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This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.
batch-20260923-real-number-rational-points · 2026-09-23 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
Convert the explicit decimal string 0.5 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
1/2
0.5 is converted to an integer numerator over 10^1 and reduced by the gcd, giving 1/2.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 1.25 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
5/4
1.25 is converted to an integer numerator over 10^2 and reduced by the gcd, giving 5/4.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string -2.4 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
-12/5
-2.4 is converted to an integer numerator over 10^1 and reduced by the gcd, giving -12/5.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 3.125 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
25/8
3.125 is converted to an integer numerator over 10^3 and reduced by the gcd, giving 25/8.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 0.04 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
1/25
0.04 is converted to an integer numerator over 10^2 and reduced by the gcd, giving 1/25.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string -0.75 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
-3/4
-0.75 is converted to an integer numerator over 10^2 and reduced by the gcd, giving -3/4.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 12.5 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
25/2
12.5 is converted to an integer numerator over 10^1 and reduced by the gcd, giving 25/2.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 0.125 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
1/8
0.125 is converted to an integer numerator over 10^3 and reduced by the gcd, giving 1/8.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 2.05 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
41/20
2.05 is converted to an integer numerator over 10^2 and reduced by the gcd, giving 41/20.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string -1.2 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
-6/5
-1.2 is converted to an integer numerator over 10^1 and reduced by the gcd, giving -6/5.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 4.375 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
35/8
4.375 is converted to an integer numerator over 10^3 and reduced by the gcd, giving 35/8.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 0.625 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
5/8
0.625 is converted to an integer numerator over 10^3 and reduced by the gcd, giving 5/8.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 7.01 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
701/100
7.01 is converted to an integer numerator over 10^2 and reduced by the gcd, giving 701/100.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string -3.5 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
-7/2
-3.5 is converted to an integer numerator over 10^1 and reduced by the gcd, giving -7/2.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 8.2 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
41/5
8.2 is converted to an integer numerator over 10^1 and reduced by the gcd, giving 41/5.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 0.09 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
9/100
0.09 is converted to an integer numerator over 10^2 and reduced by the gcd, giving 9/100.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string -0.01 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
-1/100
-0.01 is converted to an integer numerator over 10^2 and reduced by the gcd, giving -1/100.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 15.625 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
125/8
15.625 is converted to an integer numerator over 10^3 and reduced by the gcd, giving 125/8.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 6.4 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
32/5
6.4 is converted to an integer numerator over 10^1 and reduced by the gcd, giving 32/5.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string -9.08 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
-227/25
-9.08 is converted to an integer numerator over 10^2 and reduced by the gcd, giving -227/25.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 0.2 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
1/5
0.2 is converted to an integer numerator over 10^1 and reduced by the gcd, giving 1/5.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 11.25 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
45/4
11.25 is converted to an integer numerator over 10^2 and reduced by the gcd, giving 45/4.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string -4.125 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
-33/8
-4.125 is converted to an integer numerator over 10^3 and reduced by the gcd, giving -33/8.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 2.75 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
11/4
2.75 is converted to an integer numerator over 10^2 and reduced by the gcd, giving 11/4.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
Convert the explicit decimal string 0.001 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
1/1000
0.001 is converted to an integer numerator over 10^3 and reduced by the gcd, giving 1/1000.
Reviewed step-by-step derivation
Real number · qf-real-terminating-decimal-fraction · candidate
The rational points are a=-12/1 and b=-6/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
-12×1 < -6×1, so -12/1 < -6/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=-11/2 and b=-5/2. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
-11×2 < -5×2, so -11/2 < -5/2.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=-10/3 and b=-4/3. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
-10×3 < -4×3, so -10/3 < -4/3.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=-9/4 and b=-3/4. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
-9×4 < -3×4, so -9/4 < -3/4.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=-8/5 and b=-2/5. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
-8×5 < -2×5, so -8/5 < -2/5.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=-7/6 and b=-1/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
-7×1 < -1×6, so -7/6 < -1/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=-6/7 and b=0/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
-6×1 < 0×7, so -6/7 < 0/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=-5/1 and b=1/3. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
-5×3 < 1×1, so -5/1 < 1/3.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=-2/1 and b=1/2. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
-2×2 < 1×1, so -2/1 < 1/2.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=-1/1 and b=3/5. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
-1×5 < 3×1, so -1/1 < 3/5.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=-1/2 and b=4/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
-1×1 < 4×2, so -1/2 < 4/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=-1/5 and b=5/2. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
-1×2 < 5×5, so -1/5 < 5/2.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=0/1 and b=2/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
<
0×1 < 2×1, so 0/1 < 2/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=1/7 and b=-3/2. Use cross multiplication to determine whether a<b, a=b, or a>b.
