Twelve are three times four; four are the third of twelve. Sixteen are four times four; four are the fourth of sixteen. Problems. 1. What part of a shilling are four pence? Ans. The third. 2. Four shillings are what part of a pound? Ans. The fifth. 3. One pound four shillings are how many times four shillings? Ans. Six times. 4. Sixteen hats are how many times four hats? Four hats are what part of sixteen hats? 5. If four lbs. of rice cost nine pence; how much will twelve lbs. of rice cost? Ans. Two shillings and three pence. Proof. Twelve are three times four; the cost of four lbs. of rice is nine pence; therefore the cost of twelve lbs. of rice will be three times nine pence, or twenty-seven pence, which is two shillings and three pence. 6. How much should I pay for four caps; when eight caps are sold for six shillings? Ans. Three shillings. Proof-Four are the half of eight; the cost of eight caps is six shillings; therefore the cost of four caps will be the half of six shillings, which will be three shillings. And so on to similar problems, depending upon the comparison of four with the multiples of four. And so on to FIVE, SIX, SEVEN, &c., respectively, compared with their multiples. SYMBOLS OR SIGNS. The language the half, or one half, is expressed by; thus, The language the third, or one third, is expressed by ; thus,— The language the fourth, or one fourth, is expressed by ; thus,— The language the fifth, or one fifth, is expressed by ; thus,— And so on. Signs of our Coins.-£ is the sign used to denote pounds; s. to denote shillings; and d. to denote pence: thus, £2. 4s. 5d. reads, two pounds four shillings and five pence. A halfpenny is written d.; a farthing is written id.; and three farthings are written d. Two pence farthing would be written 24d.; and so on. MIXED PROBLEMS. 1. Add the fourth of a pound to the third of a shilling. Ans. Five shillings and four pence. 2. Take the half of a shilling from the tenth of a pound. Ans. One shilling and six pence. 3. I asked a man to tell me his age: he said, that in two years' time he would be twice my present age: now my present age is twenty; what is the man's age? Ans. Thirty-eight. Proof.-Twice twenty are forty. But the man will not be forty until he is two years older. Therefore his age must be thirty-eight. 4. How many oranges should I get for ten pence, when the oranges are sold for two shillings a dozen? Ans. Five. 5. A carpenter earns twenty-four shillings in the week; how much must he spend a day, so as to lay by three shillings every week? Ans. Three shillings. And so on. EXERCISE IV. FRACTIONAL PARTS OF UNITY. [The teacher should cut a few potatoes, or any other familiar objects, into the parts required, for illustrating this exercise.] Halves. If an apple (or any other thing) be divided into two equal parts, each part is called the half of the apple. Two halves are one whole; one whole is two halves. Three halves are one whole and a half; one whole and a half are three halves. Four halves are two wholes; two wholes are four halves. Five halves are two wholes and one half; two wholes and one half are five halves. And so on. Problems. 1. Suppose I take six apples, and cut each of them into two equal parts; how many halves will there be in the six apples? Ans. Twelve halves because each apple contains two halves, therefore six apples will contain six times two halves, or twelve halves. : How many whole apples will there be in seven of the halves? Ans. Three wholes and one half; because every two halves make a whole, therefore six halves will make three wholes, and seven halves will make three wholes and one half. And so on to other questions. 2. How many half-pennies are there in four pence? Ans. Eight. 3. How many half-pennies are there in three pence and a half-penny? Ans. Seven; because each penny contains two half-pennies, therefore three pence will contain three times two half-pennies, or six half-pennies, and three pence and a half-penny will contain seven half-pennies. 4. How many pence are there in eleven half-pennies? Ans. Five pence and one half-penny. Thirds. If an apple (or any other thing) be divided into three equal parts, each part is called the third of the apple. Two of these parts are called two thirds, and so on. Three thirds are one whole; one whole is three thirds. Four thirds are one whole and one third; one whole and one third are four thirds. Five thirds are one whole and two thirds; one whole and two thirds are five thirds. Six thirds are two wholes; two wholes are six thirds. Seven thirds are two wholes and one third; two wholes and one third are seven thirds, And so on. Problems. 1. Suppose I take four apples, and cut each of them into three equal parts; how many thirds will there be in the four apples? Ans. Twelve thirds; because each apple contains three thirds; therefore four apples will contain four times three thirds, or twelve thirds. How many whole apples will there be in eight of the thirds? Ans. Two wholes and two thirds; because every three thirds make a whole, therefore six thirds will make two wholes, and eight thirds will make two wholes and two thirds. If I gave two thirds to one boy, and five thirds to another boy; how many apples would I have given away? Ans. Two wholes and one third; because two thirds and five thirds are seven thirds, or two wholes and one third. And so on to other questions. 2. If I take away two thirds from seven thirds; how many will be left? Ans. Five thirds, or one whole and two thirds. 3. If I take away two thirds from a whole; what will be left? Ans. One third. 4. Add four thirds and five thirds together. Ans. Nine thirds, or three wholes. 5. How many wholes are there in ten thirds? Ans. Three wholes and one third. 