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FInde twoo numbers, where of the 2/•• of the one number may bee egal vnto the 〈◊〉〈◊〉 of the other. Aun∣swere: you shall reduce 2/7 & ⅜ crossewise, and you shall finde 16. ouer the ⅔ and 21. ouer the ⅜, which are the two num∣bers that you seeke: for the ⅜ of 16. are 6. and so are the 2/•• of 21. lykewise 6. wherefore you may perceiue that the
the ⅜ of 16. which are 6. are egall vnto the 2/7 of 21. whiche is also 6.
2. Finde twoo numbers, wherof y• 2/•• of the one may be double to the ¼ of the other. Aunswere: double ¼ & you shal haue 2/4, which being abbreuiated is ½: thē reduce ⅔ & ½ crossewise, & you shall finde 4. ouer the ⅔ & three ouer the ½ which are the two numbers that you seeke. For the 2/1 of 3. which is 2. is double vnto the ¼ of 4. which is but 1.
3. Finde two numbers whereof the ⅔ and the ¼ of the one, maye bee egall vnto the ¼ & ⅕ of the other. Aunswere: Adde the ⅓ and ¼ togither, and they make 7/12 then adde ¼ and ••/5 togither, & they are 6/20, then reduce 7/17 & 9/20 crosse∣wise, & you shall haue 140. ouer the 7/12 & 108. ouer the 9/20, whiche are the two nūbers that you seke. For 63. whiche are the 7/12 of 108. are also the 9/20 of 140.
4. Finde two numbers, wherof the ••/2 the and the ¼ of the one of them, maye by egall vnto the ⅕ the ⅙ and 1/7 of the other number. Aunswere: first you
must adde ½, ⅓, and ¼ togither, & they make 13/12: then adde ⅕, ⅙ and 1/7 togi∣ther, & they make 207/210. Then reduce 13/12 and 107/210 crossewise, as by the fyrste question of reduction, and you shall finde 2730. ouer the 13/12 and 1284. ouer the 107/210, whiche are the twoo nombers that you seeke: for 1391 which is the ½ the ⅓ and ¼ of 1284. is lyke to the 11/56 & ¼ of 2730, which is also 1391.
5. Finde three nombers, whereof the ⅖ of the first, the 4/7 of the seconde, & the 4/9 of the thirde, maye be egall the one to the other. Aunswere: set downe the 23/57 and 〈◊〉〈◊〉, and then multiplie the Denominator of the ⅖ that is to saye 5. by the Numerators of the other twoo Fractions, that is to saye, by the Nu∣merator of 3/7, and by the Numerator of 4/9, whiche is 3. and 4. And thereof commeth 60. for your fyrste nomber, then shall you multiplye the Deno∣minator of the 3/7 whiche is 7. by the Numerators of ⅕ and 4/9, that is to say by 2. and 4. and thereof commeth 56.
for the seconde number: Then multi∣plie the Denominator of 4/9, that is 9. by the Numerators of ⅖ and ••/7 that is by 2. and by 3. and thereof commeth 54. for the third nomber
And thus the ⅖ of 60. which is 24. is li∣kewise the 3/7 of 56. whiche is the se∣cond nomber and the 4/9 of 54. whiche is the thirde nomber.
6. Finde three nombers, of whiche the fyrste and the seconde maye bee in suche proporcion as ½ and ⅓, and the se∣conde and thirde in suche proportion as ¼ and ⅕. Aunswere: reduce ½ and ⅓ crossewise, and you shall haue 3. ouer the ½ and 2. ouer the ⅓, then reduce ¼ and ⅕ in lyke maner, and you shall fynde 5. ouer the ¼ and 4. ouer the 3/••. Then say by the Rule of three, •••• 5. do gyue me 4. what shall twoo gyue me, whiche is the seconde proportio∣nall, multiply the seconde nomber 4. by the thyrde nomber twoo, and ther∣of commeth eyght, the whiche diuide
by the first number 5. and therof com∣meth 1. ⅗ for the third proportionall, and you shal fynde that 3. 2. 1. ⅗ are the three nombers proportionall that I demaunde, or els 15. 10. & 8. in whole numbers.
