# Ratio and Proportion Foundations

This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.

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-20260930-r02-ratio-proportion-foundations · 2026-09-30 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of -12:(1). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation-12/1

Divide the antecedent by the consequent in the stated order and normalize the result to -12/1.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0001/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 2. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of -11:(-2). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation11/2

Divide the antecedent by the consequent in the stated order and normalize the result to 11/2.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0002/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 3. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of -10:(3). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation-10/3

Divide the antecedent by the consequent in the stated order and normalize the result to -10/3.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0003/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 4. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of -9:(-4). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation9/4

Divide the antecedent by the consequent in the stated order and normalize the result to 9/4.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0004/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 5. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of -8:(5). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation-8/5

Divide the antecedent by the consequent in the stated order and normalize the result to -8/5.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0005/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 6. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of -7:(-6). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation7/6

Divide the antecedent by the consequent in the stated order and normalize the result to 7/6.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0006/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 7. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of -6:(7). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation-6/7

Divide the antecedent by the consequent in the stated order and normalize the result to -6/7.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0007/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 8. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of -5:(-8). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation5/8

Divide the antecedent by the consequent in the stated order and normalize the result to 5/8.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0008/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 9. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of -4:(1). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation-4/1

Divide the antecedent by the consequent in the stated order and normalize the result to -4/1.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0009/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 10. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of -3:(-2). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation3/2

Divide the antecedent by the consequent in the stated order and normalize the result to 3/2.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0010/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 11. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of -2:(3). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation-2/3

Divide the antecedent by the consequent in the stated order and normalize the result to -2/3.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0011/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 12. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of -1:(-4). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation1/4

Divide the antecedent by the consequent in the stated order and normalize the result to 1/4.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0012/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 13. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 0:(5). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation0/1

Divide the antecedent by the consequent in the stated order and normalize the result to 0/1.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0013/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 14. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 1:(-6). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation-1/6

Divide the antecedent by the consequent in the stated order and normalize the result to -1/6.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0014/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 15. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 2:(7). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation2/7

Divide the antecedent by the consequent in the stated order and normalize the result to 2/7.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0015/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 16. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 3:(-8). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation-3/8

Divide the antecedent by the consequent in the stated order and normalize the result to -3/8.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0016/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 17. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 4:(1). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation4/1

Divide the antecedent by the consequent in the stated order and normalize the result to 4/1.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0017/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 18. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 5:(-2). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation-5/2

Divide the antecedent by the consequent in the stated order and normalize the result to -5/2.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0018/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 19. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 6:(3). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation2/1

Divide the antecedent by the consequent in the stated order and normalize the result to 2/1.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0019/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 20. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 7:(-4). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation-7/4

Divide the antecedent by the consequent in the stated order and normalize the result to -7/4.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0020/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 21. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 8:(5). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation8/5

Divide the antecedent by the consequent in the stated order and normalize the result to 8/5.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0021/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 22. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 9:(-6). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation-3/2

Divide the antecedent by the consequent in the stated order and normalize the result to -3/2.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0022/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 23. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 10:(7). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation10/7

Divide the antecedent by the consequent in the stated order and normalize the result to 10/7.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0023/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 24. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 11:(-8). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation-11/8

Divide the antecedent by the consequent in the stated order and normalize the result to -11/8.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0024/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 25. Exact Value of a Numerical Ratio

In the rational numerical-ratio setting, find the exact value of 12:(1). The consequent is nonzero; answer as a reduced p/q with a positive denominator.

View answer and explanation12/1

Divide the antecedent by the consequent in the stated order and normalize the result to 12/1.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-ratio-exact-value-0025/)

Ratio and proportion · qf-ratio-exact-value · candidate





## 26. Exact Proportion Check

In the rational numerical-ratio setting, is -12:(-1)=-24:(-2) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are 24 and 24; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0001/)

Ratio and proportion · qf-proportion-verification · candidate





## 27. Exact Proportion Check

In the rational numerical-ratio setting, is -11:(2)=34:(-6) a valid proportion? Both consequents are nonzero.

View answer and explanationNo

The exact cross products are 66 and 68; they are different, so the answer is No.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0002/)

Ratio and proportion · qf-proportion-verification · candidate





## 28. Exact Proportion Check

In the rational numerical-ratio setting, is -10:(3)=-40:(12) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are -120 and -120; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0003/)

Ratio and proportion · qf-proportion-verification · candidate





## 29. Exact Proportion Check

In the rational numerical-ratio setting, is -9:(-4)=46:(20) a valid proportion? Both consequents are nonzero.

