Multiply fraction by fraction. 2/3 times 4/5: 2/3 and 4/5 make 8/15. Multiplication of a fraction with a whole-and-fraction. 3/4 times 5 and 2/7: 3/4 and 5 and 2/7 (that is 37/⁷ make 111/28; taking out the whole numbers, 111/28 makes 3 and 27/28. Multiplication of fractions with whole numbers. 5/6 times 30: 5/6 and 30 give 150/6; making them whole, 150/6 makes 25 whole.

It seems better to me to say 5/6 of 30 than 5/6 times 30, not adding to the unit, but it has such proportion with the fraction as 25 has with 30 whole. Therefore to say 5/6 times 30 is as much as to say 5/6 of 30, which makes only 25 whole. And to say 2/3 times 3/4 times 4/8 is as much as to say ...

3 and 4/9 times 5 and 3/8: 3 and 4/9 (that is 31/⁹ times 5 and 3/8 (that is 43/⁸ make 1333/72; making them whole, 1333/72 makes 18 and 37/72. Multiplication of whole numbers against whole-and-fractions. 9 times 3 and 4/5: this gives 171/5; making them whole, 171/5 is 34 and 1/5. Adding fractions with fractions: 2/3 with 3/4. Adding 5/6 with 7 and 3/8: add the 7 that you set aside, without breaking it, which will make 8 and 3/12. Keep the whole number apart and then sum it with the whole numbers. Adding fractions with whole numbers: it is enough to name the whole numbers by themselves and then the fraction where the whole does not fit, as in saying 'one and 3/4.' Add in your way, for you can never name it otherwise; but if it were 1 and 18/12, then set the unit aside and divide 18 by 12, and you will get 1 and 1/2, and this suffices without breaking the whole numbers. When adding whole-and-fractions with whole-and-fractions, set the whole numbers aside; then gather the fractions and make them whole and join them with the other whole numbers, and let the fractions remain by themselves in their ordered place. As if you had to join 3 and 1/2 with 6 and 1/3: join 3 and 6, which makes 9, and set it apart; then join 1/2 with 1/3, and you will have 5/6, so you will have made 9 and 5/6. And thus it is a short method without breaking whole numbers. Adding whole numbers with whole-and-fractions: sum first the whole numbers and then add the fractions. As in joining 6 with 3 and 1/5: add first the 6 with the 3 and you will have 9, which add with 1/5 and you will have 9 and 1/5. Therefore always make one body of the whole numbers and one of the fractions; the whole numbers that come from such fractions, render them to whole numbers, and leave the fractions in their place. Subtracting fractions from fractions: take 2/3 from 3/4, where 12 is the denominator. Say '3 times 3 makes 9' and put 9 above 3/4; then say '4 times 2 makes 8' and put 8 above 2/3; then take 8 from 9, remains 1, which put above a line; then say '3 times 4 makes 12' and put 12 under the one; and you will have that to take 2/3 from 3/4 leaves 1/12. On subtracting a fraction from a whole-and-fraction: if the fraction found with the whole number is greater than the fraction you wish to take from it, there is no need to break the whole number; but if that fraction is smaller, it is necessary to break one unit of that whole number, or two, for the said fraction. As in saying '4/9 of 6 and 9/10': take only 4/9 of 9/10 and there will remain 41/90, and join it with the whole 6 that you left, and you will have 6 and 41/90. Subtracting a fraction from a whole number: it is enough to take one unit from those whole numbers and from it take whatever fraction you please, and the remainder of that broken unit you can add after the remainder of the aforesaid whole numbers. As in saying 'take 4/7 from 12': take 1 from 12, remains 11; make of that unit sevenths, which are 7/7, and take 4/7 from it; then remains 11 and 3/7. You may also do thus: take 4/7 of it, put the 12 above the unit and it is worth 80/7; so 80/7 makes 11 and 3/7. Subtracting whole numbers from whole-and-fractions: take the whole numbers from the whole numbers, and the remainder will be whole-and-fractions or simply fractions. As in saying: to subtract 9 from 13 and 3/5 you take 9 from 13, and there remains 4, which you join with the fraction, making 4 and 3/5. Subtracting whole-and-fractions from whole-and-fractions: here you must make the whole numbers into fractions. As in saying: subtract 3 and 2/5 from 4 and 2/3. Bring 3 to fifths, adding the 2 that stands above the 5, and it will be 17/5; and bring the 4 to thirds, adding the 2 that stands above the 3, and it will be 14/3.