1. What number is that, vnto the whiche if you doe adde 13. the whole amounteth to 31. Aunswere: rebate 13. from 31. and there wyll remaine 18. which is the number that you seeke.
2. What number is that, vnto the which if you adde ⅖ the addition wyll be ⅚. Answere: abate ⅖ from ⅚, and there will remaine 13/30, whiche is the number that you desire.
3. What number is that, whereun∣to if you adde 7. ⅔, the whole additiō will be 12. ¼. Aunswere: abate 7. ⅔ frō 12. ¼. & the remaine will be 4 7/12 which is the number yt you desire to know.
4. What number is that, where∣into if you adde the ¾ of it selfe, that is to say, of the nūber that your séeke, the whole addition may be ⅚.
Aunswere: Here followeth a generall rule for all suche like questions. First, of. 3. whiche is the numeratour of. ¾. make still the numeratour, and like∣wise of. 3. and. 4 together, whiche is bothe the numerator, and the deno∣minator of the. ¾. make your denomi∣natour, so you shall finde. 3/7, then take the 3/7 of ⅚, whiche is 15/42, or 5/14; and sub∣stracte theim from ⅚, and there will remaine 10/21, whiche is the nomber that you seke.
5. What nomber is that, vnto the whiche if you adde his owne ⅔. that is to saie ⅔. of it self, the whole addition shall bee. 20. Aunswere: do••e as in the laste question: of the numeratour of ⅔ that is to saie, of. 2. make stil your nu∣merator. And likewise of the nume∣rator. 2. and the denominator. 3. of the ⅔, make of them bothe, your denomi∣nator, and you shall finde ⅖, then take the ⅖. of. 20. whiche are. 8. And abate them from. 20. and there will remain 12. whiche is the nomber that you de∣sire,
and so is to bee dooen of all suche like reasons.
1. What nomber is that, from the whiche if you dooe abate. 17. the reste maie bee. 19. Aunswere: adde. 17. and 19. together, and you shall finde. 36. whiche is the nomber that you seke.
2. What nomber is that, from the whiche if you abate ⅗, the rest maie bée ⅛. Aunswere: adde ⅗ and ⅛ together, and you shall finde 29/40, whiche is the nomber that you demaunde.
3. What nomber is that, from the whiche if you deduct. 13. ½ the rest maie be. 5. 5/7. Aunswere: adde. 13. ½ and. 5. 5/7. together, and there of commeth. 19. 1¾, whiche is the nomber that you seke.
4. What nomber is that, from the whiche if you substracte his ⅖, the reste maie bee. 12. Aunswere: and a rule for * 1.1 suche like reasons, that is to saie, from the denominator of 5/2. whiche is. 5. a∣bate. 2. whiche is his numerator, and there resteth. 3. for the denominator, and thus of ⅖. you haue you made ⅖,
then take the 〈◊〉〈◊〉 of. 12. whiche are 8: and adde them vnto. 12. and therof cōmeth 20. for the nomber whiche you desire.
5. What nomber is that, from the whiche if you doe abate his ¾, the reste maie bee 8/••. Aunswere: from the deno∣minator of ¾, whiche is. 4. substracte his numerator. 3. and there resteth. 1. Thus of ¾. you haue made. 3/1. Then multiplie 5/•• by 8/9, and therof commeth 2. ⅔, the whiche adde vnto 8/9, and you shall haue. 3. 5/9, whiche is the nomber that you seke.
6. What nomber is that, from the whiche if ye abate his ⅘, the rest maie be. 12. ⅔. Aunswere: Doe as you did in the laste question, and you shall finde that the ⅘. will bee 4/1. And therefore multiplie. 12. ⅔ by 4/1, and thereof com∣meth. 50 ⅔, the whiche adde vnto. 12 ⅔, and you shall finde. 93. 〈◊〉〈◊〉, for the nom∣ber that you demaunde. And thus of all like questions.
1. What nomber is that, which be∣yng multiplied by 13. the whole. Mul∣••iplication
shal m••••nte to. 221. Aun∣swere: 〈…〉〈…〉de. 221. by. 13. and thereof comnieth. 17. whiche is the nomber that you seeke.
2. What nomber is that, whiche beyng multiplied by. 15. the whole multiplication wil amount to ¾. Aun∣swere: diuide ¼. by 15/1. and thereof com∣meth 1/20. whiche is the noumber, that you seeke.