View answer and explanationNo

The exact cross products are -180 and -184; they are different, so the answer is No.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0004/)

Ratio and proportion · qf-proportion-verification · candidate





## 30. Exact Proportion Check

In the rational numerical-ratio setting, is -8:(5)=-48:(30) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are -240 and -240; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0005/)

Ratio and proportion · qf-proportion-verification · candidate





## 31. Exact Proportion Check

In the rational numerical-ratio setting, is -7:(6)=15:(-12) a valid proportion? Both consequents are nonzero.

View answer and explanationNo

The exact cross products are 84 and 90; they are different, so the answer is No.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0006/)

Ratio and proportion · qf-proportion-verification · candidate





## 32. Exact Proportion Check

In the rational numerical-ratio setting, is -6:(-7)=-18:(-21) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are 126 and 126; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0007/)

Ratio and proportion · qf-proportion-verification · candidate





## 33. Exact Proportion Check

In the rational numerical-ratio setting, is -5:(8)=21:(-32) a valid proportion? Both consequents are nonzero.

View answer and explanationNo

The exact cross products are 160 and 168; they are different, so the answer is No.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0008/)

Ratio and proportion · qf-proportion-verification · candidate





## 34. Exact Proportion Check

In the rational numerical-ratio setting, is -4:(1)=-20:(5) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are -20 and -20; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0009/)

Ratio and proportion · qf-proportion-verification · candidate





## 35. Exact Proportion Check

In the rational numerical-ratio setting, is -3:(-2)=19:(12) a valid proportion? Both consequents are nonzero.

View answer and explanationNo

The exact cross products are -36 and -38; they are different, so the answer is No.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0010/)

Ratio and proportion · qf-proportion-verification · candidate





## 36. Exact Proportion Check

In the rational numerical-ratio setting, is -2:(3)=-4:(6) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are -12 and -12; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0011/)

Ratio and proportion · qf-proportion-verification · candidate





## 37. Exact Proportion Check

In the rational numerical-ratio setting, is -1:(4)=4:(-12) a valid proportion? Both consequents are nonzero.

View answer and explanationNo

The exact cross products are 12 and 16; they are different, so the answer is No.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0012/)

Ratio and proportion · qf-proportion-verification · candidate





## 38. Exact Proportion Check

In the rational numerical-ratio setting, is 0:(-5)=0:(-20) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are 0 and 0; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0013/)

Ratio and proportion · qf-proportion-verification · candidate





## 39. Exact Proportion Check

In the rational numerical-ratio setting, is 1:(6)=-4:(-30) a valid proportion? Both consequents are nonzero.

View answer and explanationNo

The exact cross products are -30 and -24; they are different, so the answer is No.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0014/)

Ratio and proportion · qf-proportion-verification · candidate





## 40. Exact Proportion Check

In the rational numerical-ratio setting, is 2:(7)=12:(42) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are 84 and 84; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0015/)

Ratio and proportion · qf-proportion-verification · candidate





## 41. Exact Proportion Check

In the rational numerical-ratio setting, is 3:(-8)=-5:(16) a valid proportion? Both consequents are nonzero.

View answer and explanationNo

The exact cross products are 48 and 40; they are different, so the answer is No.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0016/)

Ratio and proportion · qf-proportion-verification · candidate





## 42. Exact Proportion Check

In the rational numerical-ratio setting, is 4:(1)=12:(3) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are 12 and 12; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0017/)

Ratio and proportion · qf-proportion-verification · candidate





## 43. Exact Proportion Check

In the rational numerical-ratio setting, is 5:(2)=-19:(-8) a valid proportion? Both consequents are nonzero.

View answer and explanationNo

The exact cross products are -40 and -38; they are different, so the answer is No.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0018/)

Ratio and proportion · qf-proportion-verification · candidate





## 44. Exact Proportion Check

In the rational numerical-ratio setting, is 6:(-3)=30:(-15) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are -90 and -90; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0019/)

Ratio and proportion · qf-proportion-verification · candidate





## 45. Exact Proportion Check

In the rational numerical-ratio setting, is 7:(4)=-41:(-24) a valid proportion? Both consequents are nonzero.

View answer and explanationNo

The exact cross products are -168 and -164; they are different, so the answer is No.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0020/)

Ratio and proportion · qf-proportion-verification · candidate





## 46. Exact Proportion Check

In the rational numerical-ratio setting, is 8:(5)=16:(10) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are 80 and 80; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0021/)

Ratio and proportion · qf-proportion-verification · candidate





## 47. Exact Proportion Check

In the rational numerical-ratio setting, is 9:(-6)=-26:(18) a valid proportion? Both consequents are nonzero.

