Division teaches how to divide a number into two or more *equal * parts, as in the division of prize-money.

Division is of great importance, whether political, ecclesiastical, commercial, civil, or social. Nothing is more likely to destroy your opponents than a *split *. *Divide et impera * is the true Machiavelian policy of all governments.

Numbers, that is the multitude, are to be divided, in a variety of ways,—by mob orators, or by mob-sneaks, or by parliamentary flounderers, or by mystifying pulpit demagogues.

The divisors should generally endeavour to work into their own hands, and the dividends may be compared to fleeced-sheep, plucked-geese, scraped sugar-casks, drained wine-bottles, and squeezed lemons.

*Divide, divide,*the Speaker cries,

*blunder*.

Social Division.—The divisions here may be a tale-bearer, a gossip, or a go-between, and the divisors will "separate" to fight like Kilkenny cats, leaving nothing behind but two tails and a bit of flue. In a township, a volunteer corps is an excellent *divisor *: you may kill the adjutant by way of a quotient, on the surgical principle of "Mangling done here."

In the division of property by will, be your own lawyer, and your property will be divided to your heart's content; for, as your heirs will most assuredly be divided amongst themselves, when they have done fighting over your coffin for what does not belong to them, they will call upon the Court of Chancery to divide it—principally among the lawyers, according to the *lex non scripta*.

In the division of profits, first take off the *cream three times *, and then divide the milk.

In all kinds of "Division of Money" endeavour to carry out the principle of the fable. Like the lion when dividing the spoil, consider that you have a right to the *first * part, because you are a lion; to the *second *, because you are strong; to the *third *, because no one dares dispute your right; and to the *fourth *, because no one is so able as yourself to defend it. This is the lion's share.

### Primary Ideas of Division

In teaching the two ideas of division—division by *measurement * (division proper) and the *fractional * idea of division (partition)—proceed very slowly and see that each step is thoroughly understood.

The following suggestions may be useful :—

#### Division by Measurement

Use blocks or any other counters in illustrating the process.

Example :

4 12

The teacher should ask the child, “How would you count this story?”

*Facts Given by Child *

12 = whole number of blocks.

4 = number in each part.

We want to know the number of parts.

We place the blocks so, 4 in each part :—

There are 3 parts.

#### Division by Partition

Make use of blocks or substitutes to show the process here.

Example : 1 ⁄4 of 12 = 3.

The teacher should ask the child, “How would you count this story?”

*Facts Given by Child *

12 = whole number of blocks.

4 = number of parts.

We want to know the number in each part.

We place the blocks so, as we know there are 4 parts :—

We have put one in each part.

Now we will put one in each part until the 12 blocks are gone :—

There are 3 in each part.

Division of Time.—"*Tempus fugit*," and therefore the due systematic and proper division of time, in a rational manner, is the bounden duty of every "beardling." All philosophers and some kings, whether from Democritus to Tim Bobbin, or from Alfred the Great to that merry old soul, "Old King Cole," have divided their time equitably, according to the maxim of Horace, "*Carpe diem, quam minimum credula postero*." Modern life teaches and exhibits the same necessity for the rigid division of the "stuff *life * is made of," and the twenty-four hours may be systematically divided, with great advantage, by young men, as follows:—

HOURS. | |||

1. | To yawning, vertigo, head-ache and soda-water, say from one to three, A.M. | 2 | |

2. | From pulling off the night-cap to putting the first leg out of bed | 1 | |

3. | To "cat-lap," "broiled chickens," Lackadaisical Magazine, "Dry Punch," and Gazette of Fashion | 2 | ½ |

4. | To the study of "cash stalking," the art of post-obits, with lessons from Professor Mœshes on the science of "Bondology." (Nocturnâ versate manu, versate diurnâ) | 1 | |

5. | To lounging, "dawdling," "muddling," sauntering, losing oneself in "ins and outs," "nowheres," &c. | 1 | ½ |

6. | To dressing for dinner, to getting on a pair of boots, half an hour, swearing at coat quarter of an hour, selecting vests half an hour, cursing pantaloons quarter of an hour, shaving, and other unnecessaries | 2 | ½ |

7. | To dining, wineing, brighting the eye, doubling the cape, getting half seas over, going into port instead of finding a champaign country | 2 | |

8. | To dressing for opera, "titivating ," "bear's greasing," curling, barbarizing, scenting, putting on opera countenance, and ogling | 1 | ½ |

9. | To tying on stock half an hour, to putting on gloves quarter of an hour, to curling whiskers half an hour, to laying on the rouge, &c. | 1 | ½ |

10. | To bowing, scraping, hemming, hawing, yawning, toying, soft-sawdering, salooning, staggering, cigaring, coaching, and finishing | 3 | ½ |

11. | To no one knows what—Nisi castè saltem cautè | 5 | |

24 |

##### Division of Fractions

(i) When the divisor is a whole number. Suppose we have to divide 7 ⁄9 by 4.

We know 7 ⁄9 = 28 ⁄36. This fraction means that the unit is divided into 36 equal parts, and 28 of the parts taken. If we divide the 28 parts by 4, we get 7 of them—*i.e.* 7 ⁄36. Hence 7 ⁄9 ÷ 4 = 7 ⁄36.

Therefore, to divide a fraction by a whole number, we multiply the denominator by that number.

In the same way as already explained for multiplication, we cancel any common factors contained in the divisor and the numerator. Hence, if the numerator be exactly divisible by the divisor, we may divide a fraction by a whole number by dividing the numerator by that number.

Example 1:

27 31 ÷ 18 = 3 27 31 × 18 2 = 3 62 *Ans.*

Example 2:

36 41 ÷ 9 = 4 41 *Ans.*

(ii) When the divisor is a fraction.

In the operation 24 ÷ 3, we have to find the number which, when multiplied by 3, will give 24. Similarly, to find the value of 3 ⁄7 ÷ 5 ⁄9 we have to find the fraction which, when multiplied by 5 ⁄9 , will give 3 ⁄7.

But 3 × 9 7 × 5 is the fraction which gives 3 ⁄7 when multiplied by 5 ⁄9. Therefore, 3 7 ÷ 5 9 = 3 × 9 7 × 5 .

Hence, to divide by a fraction, invert the divisor and multiply.

As in multiplication, mixed numbers must first be reduced to improper fractions.

Example 3: Divide 3 1 ⁄14 by 5 5 ⁄42.

3 1 14 ÷ 5 5 42 = 43 14 ÷ 215 42 = 43 14 × 3 42 215 5 = 3 5 *Ans.*