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2176                                                               ARITHMETIC

ADDITION OF FRACTIONS.

Add fractions having the same denominator by adding the numerators and placing the sum over the common denominator. Eeduce the answer to its simplest form.

Fractions having the same denominator are called similar fractions. Fractions must be made similar before they can be added or subtracted. Add | and f

To add these fractions we must make them similar by reducing them to fractions having the same denominator.

The least common denominator of 2 and 3 is 6.

= -*   Thus

1.

i + i + i + t = i + i + A + 4 =

I + A + i + f = 4 + 4 + 1 +A =

+   +    +    =

3.

i  + TV +   f   +   *  =


 * +i+H+f= 4J+ 4 + 4 +A = A+A +I + 1 =

+.   +    +    =

5.

t + £,+ T3* + i = I + 4H-M + t = A+ I-+ f +^ = i + f +A + H=

+    +     +    =

Add 9f, 25£ and 205f. To add mixed numbers, add to the sum of the integers the sum of the fractions, and reduce to lowest terms.

First change the fractions to similar fractions having the L. C. D. 24. Adding 18, 21 and 16 24ths we have -ff = 2^j. Place ^ under the fraction column and add 2 to the units.

EXERCISE 21.

2.

I + i +A+ 4 = i + i + * +A= 1 + t +A+ t = _f +A+JJ+ 1 =

+   +    +    =

4.

I + f +A+ 4 = 4* + * + § + i =

f  +A+   *   +T% =

i + * +' I + f =

+    +     +     = 6.

i  +   I   +T%+H =

f + i +A+1 =

4  +TV+   f   +A =

A+i + t+&=

+    +     +    -