View answer and explanationNo

The exact cross products are 162 and 156; they are different, so the answer is No.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0022/)

Ratio and proportion · qf-proportion-verification · candidate





## 48. Exact Proportion Check

In the rational numerical-ratio setting, is 10:(7)=40:(28) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are 280 and 280; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0023/)

Ratio and proportion · qf-proportion-verification · candidate





## 49. Exact Proportion Check

In the rational numerical-ratio setting, is 11:(8)=-54:(-40) a valid proportion? Both consequents are nonzero.

View answer and explanationNo

The exact cross products are -440 and -432; they are different, so the answer is No.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0024/)

Ratio and proportion · qf-proportion-verification · candidate





## 50. Exact Proportion Check

In the rational numerical-ratio setting, is 12:(-1)=72:(-6) a valid proportion? Both consequents are nonzero.

View answer and explanationYes

The exact cross products are -72 and -72; they are equal, so the answer is Yes.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-verification-0025/)

Ratio and proportion · qf-proportion-verification · candidate





## 51. Missing Term in a Proportion

Solve the rational proportion -12/(1)=x/(-2). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation24/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=24/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0001/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 52. Missing Term in a Proportion

Solve the rational proportion -11/(-2)=x/(3). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation33/2

From bx=ad, x=ad/b. Exact substitution and reduction give x=33/2, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0002/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 53. Missing Term in a Proportion

Solve the rational proportion -10/(3)=x/(4). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation-40/3

From bx=ad, x=ad/b. Exact substitution and reduction give x=-40/3, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0003/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 54. Missing Term in a Proportion

Solve the rational proportion -9/(-4)=x/(-5). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation-45/4

From bx=ad, x=ad/b. Exact substitution and reduction give x=-45/4, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0004/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 55. Missing Term in a Proportion

Solve the rational proportion -8/(5)=x/(6). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation-48/5

From bx=ad, x=ad/b. Exact substitution and reduction give x=-48/5, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0005/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 56. Missing Term in a Proportion

Solve the rational proportion -7/(-6)=x/(2). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation7/3

From bx=ad, x=ad/b. Exact substitution and reduction give x=7/3, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0006/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 57. Missing Term in a Proportion

Solve the rational proportion -6/(7)=x/(-3). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation18/7

From bx=ad, x=ad/b. Exact substitution and reduction give x=18/7, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0007/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 58. Missing Term in a Proportion

Solve the rational proportion -5/(-1)=x/(4). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation20/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=20/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0008/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 59. Missing Term in a Proportion

Solve the rational proportion -4/(2)=x/(5). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation-10/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=-10/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0009/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 60. Missing Term in a Proportion

Solve the rational proportion -3/(-3)=x/(-6). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation-6/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=-6/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0010/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 61. Missing Term in a Proportion

Solve the rational proportion -2/(4)=x/(2). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation-1/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=-1/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0011/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 62. Missing Term in a Proportion

Solve the rational proportion -1/(-5)=x/(3). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation3/5

From bx=ad, x=ad/b. Exact substitution and reduction give x=3/5, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0012/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 63. Missing Term in a Proportion

Solve the rational proportion 0/(6)=x/(-4). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation0/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=0/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0013/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 64. Missing Term in a Proportion

Solve the rational proportion 1/(-7)=x/(5). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation-5/7

From bx=ad, x=ad/b. Exact substitution and reduction give x=-5/7, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0014/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 65. Missing Term in a Proportion

Solve the rational proportion 2/(1)=x/(6). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation12/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=12/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0015/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 66. Missing Term in a Proportion

Solve the rational proportion 3/(-2)=x/(-2). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation3/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=3/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0016/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 67. Missing Term in a Proportion

Solve the rational proportion 4/(3)=x/(3). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation4/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=4/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0017/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 68. Missing Term in a Proportion

Solve the rational proportion 5/(-4)=x/(4). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation-5/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=-5/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0018/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 69. Missing Term in a Proportion

Solve the rational proportion 6/(5)=x/(-5). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation-6/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=-6/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0019/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 70. Missing Term in a Proportion

Solve the rational proportion 7/(-6)=x/(6). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation-7/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=-7/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0020/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 71. Missing Term in a Proportion

Solve the rational proportion 8/(7)=x/(2). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation16/7

From bx=ad, x=ad/b. Exact substitution and reduction give x=16/7, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0021/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 72. Missing Term in a Proportion

Solve the rational proportion 9/(-1)=x/(-3). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation27/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=27/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0022/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 73. Missing Term in a Proportion

Solve the rational proportion 10/(2)=x/(4). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation20/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=20/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0023/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 74. Missing Term in a Proportion

Solve the rational proportion 11/(-3)=x/(5). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation-55/3

From bx=ad, x=ad/b. Exact substitution and reduction give x=-55/3, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0024/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 75. Missing Term in a Proportion

Solve the rational proportion 12/(4)=x/(-6). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.

