Example 1

1. Add 4 5 + 3 5 . 4 fifths , plus , 3 fifths , .

   4 5 + 3 5 = 4 + 3 5 = 7 5 = 1 2 5 ← Add or subtract the numerators and keep the same denominator . table with 1 row and 2 columns , row1 column 1 , 4 fifths , plus , 3 fifths , equals . fraction 4 plus 3 , over 5 end fraction . equals , 7 fifths , equals 1 , and 2 fifths , leftwards arrow , column 2 table with 2 rows and 1 column , row1 column 1 , cap addorsubtractthenumeratorsand , row2 column 1 , keepthesamedenominator . . , end table , end table

2. Subtract 5 9 − 2 9 . 5 ninths , minus , 2 ninths , .

   5 9 − 2 9 = 5 − 2 9 = 3 9 = 1 3 ← Add or subtract the numerators and keep the same denominator . 5 ninths , minus , 2 ninths , equals . fraction 5 minus 2 , over 9 end fraction . equals , 3 ninths , equals , 1 third . leftwards arrow . table with 2 rows and 1 column , row1 column 1 , cap addorsubtractthenumeratorsand , row2 column 1 , keepthesamedenominator . . , end table

Example 2

Add 3 4 + 5 6 . 3 fourths , plus , 5 sixths , .

3 4 + 5 6 = 9 12 + 10 12 Find the LCD . The LCD is the least common multiple (LCM) of the denominators . The LCD of  4  and  6  is  12.  Write equivalent fractions .   = 9 + 10 12 = 19 12 ,  or  1 7 12 Add like fractions and simplify. table with 2 rows and 3 columns , row1 column 1 , 3 fourths , plus , 5 sixths , column 2 equals , 9 twelfths , plus , 10 over 12 , column 3 table with 2 rows and 1 column , row1 column 1 , cap findthecap lcap ccap d . .cap thecap lcap ccap distheleastcommonmultipleopencap lcap ccap mcloseofthedenominators . . , row2 column 1 , cap thecap lcap ccap dof . 4 , and , 6 , is , 12. . cap writeequivalentfractions . . , end table , row2 column 1 , , column 2 equals . fraction 9 plus 10 , over 12 end fraction . equals , 19 over 12 , comma , or , 1 , and 7 twelfths , column 3 cap addlikefractionsandsimplify. , end table

Example 3

Subtract 5 1 4 − 3 2 3 . 5 , and 1 fourth , minus . 3 , and 2 thirds , .

5 1 4 − 3 2 3 = 5 3 12 − 3 8 12 Write equivalent fractions with the same denominator .   = 4 15 12 − 3 8 12 Write  5 3 12  as  4 15 12  so you can subtract the fractions .   = 1 7 12 Subtract the fractions . Then subtract the whole numbers . table with 1 row and 1 column , row1 column 1 , table with 3 rows and 3 columns , row1 column 1 , 5 , and 1 fourth , minus 3 , and 2 thirds , column 2 equals 5 , and 3 twelfths , minus 3 , and 8 twelfths , column 3 cap writeequivalentfractionswiththesamedenominator . . , row2 column 1 , , column 2 equals 4 , and 15 over 12 , minus 3 , and 8 twelfths , column 3 cap write , 5 , and 3 twelfths , as , 4 , and 15 over 12 . soyoucansubtractthefractions . . , row3 column 1 , , column 2 equals 1 , and 7 twelfths , column 3 cap subtractthefractions . .cap thensubtractthewholenumbers . . , end table , end table