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458. Oral Problems.

1. I spent į of a dollar for a ball and of a dollar for a bat. What part of a dollar did I spend for both ?

2. = how many fourths ?

3. What will be the cost of a pen-knife at of a dollar, and a book at 1 of a dollar?

4. Write 28 with smaller numerator and denominator.

5. I need of a yard of ribbon for one hat and of a yard for another. How much ribbon must I buy ?

6. Write a fraction equal to in with the smallest numbers you can. (This is called reducing a fraction to lowest terms.)

7. Sold of a pound of tea to one customer and { to another. How much was sold to both ?

8. What quantity of oats must I buy to give of a peck to one horse and to another?

9. If I sell of a dozen of oranges to one person and of a dozen to another person, what part of a dozen do I sell ?

10. What part of an hour is 45 minutes ?

11. f of an hour is how

many

minutes ? 12. I spent of an hour reading and % of an hour writing. What part of an hour did I spend at both ?

13. A boy is carrying 67 lb. of flour, and 6 lb. of ham. What is the weight of his load ?

14. Reduce 45 to lowest terms.
15. 18 hours is what part of a day?
16. Reduce to lowest terms.

ADDITION OF MIXED NUMBERS.

459. Add 12, 63, 87, 15%, š.

In the fractions }, }, }, , I, the numbers above the line, 1, 2, 1, 5, 3, are called numerators; the numbers below the line, 2, 3, 4, 6, 8, are called denominators.

To add fractions, they must have the same denominator. An inspection of the denominators, 2, 3, 4, 6, 8, shows that 48 or 24 will contain each without remainder. 24, which is the smallest number that will contain all, is called the least common denominator.

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Instead of writing the common denominator 24, with each fraction, we may place it above, and write only the new numerators. =}}, f- jf, 1-4, etc. Write 12, 16, 6, 20,9. The sum of these fractions is ft=211 = 25.

is placed under the fractions to be added, 2 is carried to the whole numbers, making 43.

NOTE. - The fractional parts of answers should be reduced to lowest terms.

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6. 12} + 3% + 273 + 81
7. 191 + 7 + 345 + $
8. 73 + 984 + } + 331
9. 5+1 + 387 + 23% + 177
10. 1004 + 75f + 9 + 494
11. 33} + 17% + 242 + 6924
12. 610 + 18} + 324 + 941
13. 103} + 84 + 251 +
14. 2183 + 3013 + 181 + 240
15. 4449 + 5185 + 374 + 95
16. 93+ 127 + 18} + 5094
17. 80 + 644 +126% +1,0574
18. 241 + 9 + 48 12+ 175
19. 994 + 88% + 774 + 664
20. 105 + 32% + 474 + 8}

MULTIPLES AND FACTORS.

461. A number that contains another number an exact numker of times is a multiple of that number.

24 is a multiple of 12; 36, 48, etc., are also multiples of 12. 30 is a multiple of 2, 3, 5, 6, 10, 15.

462. Oral Exercises.
1. 95 is a multiple of what two numbers ?
2. Give two factors of 51.
3. What number is a multiple of both 8 and 6?

4. Mention another number that is a multiple of both 8 and 6.

5. Find the smallest number that can be exactly divided by 8 and 12.

6. Give two factors of 91.
7. 57 is a multiple of what two numbers ?

8. What is the smallest number that can be exactly divided by 4, 6, and 8.

463. The smallest number that is a multiple of two or more numbers is called the least common multiple of such numbers.

9. Find the least common multiple of 5, 10, 15. 10. Find the least common multiple of 2, 7, 14. 11. What part of a dollar is 70 cents ? 12. ģ= how many 40ths ? 13. Reduce 17% to thirds. 14. Change 74 to a mixed number. 15. Reduce 4 to lowest terms. 16. What part of a dollar is 15 cents ? 17. Add and 18. From 1 take 5. 19. Reduce if to 60ths. 20. Which is largest, &, f, or f? 21. of 84 = ? 22. From 1 take 23. From take 24. From 1 take 16. 25. From H take o

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1-1=? 11-1=? 10–1=? 104-1= ? 104-14=?

467. From 197take 687. 15

Reduce the fractions to a common denominator (15), as in 1974 9 addition of fractions. tbeing greater than 15, we find the

687 10 difference between 1. and 1195, or it. Writing this difference, 12814 | 15

14, we add 1 to 68 and subtract.

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