View answer and explanation-18/1

From bx=ad, x=ad/b. Exact substitution and reduction give x=-18/1, uniquely because b≠0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-missing-term-0025/)

Ratio and proportion · qf-proportion-missing-term · candidate





## 76. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=-12. Does the explicit point (x,y)=(-3,36) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=36 and the stated y is 36; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0001/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 77. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=-11. Does the explicit point (x,y)=(-2,23) satisfy y=kx? Check only this point.

View answer and explanationNo

kx=22 and the stated y is 23; comparison gives No and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0002/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 78. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=-10. Does the explicit point (x,y)=(-1,10) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=10 and the stated y is 10; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0003/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 79. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=-9. Does the explicit point (x,y)=(0,1) satisfy y=kx? Check only this point.

View answer and explanationNo

kx=0 and the stated y is 1; comparison gives No and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0004/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 80. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=-8. Does the explicit point (x,y)=(1,-8) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=-8 and the stated y is -8; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0005/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 81. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=-7. Does the explicit point (x,y)=(2,-13) satisfy y=kx? Check only this point.

View answer and explanationNo

kx=-14 and the stated y is -13; comparison gives No and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0006/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 82. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=-6. Does the explicit point (x,y)=(3,-18) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=-18 and the stated y is -18; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0007/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 83. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=-5. Does the explicit point (x,y)=(-3,16) satisfy y=kx? Check only this point.

View answer and explanationNo

kx=15 and the stated y is 16; comparison gives No and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0008/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 84. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=-4. Does the explicit point (x,y)=(-2,8) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=8 and the stated y is 8; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0009/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 85. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=-3. Does the explicit point (x,y)=(-1,4) satisfy y=kx? Check only this point.

View answer and explanationNo

kx=3 and the stated y is 4; comparison gives No and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0010/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 86. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=-2. Does the explicit point (x,y)=(0,0) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=0 and the stated y is 0; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0011/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 87. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=-1. Does the explicit point (x,y)=(1,0) satisfy y=kx? Check only this point.

View answer and explanationNo

kx=-1 and the stated y is 0; comparison gives No and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0012/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 88. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=0. Does the explicit point (x,y)=(2,0) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=0 and the stated y is 0; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0013/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 89. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=1. Does the explicit point (x,y)=(3,4) satisfy y=kx? Check only this point.

View answer and explanationNo

kx=3 and the stated y is 4; comparison gives No and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0014/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 90. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=2. Does the explicit point (x,y)=(-3,-6) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=-6 and the stated y is -6; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0015/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 91. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=3. Does the explicit point (x,y)=(-2,-5) satisfy y=kx? Check only this point.

View answer and explanationNo

kx=-6 and the stated y is -5; comparison gives No and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0016/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 92. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=4. Does the explicit point (x,y)=(-1,-4) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=-4 and the stated y is -4; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0017/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 93. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=5. Does the explicit point (x,y)=(0,1) satisfy y=kx? Check only this point.

View answer and explanationNo

kx=0 and the stated y is 1; comparison gives No and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0018/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 94. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=6. Does the explicit point (x,y)=(1,6) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=6 and the stated y is 6; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0019/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 95. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=7. Does the explicit point (x,y)=(2,15) satisfy y=kx? Check only this point.

View answer and explanationNo

kx=14 and the stated y is 15; comparison gives No and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0020/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 96. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=8. Does the explicit point (x,y)=(3,24) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=24 and the stated y is 24; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0021/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 97. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=9. Does the explicit point (x,y)=(-3,-26) satisfy y=kx? Check only this point.

View answer and explanationNo

kx=-27 and the stated y is -26; comparison gives No and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0022/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 98. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=10. Does the explicit point (x,y)=(-2,-20) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=-20 and the stated y is -20; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0023/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 99. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=11. Does the explicit point (x,y)=(-1,-10) satisfy y=kx? Check only this point.

View answer and explanationNo

kx=-11 and the stated y is -10; comparison gives No and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0024/)

Ratio and proportion · qf-proportion-fixed-factor · candidate





## 100. Fixed-Factor Proportion Check

In the rational setting, the fixed factor is k=12. Does the explicit point (x,y)=(0,0) satisfy y=kx? Check only this point.

View answer and explanationYes

kx=0 and the stated y is 0; comparison gives Yes and does not justify any claim about other inputs.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260930-r02-proportion-fixed-factor-0025/)

Ratio and proportion · qf-proportion-fixed-factor · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20260930-r02-ratio-proportion-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20260930-r02-ratio-proportion-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20260930-r02-ratio-proportion-foundations/validation-report.json)