6. How many thirds are there in four wholes and one third? Ans. Thirteen thirds. And so on. Fourths. If an apple (or any other thing) be divided into four equal parts, each part is called the fourth of the apple. Two of these parts are called two fourths; three of them three fourths; and so on. Four fourths are one whole; one whole is four fourths. Five fourths are one whole and one fourth; one whole and one fourth are five fourths. Six fourths are one whole and two fourths; one whole and two fourths are six fourths. Seven fourths are one whole and three fourths; one whole and three fourths are seven fourths. Eight fourths are two wholes; two wholes are eight fourths. Nine fourths are two wholes and one fourth; two wholes and one fourth are nine fourths. And so on. Problems. 1. What part of a penny is a farthing? Ans. The fourth. Why? Because four farthings make one penny. 2. How many farthings, or fourths, are there in three pennies? Ans. Twelve fourths, or farthings. 3. A fourth is frequently called a quarter. How many quarters are there in two wholes and three quarters? Ans. Eleven quarters, or eleven fourths. 4. How many wholes are there in nine quarters? Ans. Two wholes and one quarter. 5. Add together two farthings and three farthings. Ans. Five farthings, or one penny and one farthing. 6. Take one farthing from a penny. And so on. Ans. Three farthings remain. The exercises on FIFTHS, SIXTHS, &c., should be deferred until the subject of fractions is systematically considered. MIXED PROBLEMS. About Half-pennies, and Quarter-pennies, or Farthings. 1. What should I pay for four lbs. of rice at three pence half-penny the lb. Ans. One shilling and two pence. Proof. The cost of one lb. is three pence half-penny; therefore the cost of four lbs. will be four times three pence half-penny. Four times one half-penny are two pence, and four times three pence are twelve pence; then twelve pence and two pence make fourteen pence, or one shilling and two pence. 2. What should I pay for five plates at two pence farthing each plate? Ans. Eleven pence farthing. Proof. Here the cost of five plates will be five times two pence farthing. Five times one farthing will be five farthings, or one penny farthing; and five times two pence will be ten pence; then ten pence and one penny farthing make eleven pence farthing. 3. If six eggs cost four pence three farthings; what will eighteen eggs cost? Ans. One shilling and two pence farthing. pence Proof. Here the cost of eighteen eggs will be three times four three farthings. Three times three farthings will be nine farthings, or two pence farthing; and three times four pence will be twelve pence; then twelve pence and two pence farthing make one shilling and two pence farthing. 4. If eight yards of calico cost ten pence half-penny; what will four yards cost? Ans. Five pence farthing. And so on. The fraction, or two thirds, may also be read, two times the third, or the third of a thing taken two times; and in like manner, the fraction , or five fourths, may also be read, five times the fourth, or the fourth of a thing taken five times; and so on to other fractions. (To be continued.) T. T. PRACTICAL HINTS FOR SCRIPTURE LESSONS.-No. 3. ST: T. MATTHEW, St. Mark, and St. Luke, each narrate the parable of the sower and the seed. It is in the thirteenth chapter of St. Matthew, in the fourth of St. Mark, and in the eighth of St. Luke. We shall make our references to the first of these versions of the parable, it being the fullest; but we shall refer, wherever occasion requires, to those given by St. Mark and St. Luke. We are told in both Gospels that earlier on the same day Jesus had made one of those broad declarations of His sympathy and comprehensive fellowship with man, which, even at that early time, was endearing Christianity to all "who had ears to hear" and hearts to feel, and enlisting myriads under its glorious and heavenly banner. The one condition is, that "whosoever shall do the will of my Father which is in Heaven, the same is my brother and sister and mother." Vv. 1 and 2. These verses enable the teacher to expand the picture of the scene; and if he have any imaginative power, which all teachers ought to have, he will rivet the attention of the children with the materials presented to him by these verses, the still waters of the great lake—the thronging multitudes on the shore-Jesus entering into the ship-the ship* itself-the Saviour addressing the disciples from it; for, as the noble Greek narrative has it, "the whole multitude stood upon the shore." We are told that He taught them many things by parables, and there is reason to think that His instruction extended to many things which are not recorded, though doubtless similar in character and import; for St. Mark puts this parable as though it were part only of what Jesus said on this occasion, using the words, "and said unto them in His doctrine," in other words, ' as He taught them.' V. 3. The sower is not our Lord only, but all who faithfully preach and declare God's truth. Otherwise we should not be told (v. 19) that, "when any one heareth the word, &c.," in general terms, without reference to who is the preacher. Besides, the parable clearly applies to future time as well as present time. Vv. 4 and 19. The seed is also comprehensive, and not confined to the Bible alone. In fact, in St. Matthew and St. Mark no noun is expressed, the thing sown is understood. It must be taken to be that which may spring up; but as the parable is designed to show, however excellent, the fruit depends on the soil that receives it. The soil represents the hearts of the hearers. And herein the distinction exists which determines the produce. First, we have the wayside hearers: the fowls devour it. These are the great multitude who hear with their ears but understand not. The devil obtains the victory, and easily enough snatches truth from the grasp of those whose minds hold it not. Dilate here on the wickedness of lip-learning; and if you are like many a superficial teacher, idly contenting yourself with telling truths and hearing them read, take a useful reproof from this: you are giving wayside instruction, and may just as well give none. The highway * A particular vessel (To Tλotov) is uniformly specified. It belonged to one of the fishermen who followed Jesus, who probably reserved it for his service.—See Matt. iv. 22, and John xxi. 3. |