Position Rational Numbers on Diagrams
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6th Grade Math › Position Rational Numbers on Diagrams
A scuba diver’s elevation relative to sea level is shown on a vertical number line (up is positive, down is negative). Which value should be placed 2.5 units below $0$?
$-25$
$-0.25$
$-2.5$
$2.5$
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, on a vertical number line, position -3, 0, 1/2, 2.5: -3 is 3 units below 0, 0 at center, 1/2 halfway above 0 and 1, 2.5 halfway above 2 and 3. The value 2.5 units below 0 is -2.5, matching choice B. A common error is placing positives below like 2.5 (A) or wrong decimals like -0.25 (C) or -25 (D), or reversing vertical direction. 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. Mistakes include vertical direction wrong (negatives up), scale ignored, or confusing below with above.
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?
Not enough information to tell.
$-\tfrac{3}{2}$
$1.4$
They are the same distance from $0$.
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. 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).
A coordinate plane uses a scale of 1 unit per grid square on both axes. Which ordered pair is in Quadrant II (left of the $y$-axis and above the $x$-axis)?
$(4,,1)$
$(1,,-4)$
$(-4,,-1)$
$(-4,,1)$
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). The ordered pair in Quadrant II (x negative, y positive) is (-4,1), matching choice B. A common error is confusing quadrants, like picking (4,1) in I (A), (-4,-1) in III (C), or (1,-4) in IV (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 coordinates reversed, wrong signs for quadrants, or ignoring scale (1 unit per grid).
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 right, then 3 units up.
Move 2 units left, then 3 units down.
Move 3 units left, then 2 units up.
Move 2 units left, then 3 units up.
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.
On a coordinate plane, each grid square represents 1 unit on both axes. Which point is located 4 units left of the $y$-axis and 1 unit above the $x$-axis?
$(-1,4)$
$(4,1)$
$(-4,1)$
$(1,-4)$
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). The correct point is (-4,1), as 4 units left of y-axis means x=-4 and 1 unit above x-axis means y=1. A common error is reversing signs, like choosing (4,1) for right instead of left as in A, or swapping coordinates like (1,-4) in B. For coordinate plane: (1) start at origin (0,0), (2) move x (first coordinate: right if +, left if -), (3) move y (second coordinate: up if +, down if -), (4) mark point. Mistakes: direction from sign wrong, coordinates reversed, or vertical direction wrong.
A thermometer is shown as a vertical number line with equal spacing for each $5^\circ\text{C}$. The temperature changes are: $-10^\circ\text{C}$, $0^\circ\text{C}$, and $+20^\circ\text{C}$. Which statement correctly describes where $-10^\circ\text{C}$ is placed relative to $0^\circ\text{C}$ on the thermometer?
$-10^\circ\text{C}$ is 10 units to the right of $0^\circ\text{C}$.
$-10^\circ\text{C}$ is 10 units above $0^\circ\text{C}$.
$-10^\circ\text{C}$ is 2 tick marks above $0^\circ\text{C}$.
$-10^\circ\text{C}$ is 2 tick marks 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, on a vertical number line, position -3, 0, 1/2, 2.5: -3 is 3 units below 0, 0 at center, 1/2 halfway above 0 and 1, 2.5 halfway above 2 and 3. On this thermometer (vertical, each tick 5°C), -10°C is 2 tick marks (10°C) below 0°C, matching choice B. A common error is confusing direction, like placing negatives above 0 as in choices A and D, or miscalculating ticks (e.g., thinking 10 units right as in C). 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. Mistakes include vertical direction wrong (negatives up), scale ignored (not accounting for 5°C per tick), or confusing left/right with up/down.
A coordinate plane uses a scale of 1 unit per grid square on both axes. Which ordered pair is in Quadrant II (left of the $y$-axis and above the $x$-axis)?
$(-4,,-1)$
$(1,,-4)$
$(4,,1)$
$(-4,,1)$
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). The ordered pair in Quadrant II (x negative, y positive) is (-4,1), matching choice B. A common error is confusing quadrants, like picking (4,1) in I (A), (-4,-1) in III (C), or (1,-4) in IV (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 coordinates reversed, wrong signs for quadrants, or ignoring scale (1 unit per grid).
A coordinate plane uses a scale of 1 unit per grid square on both axes. Which point is in Quadrant II?
(Quadrant II has $x<0$ and $y>0$.)
$(3,,-2)$
$(-2,,-3)$
$(-4,,1)$
$(4,,1)$
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 correct point in Quadrant II (x<0, y>0) is (-4,1), matching choice B. A common error is selecting (4,1) in QI (choice A), or (-2,-3) in QIII (choice C), or (3,-2) in QIV (choice D), misidentifying signs for quadrants. To plot 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 coordinates reversed, wrong quadrant from signs.
A scuba diver’s elevation relative to sea level is shown on a vertical number line (up is positive, down is negative). Which value should be placed 2.5 units below $0$?
$-2.5$
$-0.25$
$-25$
$2.5$
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, on a vertical number line, position -3, 0, 1/2, 2.5: -3 is 3 units below 0, 0 at center, 1/2 halfway above 0 and 1, 2.5 halfway above 2 and 3. The value 2.5 units below 0 is -2.5, matching choice B. A common error is placing positives below like 2.5 (A) or wrong decimals like -0.25 (C) or -25 (D), or reversing vertical direction. 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. Mistakes include vertical direction wrong (negatives up), scale ignored, or confusing below with above.
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?
Not enough information to tell.
$-\tfrac{3}{2}$
$1.4$
They are the same distance from $0$.
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. 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).