3. What nomber is that, whiche beeyng multiplied by. 21. the whole multiplication will bee: 16. ⅘. Aun∣swere: diuide. 16. ⅘. by. 21/5, and you shall finde ⅘, whiche is the nomber that you demaund••.
4. What nomber is that, whiche beyng multiplied by ¾. the multipli∣plication will amounte to. 18. Aun∣swere: diuide 18/1 by ¾, and there of com∣meth. 24. whiche is the nomber that you desire to knowe.
5. What nomber is that, whiche if it bee multiplied by ⅔. the whole mul∣tiplication will bee. ••/4. Aunswere: di∣uide
¼ by ⅔. and the quotient will bee ⅜, whiche is the nomber that you re∣quire to knowe.
6. What noumber is that, whiche beyng multiplied by ⅝, the product of that multiplication will bee. 16. ⅔. Aunswere: diuide. 16. by ⅔. by 〈◊〉〈◊〉. and thereof commeth. 26. ⅔, whiche is the nomber that you seeke.
I Demaunde howe muche the ⅝ of. 20. shillynges are worth or what are the ⅝. of. 20. shil∣lynges. Aunswere: you muste multiplie ⅝ by 1••/5, and the product will bee 100/8, therefore diuide. 100. by. 8. and thereof commeth. 12. ½, whiche is to saie. 12. shillynges. 6. pence, and so muche are the 5/••. of. 20. shillynges worthe.
2. I demaunde what the ¼ of ⅚ of 〈◊〉〈◊〉 pounde of money are worthe, that is to sa••e, of. 20. shillynges. Aunswere: multiplie. ¾. by ⅚. And thereof com∣meth 5/2. Then take the 5/•• of 20. shillin∣ges, as in the last questiō goyng before and you shall finde. 12. shillynges. 6. pence, and so muche are the ¾ of ⅚, of 20 shillynges worthe.
3. I demaunde what the ⅔ of. 8. pence ••/2 are worth. Aunswere: multiplie. 8. ••/2 by ⅔, or els ⅔ by. 8. & ••/2 whiche is all one, and you shall finde 34/6. Then diuide 34 by. 6. and your quotient will bee fiue pence ⅔, and so muche are the. 〈◊〉〈◊〉. of. 8. pence 〈◊〉〈◊〉 〈…〉〈…〉the.
4. What are the ¾. of. 14. pence 〈◊〉〈◊〉, Aunswers multiplie. 14. ⅗ by ¾, and therof commeth 219/20. Therefore diuide 219. by. 20. and your quotiente will bee. 10. pence 19/20. and so muche are the ••/4 of. 14. ••/5.
5. How many 〈◊〉〈◊〉 of sworth 〈◊〉〈◊〉 ••••••contain••r in. 7. ⅔. Aunswer multiplie, 7. ⅔ by 4/•• (because one whole
containeth. 4. quarters) and thereof commeth, 30. ⅔, and so many quarters are in the. 7. ⅔. that is to saie. 30. quar∣ters, and ⅔ of a quarter.
6. Howe many thirdes are in ¾ and ••/2, that is to saie in. 3, quarters, and ••/2 of one quarter, whiche are ⅞ by the 〈◊〉〈◊〉 reduction. Aunswere: multiplie 7/•• by 〈◊〉〈◊〉 (for because that in one whol•• are cō∣tained. 3. thirdes) and thereof wil come ⅔ and ⅝ of a third, and so many thirdes are in ¾ and ½ or in ⅞, whiche is al one
WHat nomber is that, which beyng diuided by. 17. the quotiente will bee. 13. Aun∣swere: multiplie. 17. by. 13. And thereof commeth. 221. whiche is the nomber that you seke.
2. What nomber is that, which be∣yng diuided by ¾, the quotient will be 21. Aunswere: multiplie 23/1. by ••/4 and therof cōmeth 63/4. Then diuide. 〈◊〉〈◊〉 by 4
and thereof commeth. 15. ¾, whiche is the nomber that you seke.
3. What nomber is that, which be∣yng diuided by. ⅛, the quotiente will bee ⅔. Aunswere: multiplie 2/1. by ⅛. and thereof commeth 2/24, whiche bee∣yng abreuiated are 1/12. for the nomber, whiche you require.
