# WORD PROBLEMS WITH MIXED FRACTIONS

Word Problems with Mixed Fractions :

In this section, we will see some example problems with mixed fractions.

## Word Problems with Mixed Fractions - Examples

Example 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

Example 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

Example 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

Example 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.

After having gone through the stuff given above, we hope that the students would have understood how to word problems with mixed fractions.

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