The vvell spryng of sciences whiche teacheth the perfecte woorke and practise of arithmeticke, bothe in whole nombers and fractions, with suche easie and compendious instruction into the said arte, as hath not heretofore been by any sette out nor laboured. Beautified with moste necessary rules and questions, not onely profitable for marchauntes, but also for all artificers, as in the table doeth partlie appere: set forthe by Humfrey Baker citezeine of Lo[n]don.

¶ The sixt Chapiter is of multi∣plication in broken nombers.

FIrste, for to multiplie in broken nomber, there is a rule, whiche is thus, multiplie the numera∣tor of the one fraction, by the numerator of the other. And then diuide that fraction if you maie, or els abreuiate it, and you haue do••en: but if there be whole nomber and broken together, you muste reduce the whole nombers into broken, and adde ther∣vnto the numerator of his brokē, and then multiplie, as is before saied, as also hereafter by examples shal more plainly appeare.

1. If you will multiplie ⅔ by ¾, you muste multiplie the numerator. 2. by the numerator. 3. and therof commeth 6. for the numerator. Likewise mul∣tiplie the denominators thone by the other, that is to saie. 3. by. 4. and there∣of

commeth. 12. for the denominator, so that this multiplication commeth to 6/12, whiche beyng abreuied doe make ½. and so muche amounteth the mul∣tiplicatiō of the ⅔. by ¾ as by practise. 〈 math 〉〈 math 〉

2. Likewise, if you will multiplie a broken nomber by whole nomber, or whole nomber by broken, whiche is all one, as ⅘. by. 18 or els. 18. by ⅘, you must set. 1. vnder. 18. thus. 18/1: and then multiplie. 18. by the numerator 4. and therof commeth. 72. the whiche diuide by the denominator. 5. and thereof cō∣meth. 14. ⅖. for the whole multiplica∣tion, or otherwise abate from. 18. his ••/5. parte, whithe is. 3. ⅗, and there re∣maineth. 14. ⅖. as aboue. 〈 math 〉〈 math 〉

3. Also if you wil multiplie a whole nomber, by whole nomber & brokē, or els whole nomber & brokē by a whole nōber, whiche is all one. As by exam∣ple. If you will multiplie. 15. by. 16. ¾. or els. 16. ¾ by. 15 First reduce. 16 ¾ all into fourthes, in multipliyng 16. by y^e deneminator of ¾ whiche is 4. & therof commeth 64 whereunto adde the nu∣merator. 3. & it maketh 67/4, whiche mul∣tiplie by 15/1, accordyng vnto thinstruc∣tion of the laste example, and you shall find y^e product of this multiplicatiō to be 251 ¼ as by practise doth here appere 〈 math 〉〈 math 〉

4. And if you will multiple a bro∣ken nomber, by whole nomber and broken, or els whole nomber and broken by a broken. As by example, if you will multiplie ¼. by. 18. ⅔, or els 18 ⅔. by ¼, whiche is all one: you muste reduce the whole noumber into his broken by the sixt reduction. And you shall finde, 56/3, whiche you shall mul∣tiplie by the ¼, after the doctrine of the first multiplication, that is to saie: in multipliyng the numerator. 56. by the Numerator of ¼, which is 1. And it is still 56. because 1. doth neither mul∣tiplie nor deuide. And likewise you muste multiplie the Denominator. 3. by the Denominatour. 4. and it ma∣keth. 12. then diuide. 56. by. 12. and thereof commeth. 4. ⅔. And so muche

amounnteth the multiplication of the 〈◊〉〈◊〉. ⅔. multiplied by ¼, as by example. 〈 math 〉〈 math 〉

5. If you will multiplie whole nō∣ber and broken, with whole and bro∣ken, you muste firste put either whole nomber into his broken, accordyng to the instruction of the sixte reduction, and 〈◊〉〈◊〉 multiplie the one numera∣〈◊〉〈◊〉 the other, and of the producte make your numerator. And likewise multiplie the denominators, the one by the other, and thereof make the de∣nominator, then diuide the numera∣tor, by the denominator, and the quo∣tient shalbe the encrease of this mul∣tiplication.

¶ Example.

If you would multiplie. 12. ⅘. b〈…〉〈…〉. ¾: firste by the sixte reduction, the. 12. ⅘

will make 64/5, and the. 6. ¾. will make 27/4 then multiplie the numerator. 64. by the numerator. 27. and thereof com∣meth. 1728. for the numerator. And then you must multiplie the denomi∣nator. 5. by the denominator. 4. and thei doe make. 20. then diuide. 1728. by. 20. and thereof commeth. 86. ⅖. for the whole multiplicatiō, as by exāple. 〈 math 〉〈 math 〉

6. If you will multiplie one bro∣ken nomber by many broken nom∣bers, thus: As to multiplie ⅔. by 5/7. and by 4/9: you muste multiplie the nume∣rators of all the fractions, the one by

the other, and of the product make the numerator, that is to saie: 2. by. 5. and thei be. 10. then. 10. by. 4. and thei bee 40. for the numerator. Likewise you must multiplie the denominators, the one by the other, that is to saie. 3. by. 7. maketh. 21. then. 21. by. 9. maketh. 189 for the denominator: then sette. 40. o∣uer the. 189. with a line betwene thē, and thei make 40/189. And so muche a∣mounteth the whole multiplication of the ⅔, multiplied by 3/7 and 4/9, as by example folowyng. And thus is to be vnderstande of all suche like. 〈 math 〉〈 math 〉