4. What nomber is that, whiche beyng diuided by ⅘. the quotient will be. 16. ⅔? Aunswere: multiplie. 16. ⅔, by ⅘, and thereof commeth 200/15. There∣fore diuide. 200. by. 15. and thereof cō∣meth. 13. ••/3, whiche is the nomber that you desire to finde.
5. What nomber is that, which be∣yng diuided by. 13. ⅓, the quotient will bee. 20. Aunswere: multiplie 〈◊〉〈◊〉, by. 13 〈◊〉〈◊〉 and thereof commeth 900/3, then diuide 800. by. 3. and thereof commeth. 266 〈◊〉〈◊〉 for the nomber, whiche you seeke,
6. What nomber is that, whiche it it hee diuided, by. 12. ½, the quotiente wil be 7/••. Answere: multiplie 7/•• by. 12 ½ and thereof commeth 175/〈…〉〈…〉, then diuide
175 by. 16. and thereof commeth. 10 15/•••• for the nomber whiche you desire.
I Demaunde what parte. 30. is of. 70. Aunswer: diuide. 30. by 70. whiche you can not, for thei are 30/7••, but abreuiate them and thei are 3/7. Thus. 30. are the 3/7. of. 70.
2. I demaunde what parte. 10. is of 16 ⅔. Aunswere: diuide. 10/〈…〉〈…〉. by. 16 ⅔, and thereof commeth 30/50, whiche beyng a∣breuiated are 〈◊〉〈◊〉. And thus 10. is found to bee ⅗ of. 16. 2/••.
3. More, what parte is. 25. of. 5/••. Aunswere: diuide 5/••. by. 25/10, and there∣of commeth 5/20••, whiche beyng abre∣niated is. 1/40. And thus. 5/••. is but the 1/40. of. 25.
4. More, ⅚ what parte are thei of ⅞ Aunswere: diuide ⅚ by ⅞, and you shal
finde 4••/42 whiche abreuiated are 20/21.
5. More, ⅘ what parte are thei of. 13. 〈◊〉〈◊〉. Aunswer: diuide ⅘ by. 13. ⅓. and you shall finde 12/200, whiche beyng abbre∣uiated are ••/50. And thus 4/1 are the 3/50. of 13. ⅓.
6. More. 12. ½. what parte are thei of. Aunswere: diuide. 12. ½. by 30/••, and you shall finde. ••5/60, whiche beyng abre∣uiated are ••/12, and thus. 12. ½, are the 5/12 of. 30.
7. More. 16. ••/3, what parte are thei of. 57. 1/7. Aunswere: diuide. 16. ⅔ by. 57 ••/7. and therof commeth 550/1200, whiche be∣yng abreuiated are 7/24, and thus. 16. ⅔. are the. 7/24 of. 57. 1/7.
8. More, ••/4 and ⅔ of ••/4, or three quar∣ters, and ⅖ of one quarter, what part are thei of. 1. Aunswere: reduce 5/4, and the ⅔ of ••/4, into one broken by the first reduction, and you shall finde 11/12. And thus the ••/4, and ••/3 of ¼ are the 11/12 of one whole.
9. More, of what nomber are. 9. the 〈◊〉〈◊〉. Aunswere: diuide. 9. by 3/3, and thereof
commeth. 13. ••/2, whiche is the nomber whereof. 9. are the 〈◊〉〈◊〉.
10. More, of what nomber are ⅘ the ••/4. Aunswere: diuide ⅖ by ¾, and thereof commeth 8/15, whiche is the nōber wher¦of 2/•• are the ¾ of the same nomber.
11. More, of what nomber are. 5. ¾. the ••/7. Aunswere: diuide. 15. ¾ by 3/••, and you shall finde. 13. 5/12, whiche is the nō∣ber whereof. 5, ••/4 are the 3/7.
12. More. 9. 〈◊〉〈◊〉 what parte are thei of. 33. Aunswere: diuide. 9. 2/•• by 33. ½. And thereof com∣meth 18/20••: and thus 9. 〈◊〉〈◊〉 are the 58/201 of 33. ½ as ap∣pereth.
A rule.