shown on a vertical number line where $0$ represents sea level, positive numbers are above sea level, and negative numbers are below sea level. Tick marks are every 1 meter. Which point should be lower on the number line?

$\frac{1}{2}$
$-1$
$-2.5$ (correct answer)
$0$

Explanation: This question tests positioning integers, fractions, and decimals (positive and negative) on number lines (horizontal or vertical) and coordinate planes, understanding that signs indicate direction from zero or the axes. On a number line, negative numbers are to the left of 0 on horizontal lines or below 0 on vertical lines, positive numbers to the right or above, and fractions or decimals are placed between integers, such as 1/2 between 0 and 1 at 0.5, or -1.5 between -2 and -1. On a coordinate plane, an ordered pair (x,y) is plotted by moving x units horizontally from the origin (negative to left, positive to right), then y units vertically (negative down, positive up), with signs determining the quadrant (I: both positive, II: x negative y positive, III: both negative, IV: x positive y negative). For example, position -3, 0, 1/2, 2.5 on horizontal number line: -3 3 left of 0, 0 at center, 1/2 halfway between 0 and 1, 2.5 halfway between 2 and 3; or plot (2,3) 2 right 3 up (QI), (-4,1) 4 left 1 up (QII), (-2,-3) 2 left 3 down (QIII), (3,-2) 3 right 2 down (QIV). On this vertical number line for elevation (negatives below 0), the correct lowest point is -2.5, which is lower than -1, 0, or 1/2, matching choice A. A common error is thinking less negative like -1 is lower (choice B), or positives like 1/2 or 0 are lower (choices C, D), reversing vertical direction for negatives. To position on a number line: (1) identify horizontal or vertical, (2) locate zero, (3) determine direction from sign (negative left/down, positive right/up), (4) measure distance (|number| from zero), (5) mark position; for fractions/decimals estimate; mistakes include vertical direction wrong, miscomparing values.

Question 20

A horizontal number line is marked in increments of $\tfrac{1}{2}$ from $-4$ to $4$ . Which list shows the numbers in the correct left-to-right order on the number line?

$-3,\,-1.5,\,0,\,3.25,\,\tfrac{2}{3}$
$-3,\,-1.5,\,0,\,\tfrac{2}{3},\,3.25$ (correct answer)
$-1.5,\,-3,\,0,\,\tfrac{2}{3},\,3.25$
$3.25,\,\tfrac{2}{3},\,0,\,-1.5,\,-3$

Explanation: This question tests positioning integers, fractions, and decimals (positive/negative) on number lines (horizontal/vertical) and coordinate planes, understanding signs indicate direction from zero/axes. On a number line, negative numbers are left of 0 (horizontal) or below 0 (vertical), positive numbers right/above, fractions/decimals between integers (1/2 between 0 and 1 at 0.5, -1.5 between -1 and -2). For example, position -3, 0, 1/2, 2.5 on horizontal number line: -3 is 3 units left of 0, 0 at center, 1/2 halfway between 0 and 1, 2.5 halfway between 2 and 3. The correct left-to-right order is -3, -1.5, 0, 2/3 (about 0.666), 3.25, which matches choice B. A common error is reversing the order like in choice D, placing positives left of negatives, or misordering decimals and fractions like swapping 2/3 and 3.25 in choice A. To position on a number line: (1) identify if horizontal or vertical, (2) locate zero, (3) determine direction from sign (negative→left/down, positive→right/up), (4) measure distance from zero, (5) mark position. For fractions/decimals, estimate position (2/3≈0.666 between 0 and 1); mistakes include wrong direction, ignoring scale (increments of 1/2), or misordering values.