>
1×2 > -3×7, so 1/7 > -3/2.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=2/1 and b=-1/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
>
2×1 > -1×1, so 2/1 > -1/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=3/2 and b=-4/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
>
3×1 > -4×2, so 3/2 > -4/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=4/3 and b=-3/2. Use cross multiplication to determine whether a<b, a=b, or a>b.
>
4×2 > -3×3, so 4/3 > -3/2.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=5/4 and b=-2/3. Use cross multiplication to determine whether a<b, a=b, or a>b.
>
5×3 > -2×4, so 5/4 > -2/3.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=6/5 and b=-1/4. Use cross multiplication to determine whether a<b, a=b, or a>b.
>
6×4 > -1×5, so 6/5 > -1/4.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=7/6 and b=0/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
>
7×1 > 0×6, so 7/6 > 0/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=8/7 and b=1/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
>
8×1 > 1×7, so 8/7 > 1/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=9/1 and b=1/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
>
9×1 > 1×1, so 9/1 > 1/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=5/1 and b=1/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
>
5×1 > 1×1, so 5/1 > 1/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=11/3 and b=1/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
>
11×1 > 1×3, so 11/3 > 1/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The rational points are a=3/1 and b=1/1. Use cross multiplication to determine whether a<b, a=b, or a>b.
>
3×1 > 1×1, so 3/1 > 1/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-order · candidate
The closed interval [-12, -11] and rational point -12/1 are explicit. Does -12/1 belong to this closed interval?
Yes
Exact cross multiplication confirms -12≤-12/1≤-11; equality with an endpoint is included in a closed interval.
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [-11, -9] and rational point -5/1 are explicit. Does -5/1 belong to this closed interval?
No
Exact cross multiplication shows that -5/1 lies outside [-11, -9].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [-10, -7] and rational point -8/3 are explicit. Does -8/3 belong to this closed interval?
No
Exact cross multiplication shows that -8/3 lies outside [-10, -7].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [-9, -5] and rational point -3/2 are explicit. Does -3/2 belong to this closed interval?
No
Exact cross multiplication shows that -3/2 lies outside [-9, -5].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [-8, -3] and rational point -4/1 are explicit. Does -4/1 belong to this closed interval?
Yes
Exact cross multiplication confirms -8≤-4/1≤-3; equality with an endpoint is included in a closed interval.
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [-7, -1] and rational point -1/1 are explicit. Does -1/1 belong to this closed interval?
Yes
Exact cross multiplication confirms -7≤-1/1≤-1; equality with an endpoint is included in a closed interval.
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [-6, -5] and rational point -2/1 are explicit. Does -2/1 belong to this closed interval?
No
Exact cross multiplication shows that -2/1 lies outside [-6, -5].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [-5, -3] and rational point -1/1 are explicit. Does -1/1 belong to this closed interval?
No
Exact cross multiplication shows that -1/1 lies outside [-5, -3].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [-4, -1] and rational point -4/1 are explicit. Does -4/1 belong to this closed interval?
Yes
Exact cross multiplication confirms -4≤-4/1≤-1; equality with an endpoint is included in a closed interval.
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [-3, 1] and rational point 1/2 are explicit. Does 1/2 belong to this closed interval?
Yes
Exact cross multiplication confirms -3≤1/2≤1; equality with an endpoint is included in a closed interval.
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [-2, 3] and rational point 2/3 are explicit. Does 2/3 belong to this closed interval?
Yes
Exact cross multiplication confirms -2≤2/3≤3; equality with an endpoint is included in a closed interval.
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [-1, 5] and rational point 3/4 are explicit. Does 3/4 belong to this closed interval?
Yes
Exact cross multiplication confirms -1≤3/4≤5; equality with an endpoint is included in a closed interval.
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [0, 1] and rational point 0/1 are explicit. Does 0/1 belong to this closed interval?
Yes
Exact cross multiplication confirms 0≤0/1≤1; equality with an endpoint is included in a closed interval.
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [1, 3] and rational point 1/1 are explicit. Does 1/1 belong to this closed interval?
Yes
Exact cross multiplication confirms 1≤1/1≤3; equality with an endpoint is included in a closed interval.
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [2, 5] and rational point 4/3 are explicit. Does 4/3 belong to this closed interval?
No
Exact cross multiplication shows that 4/3 lies outside [2, 5].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [3, 7] and rational point 3/4 are explicit. Does 3/4 belong to this closed interval?
No
Exact cross multiplication shows that 3/4 lies outside [3, 7].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [4, 9] and rational point 8/1 are explicit. Does 8/1 belong to this closed interval?
Yes
Exact cross multiplication confirms 4≤8/1≤9; equality with an endpoint is included in a closed interval.
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [5, 11] and rational point 4/1 are explicit. Does 4/1 belong to this closed interval?
No
Exact cross multiplication shows that 4/1 lies outside [5, 11].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [6, 7] and rational point 2/1 are explicit. Does 2/1 belong to this closed interval?
