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(b) Find the sum of the nine products.

III. Find the product. (See p. 246, problems 23 and 24.)

1. 372| x f 4. 523f x f 7. 523f x J.

2. 372£ x TV 5. 523f x f 8. 153^ x f.

3. 3721- x f 6. 523f xf . 9. 153£ x f.

(c) Find the sum of the nine products.

(See p. 246, problems 25 and 26.)

6. 346 J x 3|.

7. 346 J x 21-.

8. 275|- x H. 9. 275^ x 3f 10. 275]- x 2\.

(d) Find the sum of the ten products.

* Take 3 times 1 tenth of 345, or 1 tenth of 3 times 345.

t Lead the pupil to see that in problems of this kind the correct result may be obtained by " multiplying the numerators together for a new numerator and the denominators together for a new denominator"; that in so doing he divides the multiplicand by the denominator of the multiplier and multiplies the quotient so obtained by the numerator of the multiplier.

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Observe that in cases like the above, in which the denominators are prime to each other, the 1. c. d. is the product of the given denominators, and each new numerator may be found by multiplying the given numerator by the denominator of the other fraction.

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x y xy xy xy

Assign a numerical value to each letter and verify.

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Solve.—Then let x = 5 and y 1 and verify.

Algebraic Fractions.

192. Problems In Multiplication And Division.

Example I.

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194. Miscellaneous Review.

1. A piece of land in the form of an equilateral triangle measures on one side 46T3T rods. What is the distance around it?

2. The perimeter of a piece of land that is an exact square is 246f feet. How far across on one side?

3. The length of a certain rectangular field is three times its breadth; its perimeter is 360 rd. What is its breadth? Its length?

4. If f of the value of a farm is $2154, what is -£ of the value of the farm?

Note If ? of a certain number is 24, what is the number?

What is I of the number?

5. I spent f of my money and had S3.60 remaining, (a) How much did I spend? (b) What I had remaining, equals what part of what I spent?

6. Change -^w to an equivalent fraction whose denominator is 30.

7. Change Jj- to an equivalent fraction whose numerator is 30.

a2

8. Change — to an equivalent fraction whose denominator is be.

9. Multiply | by -| and multiply the product by 25.

10. Multiply || by ££ and multiply the product by 25.

11. If f of an acre of land is worth $36, how much are 37^ acres worth at the same rate?

12. The rent of a house for 2 yr. 4 mo. was $840. What was the rate per year?

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