WORD PROBLEMS WITH MIXED FRACTIONS
Problem 1 :
Peter had $75 3/4 in his purse. He spent $40 1/2 for his text books and $20 3/4 for his note books. How much will remain with him ?
Solution :
Money had by Peter = 75 3/4
Remaining money = 75 3/4 - ( 40 1/2 + 20 3/4)
= 303/4 - (81/2 + 83/4)
= 303/4 - { (81/2) ⋅ (2/2) + 83/4 }
= 303/4 - { (162/4 + 83/4 }
= 303/4 - { (162 + 83)/4 }
= (303/4) - (245/4)
= 58/4
= 29/2
Problem 2 :
The total weight of 4 girls is 155 1/4. If three of them weighs 20 1/5 kg 44 1/2 kg and 30 1/3 kg. Find the weight o the remaining girl.
Solution :
Total weight of 4 girls = 155 1/4
Let x be the weight of required girl.
Sum of the weight of three girls
= (20 1/5 + 44 1/2 + 30 1/3)
= (101/5) + (89/2) + (91/3)
Here L.C.M is 5 ⋅ 2 ⋅ 3 = 30
= (101/5) ⋅ (6/6) + (89/2) ⋅ (15/15) + (91/3) ⋅ (10/10)
= (606/30) + (1335/30) + (910/30)
= (606 + 1335 + 910) / 30
= 2851 /30
Weight of required girl = 155 1/4 - 2851 /30
= (621/4) - (2851/30)
L.C.M = 60
= (621/4) ⋅ (15/15) - (2851/30)
= (9315 - 2851)/30
= 6464/30
= 215 7/15
Problem 3 :
In three packets there were $13 2/3, $25 1/3 and $30 1/6. The total amount in all the four packets is $95. What is the amount in the fourth packet ?
Solution :
Sum of amount of three packets = 13 2/3 + 25 1/3 + 30 1/6
= (41/3) + (76/3) + (181/6)
= (82 + 152 + 181)/6
= 415/6
Let x be the amount of fourth packet
Remaining amount of fourth packet = 95 - (415/6)
= (570 - 415)/6
= 155/6
Problem 4 :
Maria worked 5 1/2 hours on Tuesday and 6 1/4 hours on Wednesday. John worked 2 1/2 on Tuesday and 5 1/4 hours on Wednesday. How many fewer hours did John work ?
Solution :
Time taken by Maria = 5 1/2 + 6 1/4
= 11/2 + 25/4
= 22/4 + 25/4
= (22+25)/4
= 47/4
Time taken by John = 2 1/2 + 5 1/4
= (5/2) + (21/4)
= (10/4) + (21/4)
= (10+21)/4
= 31/4
Difference of time taken between Maria and John
= 47/4 - 31/4
= (47-31)/4
= 16/4
= 4 hours
Maria had worked 4 hours fewer than John.
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WORD PROBLEMS
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Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
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Word problems on compound interest
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Complementary and supplementary angles word problems
Trigonometry word problems
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Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
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Word problems on average speed
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Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
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Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
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Sum of all three four digit numbers formed with non zero digits
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