The welspring of sciences, which teacheth the perfecte worke and practise of arithmeticke both in vvhole numbers & fractions, with such easie and compendious instruction into the saide art, as hath not heretofore been by any set out nor laboured, : Beautified vvith most necessary rules and questions, not onely profitable for marchauntes, but also for all artificers, as in the table doth plainely appere..

¶The 4. Chapter treateth of the assem∣bling of two or many broken num∣bers togither, as by example.

FOr to adde broken numbers togither, there is a generall rule, which is thus, if y^e nū∣bers be vnlike the one to y^e other you must reduce thē into a cōmon deno∣minatiō, which after you haue redu∣ced thē, you must then adde both the numerators togither, & set y^e product of the saide addition ouer the crosse, & diuide the same by the cōmon deno¦minator as by this exāple folowing.

1. If you wyll adde ⅔ with ¾, you must fyrst reduce the twoo fractions both into one denomination, accor∣ding to the introduction of the fyrste reduction, that is to saye, in mul∣tiplying the denominator of the firste fraction which is 3, by the denomi∣nator of the other fraction whiche is foure, and they make 12. for your common de∣nominator, y^e which 12. set vnder the crosse, thē multiplie y^e fyrst nume∣rator 2. by the last deno∣minator 4. and thereof commeth 8. which set o∣uer the ⅔, and then mul∣tiply y^e last numerator 3. by the fyrst denominator 3. and ther∣of commeth 9. which you must set o∣uer the ¾, then adde the numerator 8. with the numerator 9. & they make 17. which set ouer the crosse, and then your fraction wyll be 17/12 which is the addition of the ⅔ wyth ¾.〈 math 〉〈 math 〉 And by∣cause

your numerator 17. is greater thā his denominator 12. therfore you must diuide 17. by 12. and thereof will come 1. and 5. remaining, which 5. are worth 5/12, and so much are y^e ⅔ added with ¾ as doth appere.

¶Addition in broken numbers.

2. Also if you wyll adde ½, ⅔, ¾, ⅘, togither, you muste fyrste adde the ½ and ⅔ togither, according to the doc∣trine of the laste rule, and you shall finde 7/6: then adde ¾ and ⅘ togither by the saide last chapter, and they make 31/20. Then finally adde the 7/6 (which came of the ½ and ⅔ added togither) with 13/20, & you shall fynde by y^e fore∣saide addition that they amount vn∣to 326/120. Wherefore diuide 326. by 120. & therof cōmeth 2. and 86. remaineth, which is 86/120 of one whole, & thei being abreuied do make 43/60: & thus y^e ½, ⅔, ¾, ⅘, added togither doe amount to 2.43/00,

as here vnder doth appere.

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¶Addition of broken numbers of broken.

3. Furthermore, if you will adde the broken numbers of broken togi∣ther, as to adde the ⅔ of ¾ of ⅘ with the ⅚ of ½ of ⅝: first you must reduce y^e nū∣bers according to y^e order of y^e fourth reduction, in multiplying the nume∣rator of the fyrst 3. fractions, the one by the other, and of the product make your numerator, & likewise you must multiplie y^e denominators of y^e fore∣said thre fractions, y^e one by the other

and of the product make your deno∣minator, and you shal finde 24/60 for the fyrst thre broken numbers, which be∣ing abbreuied do make ⅖, thē reduce the other 3. fractiōs, by y^e saide fourth reduction, in multiplying the nume∣rators by numerators, & denomina∣tors, by denominators, as you did by the first 3. broken numbers, & you shal finde 25/96 thē must you adde y^t ⅖ which came of the fyrst 3. broken numbers, & 25/96 which are of the last 3. fractions, both togither, by the instruction of y^e first additiō & you shal find 317/480 which cannot be abbreuied, but is y^e product of y^e additiō: so much are the ⅔ of ¾ of ⅘ added with the ⅚ of ½ of ⅝ as hereaf∣ter by practise doth euidently appere.

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¶Addition of broken number with the partes of broken togither.

4. Likewise if you will adde the ⅓, and the ½ of ⅓ with the ⅘ and ¼ of ⅕, you must reduce the ⅔ ½ by the fyft reduc∣tion and therof cōmeth ⅚ for the ⅔ & ½, of one of the saide thirdes, thē reduce the ⅘ and ¼ by the saide fift reduction, and thereof commeth 17/20.

Last of all adde the ⅚ and 17/20 togither according to the fyrst rule of additiō, and you shall fynde 202/120 which beyng diuided bringeth 1. & 82/120 part remai∣ning, which abreuied maketh 41/60 and thus you doe perceaue that the ⅔ & ½ added with the ⅘ and ¼ doe amount vnto 1.41/60 as hereafter by practise doth plainely appere.

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¶Addition of whole number and broken togither.

5. Also if you will adde 12. ⅘ with 20. ⅚, you may (if you will) adde 12. & 20. togither, and they make 32. & then adde the twoo broken numbers togi∣ther, that is to saye ⅘ and ⅚ by y^e order of the fyrst addition & they make 49/30: therefore diuide 49. by 30. and thereof commeth 1. and 19/30 partes remaine, which 1. you must adde vnto the 32. & the whole addition wil be 33. 19/30, or o∣therwise, you may reduce 12. ⅘ into the likenesse of a Fraction by the syxt reduction and they will be 64/5, & like∣wise by the same reductiō, reduce 20. ⅚ and they bee 125/6, then adde 84/5 with the 125/6, by the fyrst addition and you shall fynde 1009/30. Therefore diuide 1009. by 30. and therof commeth 33.19/30

as before, & as by practise of the same both the wayes, doth here vnder ap∣pere.

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