PROBLEMS ON ADDING AND SUBTRACTING MIXED FRACTIONS
Add or subtract the following mixed numbers. Simplify and reduce when possible.
Problem 1 :
Solution:
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