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ORAL DRILL In each of the following examples, find the sum of the numbers given. 1. } } 11. ,

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30. ģ Fractions Whose Numerators Are 1. When two fractions are to be added where both numerators are 1, and the denominators are prime to each other, observe the following rule.

Rule. (1) Add the denominators together for the numerator of the answer; (2) multiply the denominators together for the denominator of the answer. EXAMPLE. Add į and }

4 +5= 9, the numerator of the answer ;

4 x 5 20, the denominator of the answer. Then +}=0, the sum.

ORAL DRILL In each of the following examples find the sum of the numbers given.

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In the subtraction of fractions, as in their addition, the denominators must be made equal.

Rule. To subtract one fraction from another, (1) reduce them to similar fractions having the least common denominator, (2) write the difference of the numerators over the least common denominator, and (3) reduce the result to lowest terms.

EXAMPLE From ž take 1:

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Exercise In each of the following examples, find the difference between the numbers given : 1. , 6. Ź,

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Prime Denominators. When the numerator of each fraction is 1, and the denominators are prime to each other, observe the following rule.

Rule. — (1) Find the difference of the denominators for the numerator of the answer; (2) multiply the denominators together for the denominator of the answer. EXAMPLE. From subtract.

5 –4=l, the numerator of the answer ;

4 x 5 20, the denominator of the answer. Then -}=0, the difference,

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ORAL DRILL In each of the following examples find the difference between the numbers given. 1. , 7. },

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30. lī, 12 Mixed Numbers.

When the numbers are mixed numbers and the fractional part of the subtrahend is greater than the fractional part of the minuend, observe the following rule.

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Rule. — (1) Increase the fraction in the minuend by 1, (2) decrease the whole number by the same amount, and (3) proceed as before. EXAMPLE. From 7 take 44

7}=7%= 638
41=416 = 411

213, the difference. It will be observed in the fraction 3 that if the numerator and denominator are added, the sum is the numerator of the fraction at the right.

Exercise In each of the following examples, find the difference between the numbers given:

1. 4ş, 14 9. 63, 24 17. 10}, 33 25. 125, 81 2. 53, 27 10. 83, 453 18. 123,73 26. 16%, 11 3. 63, 3 11. 83, 23 19. 163, 113 27. 13, 103 4. 73, 44 12. 103, 41 20. 144, 123 28. 155, 107 5. 43, 14 13. 12}, 63 21. 143, 45 29. 125, 82 6. 53, 2) 14. 93, 13 22. 12, 23 30. 185, 125 7. 63, 31 15. 143, 63 23. 105, 7} 31. 2416, 17} 8. 73, 3 16. 114, 31 24. 85, 44 32. 324, 74

Exercise Using the best method in each case, find in the first fifteen of the following examples the difference between the numbers given, and in the last seventeen, the sum:

1. 33, 23 5. 54,23 9. 51, 2} 13. 41, 24 2. 31, 11 6. 43, 1} 10. 114, 3 14. 511, 2 3. 41, 21 7. 31, 11 11. 2}, 11

15. 6, 3 4. 53, 21 8. 43, 33 12. 31, 14 16. 74, 37

17. 63, 31 18. 55, 2} 19. 41, 21 20. 514, 2}

21. 64,21
22. 511, 21
23. 445, 116
24. 43, 24

25. 59,34
26. 610,21
27. 812, 44
28. 104, 73

29. 1415, 81
30. 1212,94
31. 151, 115
32. 444, 33}

Multiplication and Division of Fractions
In the multiplication and division of fractions it is well
to keep in mind the following Principles :

1. Multiplying the numerator multiplies the fraction.
2. Multiplying the denominator divides the fraction.
3. Dividing the numerator divides the fraction.
4. Dividing the denominator multiplies the fraction.

5. Multiplying both numerator and denominator by the same number does not change the value of the fraction.

6. Dividing both numerator and denominator by the same number does not change the value of the fraction.

Multiplication of Fractions Rule. — To multiply one fraction by another : (1) multiply the numerators together for the numerator of the answer; (2) multiply the denominators together for the denominator of the answer.

EXAMPLE 1. Multiply by 4.

2 X4=8, the numerator of the answer ;

3 x 5 = 15, the denominator of the answer. Thenx=1

When a fraction is to be multiplied by a whole number the whole number can be considered as a fraction whose denominator is 1. EXAMPLE 2. Multiply s by 5.

3 x 5 = 3 x <= =34.

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