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Here is a pipe broken into several pieces ; each of these pieces is a fraction.

If you count the pieces you will see there are ten of them, and all these ten pieces when put together make one whole pipe.

The figure under the line is called the Denominator, and it shows how many equal parts a thing is divided into.

This pipe is divided into 10 pieces. figure under the line then will be 10.

The

The figure above the line is called the Numerator, and it shows how many of these pieces or parts of a thing is meant.

If I write of a pipe, it means the pipe is broken into 10 equal pieces and I take one of them.

If I say I have of a pipe in my hand, I mean the pipe is broken into 10 equal pieces and I have 3 of them.

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Here is a large card of gingerbread cut into 9 equal parts.

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If Charles takes two of these pieces, he will have two ninths of the whole card, and you must write it so, ; because the gingerbread is cut into 9 equal parts, you must put 9 under the line for the denominator; and because Charles takes 2 of these pieces, you must put 2 above the line for the numerator.

ADDITION OF FRACTIONS.

When the denominators are the same, you can add fractions, by adding the numerators; then place the sum over the common denomi

nator.

Sum 1.-Add and together.

Set down the figures above the line one under the other and add them thus,

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Place the sum over the denominator, 9, and you have the answer, §, five ninths.

You will see this is true, if you take 2 pieces of the gingerbread, which are of it, and then 3 pieces more which are of it, and count them all together, one, two, three, four, five pieces, which are or five ninths of the whole card of gingerbread.

Sum 2.-Add and together.

Sum 3.-Add, and together.

Sum 4.-How many ninths are there to a thing? How many pieces of gingerbread in the whole card?

Sum 5.-If I cut an orange into nine pieces, and give Mary 5 pieces and George 3 pieces, how many ninths of the orange shall I give away?

Sum 6.--John had of a dollar, Charles had of a dollar, and William had of a dollar; what part of a dollar had they all?

Sum 7.--A merchant went from Hartford to Boston to buy goods; his journey took him of a week, he staid in Boston of a week, and returned home in of a week; how long he gone?

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SUBTRACTION OF FRACTIONS.

Where the denominators are the same, you can subtract fractions by taking the smallest numerator from the other; and place the dif

ference above the line and the denominator under the line.

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Here is a nice pie cut into seven equal parts; one of these pieces is called a seventh, and is written thus; and the whole seven pieces together seven sevenths or 1, because they make the whole pie. Now if you take out three pieces of the pie there will be four pieces left, that is subtracted from there remain 4.

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Place the difference 3 over the denominator 7, you have the answer, .

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Sum 7.--If I take out six pieces, or of the pie, and give away three pieces, or of it, how many sevenths or pieces should I have left?

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Sum 8.-A little boy's papa gave him of a dollar, and he gave his sister of a dollar, and paid of a dollar for the "Child's Arithmetic;" how much money had he left?

MULTIPLICATION OF FRACTIONS.

A fraction cannot properly be said to be multiplied by another fraction, but it may be multiplied by a number larger than 1. Here is a cheese, cut into 12 equal parts.

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One of these pieces would be written, and may be multiplied by 2, 3, 4, and so on. Sum 1.-Multiply by 3.

We wish to take three times, thus, ; which added together, make. You see the numerator is increased, while the denominator is not changed. If you multiply the numerator by 3, you will have the same answer, thus;

11*

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