PROBLEMS ON ADDING AND SUBTRACTING MIXED FRACTIONS

Add or subtract the following mixed numbers. Simplify and reduce when possible.

Problem 1 :

845+8110=

Solution:

=845+8110=8+45+8+110Grouping the integers part and fractional part.=(8+8)+45+110=16+45+110By taking the least common multiple, we getLCM of (5,10)=104×25×2=8101×110×1=110=16+(8+1)10=16+910=16910

Problem 2 :

123+37=

Solution:

=123+37=1+23+37By taking the least common multiple, we getLCM of (3,7)=2123=2×73×7=142137=3×37×3=921=(21+14+9)21=4421=2221

Problem 3 :

1658+1112=

Solution:

=1658+1112=16+58+1112By taking the least common multiple, we getLCM of (8,12)=245×38×3=152411×212×2=2224=16+(15+22)24=16+3724=163724163724=16+11324=16+1+1324=171324

Problem 4 :

345+623+51115=

Solution:

=345+623+5115=3+45+6+23+5+1115Grouping the integers part and fractional part.=(3+6+5)+45+23+1115=14+45+23+1115By taking the least common multiple, we getLCM of 5,3 and 15=154×35×3=12152×53×5=101511×115×1=1115=14+(12+10+11)15=14+3315=143315
143315=14+2315=14+2+315=16315

Problem 5 :

11112-23=

Solution:

=11112-23=1+1112-23

Here the two proper fractions denominators are not the same.

So, we take the least common multiple of 12 and 3.

=1+(11-8)12=1+312=1312

Problem 6 :

418-1=

Solution:

=418-1=4+18-1=(4-1)+18=3+18=318

Problem 7 :

516-213=

Solution:

=516-213=5+16-2+13Grouping the integers part and fractional part.=(5-2)+16-13=3+16-13By taking the least common multiple, we getLCM of 6,3 =61×16×1=161×23×2=26=3+16-26=3-16=2+1-16=2+56=256

Problem 8 :

1412-218=

Solution:

=1412-218=14+12-2+18GRouping the integers part and fractional part.=(14-2)+12-18=12+12-18By taking the least common multiple, we getLCM of 2,8=81×42×4=481×18×1=18=12+(4-1)8=12+38=1238

Problem 9 :

725+115=

Solution:

=725+115=7+25+1+15Grouping the integers part and fractional part.=(7+1)+25+15=8+25+15=8+35=835

Problem 10 :

223-14=

Solution:

=223-14=2+23-14By taking the least common multiple, we get=2+8-312=2+512=2512

Problem 11 :

1217-823=

Solution:

=1217-823=12+17-8+23Grouping the integers part and fractional part.=(12-8)+17-23=4+17-23By taking the least common multiple, we get=4+3-1421=4+-1121=2+2-1121=2+42-1121=2+3121=23121
23121=2+11021=2+1+1021=3+1021=31021

Problem 12 :

447-367=

Solution:

=447-367=4+47-3+67Grouping the integers part and fractional part.=(4-3)+47-67=1+-27=57

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