No
Exact cross multiplication shows that 2/1 lies outside [6, 7].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [7, 9] and rational point 2/1 are explicit. Does 2/1 belong to this closed interval?
No
Exact cross multiplication shows that 2/1 lies outside [7, 9].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [8, 11] and rational point 8/1 are explicit. Does 8/1 belong to this closed interval?
Yes
Exact cross multiplication confirms 8≤8/1≤11; equality with an endpoint is included in a closed interval.
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [9, 13] and rational point 5/1 are explicit. Does 5/1 belong to this closed interval?
No
Exact cross multiplication shows that 5/1 lies outside [9, 13].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [10, 15] and rational point 14/3 are explicit. Does 14/3 belong to this closed interval?
No
Exact cross multiplication shows that 14/3 lies outside [10, 15].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [11, 17] and rational point 13/4 are explicit. Does 13/4 belong to this closed interval?
No
Exact cross multiplication shows that 13/4 lies outside [11, 17].
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
The closed interval [12, 13] and rational point 12/1 are explicit. Does 12/1 belong to this closed interval?
Yes
Exact cross multiplication confirms 12≤12/1≤13; equality with an endpoint is included in a closed interval.
Reviewed step-by-step derivation
Real number · qf-real-rational-closed-interval · candidate
Two rational real points are -10/1 and 12/1. Find the exact distance |-10/1−12/1| as a lowest-terms fraction.
22/1
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 22/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are -9/2 and 11/2. Find the exact distance |-9/2−11/2| as a lowest-terms fraction.
10/1
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 10/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are -8/3 and 10/3. Find the exact distance |-8/3−10/3| as a lowest-terms fraction.
6/1
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 6/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are -7/4 and 9/4. Find the exact distance |-7/4−9/4| as a lowest-terms fraction.
4/1
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 4/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are -6/5 and 8/5. Find the exact distance |-6/5−8/5| as a lowest-terms fraction.
14/5
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 14/5.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are -5/1 and 7/6. Find the exact distance |-5/1−7/6| as a lowest-terms fraction.
37/6
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 37/6.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are -2/1 and 6/7. Find the exact distance |-2/1−6/7| as a lowest-terms fraction.
20/7
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 20/7.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are -1/1 and 5/1. Find the exact distance |-1/1−5/1| as a lowest-terms fraction.
6/1
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 6/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are -1/2 and 2/1. Find the exact distance |-1/2−2/1| as a lowest-terms fraction.
5/2
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 5/2.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are -1/5 and 1/1. Find the exact distance |-1/5−1/1| as a lowest-terms fraction.
6/5
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 6/5.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 0/1 and 1/2. Find the exact distance |0/1−1/2| as a lowest-terms fraction.
1/2
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 1/2.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 1/2 and 1/5. Find the exact distance |1/2−1/5| as a lowest-terms fraction.
3/10
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 3/10.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 2/3 and 0/1. Find the exact distance |2/3−0/1| as a lowest-terms fraction.
2/3
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 2/3.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 3/4 and -1/7. Find the exact distance |3/4−-1/7| as a lowest-terms fraction.
25/28
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 25/28.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 4/5 and -2/1. Find the exact distance |4/5−-2/1| as a lowest-terms fraction.
14/5
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 14/5.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 5/1 and -3/2. Find the exact distance |5/1−-3/2| as a lowest-terms fraction.
13/2
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 13/2.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 3/1 and -4/3. Find the exact distance |3/1−-4/3| as a lowest-terms fraction.
13/3
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 13/3.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 7/3 and -5/4. Find the exact distance |7/3−-5/4| as a lowest-terms fraction.
43/12
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 43/12.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 2/1 and -6/5. Find the exact distance |2/1−-6/5| as a lowest-terms fraction.
16/5
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 16/5.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 9/5 and -7/6. Find the exact distance |9/5−-7/6| as a lowest-terms fraction.
89/30
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 89/30.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 10/1 and -8/7. Find the exact distance |10/1−-8/7| as a lowest-terms fraction.
78/7
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 78/7.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 11/2 and -9/1. Find the exact distance |11/2−-9/1| as a lowest-terms fraction.
29/2
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 29/2.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 4/1 and -5/1. Find the exact distance |4/1−-5/1| as a lowest-terms fraction.
9/1
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 9/1.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 13/4 and -11/3. Find the exact distance |13/4−-11/3| as a lowest-terms fraction.
83/12
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 83/12.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
Two rational real points are 14/5 and -3/1. Find the exact distance |14/5−-3/1| as a lowest-terms fraction.
29/5
Subtract the integer numerator-denominator pairs exactly and take the absolute value, giving 29/5.
Reviewed step-by-step derivation
Real number · qf-real-rational-point-distance · candidate
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