SOLVING MULTI STEP PROBLEMS WITH FRACTIONS AND MIXED NUMBERS WORKSHEET

On the webpage, "Solving multistep problems with fractions and mixed numbers worksheet" we are going to see some practice problems .

(1) A fruit merchant bought mangoes in bulk. He sold ⅝ of the mangoes. 1/16 of the mangoes were spoiled. 300 mangoes remained with him. How many mangoes did he buy?

(2) A family requires 2 ½ liters of milk per day.How much milk would family require in a month of 31 days?  

(3) A ream of paper weighs 12 ½ kg What is the weight per quire, if 20 quire make one ream? 

(4) It was Richard's birthday. He distributed 6 kg of sweets among her friends. If he gave ⅛  kg of sweet to each.How many friends are there?  

(5) 6 students went on a picnic.One student agreed to bear half of the expenses. The remaining 5 students shared the remaining expenses equally. What fraction of the expenses does each of 5 students pay?

(6) I have 2 ½ times money that david has. If i have $100, how much money does David have? 

(7) In a basket there are two kinds of sweet packets. There are 7 packets of the first kind each weighing 1 ¼ kg and 9 packets of the second kind each weighing ¾ kg . What is the total weight of the sweets in the basket?

(8) How many half-liter bottles can be filled from a can containing 37 ½ liter of milk? 

(9) A gentleman bought 200 liters of milk for a function. ⅘ of it was used for preparing candies. ¾ of the remaining milk was used for preparing coffee. How much of the milk remained.  

(10) Two third of a tank can be filled in 18 minutes. How many minutes will it require to fill the whole tank?  

Solving multi step problems with fractions and mixed numbers worksheet - Solution

Question 1 :

A fruit merchant bought mangoes in bulk. He sold ⅝ of the mangoes. 1/16 of the mangoes were spoiled. 300 mangoes remained with him. How many mangoes did he buy?

Solution :

Let "x" be the total number of mangoes

Number of mangoes sold = (5/8) x x ==> 5x/8

Number of mangoes spoiled = (1/16) x ==> x/16

Number of mangoes remained = 300

Total no.of mangoes =  5x/8 + x/16 + 300

Since the denominators of those fractions are not same, we have to take LCM.

LCM (8 and 16)  =  16

x  =  (10x + x + 4800) / 16

x  = (11x + 4800)/16

16x  = 11x + 4800

5x = 4800

x = 960 

Hence, total number of mangoes is 960

Let us see the solution of next problem on "Solving multi step Problems with Fractions and mixed numbers worksheet".

Question 2 :

A family requires 2 ½ liters of milk per day.How much milk would family require in a month of 31 days?  

Solution :

Milk required for a day = ½ liters  ==> 5/2 liters

Required quantity of milk for 31 days = (5/2) x 31

  = (5 x 31)/2 ==> 155/2 

Now we have to  change this improper fraction to mixed fraction.

Hence, quantity of milk required for 31 days = 77 1/2 liters

Let us see the solution of next problem on "Solving multi step Problems with Fractions and mixed numbers worksheet".

Question 3 :

A ream of paper weighs 12 ½ kg What is the weight per quire, if 20 quire make one ream? 

Solution :

Weight of 20 quires  = 12 ½ kg

To find the weight of 1 quire we need to divide weight of 20 quire by 20.

Weight of 1 quire = Weight of 20 quires / 20

Weight of 1 quire =  12 ½  ÷ 20

Here we have to change this mixed fraction into improper fraction

  =  25/2 ÷ 20 

By simplifying the numerator of the first fraction (25) and denominator of the second fraction (20) by 5 times table, we get

  =  (5/2) x (1/4) ==> 5/8 kg

Let us the example problem of "Solving Multistep Problems with Fractions and Mixed Numbers".

Question 4 :

It was Richard's birthday. He distributed 6 kg of sweets among her friends. If he gave ⅛  kg of sweet to each.How many friends are there?  

Solution :

Total quantity of sweet = 6 kg

Share of each person = ⅛  kg

Let be the number of friends that Richard has

 x/8 = 6 ==> =  6 x 8 ==> 48 

Let us the example problem of "Solving Multistep Problems with Fractions and Mixed Numbers".

Question 5 :

6 students went on a picnic.One student agreed to bear half of the expenses. The remaining 5 students shared the remaining expenses equally. What fraction of the expenses does each of 5 students pay?

Solution :

Let "x" be the total expense 

Share of one student = (x/2)

Share of remaining 5 students =  (x/2)  ÷ 5

  =  (x/2) x (1/5) ==> x/10 

Let us the example problem of "Solving Multistep Problems with Fractions and Mixed Numbers".

Question 6 :

I have 2 ½ times money that david has. If i have $100, how much money does David have? 

Solution :

Let "x" be the money that David has  

Value of money that i have =   $100 

So,  2 ½ x x = 100

Now we have to change this mixed fraction in to improper fraction.

(4+1)/2 x  = 100 ==> (5/2) = 100 ==> (5x/2) = 100

5x = 200

If we divide by 5 on both sides we will get

x = 200/5 ==> x = 40

Hence, David has $40

Question 7 :

In a basket there are two kinds of sweet packets. There are 7 packets of the first kind each weighing 1 ¼ kg and 9 packets of the second kind each weighing ¾ kg . What is the total weight of the sweets in the basket?

Solution :

Number of packets in Type A = 7

Weight of each packet  =  ¼ kg

Number of packets in Type B = 9

Weight of each packet  =  ¾ kg

Weight of packet A = 7 x ¼ ==> 7 x (5/4)

= 35/4 kg 

Weight of packet B = 9 x ¾ ==> (9x3)/4

 =  27/4

Total weight = Weight of packet A + Weight of packet B

  =  (35/4) + (27/4) ==> (35+27)/4 ==> 62/4 ==> 31/2 

Hence, total weight of sweets in the basket is 15 ½.

Question 8 :

How many half-liter bottles can be filled from a can containing 37 ½ liter of milk? 

Solution :

Total quantity of milk = 37 ½ liter

Number of half liters to be filled   = 37 ½ ÷ (1/2)

  =  (75/2) x (2/1) ==> 75

Number of bottles required = 75

Question 9 :

A gentleman bought 200 liters of milk for a function. ⅘ of it was used for preparing candies. ¾ of the remaining milk was used for preparing coffee. How much of the milk remained.  

Solution :

Total quantity of milk  =   200 liters  fraction word problems 9

Milk used for preparing candies  = 200 x (4/5)

 =  (200x4)/5 ==> 800/5 ==> 160 liters

Remaining quantity of milk  = 200 - 160 ==> 40 

Quantity of milk used for preparing coffee   = 40 x (3/4)

  =  (40 x 3)/4 ==> 120/4 ==> 30 liters

Milk used for preparing candies and coffee  = 160 +30

  =  190 liters 

Remaining quantity of milk  = 200 - 190 ==> 10 liters

Question 10 :

Two third of a tank can be filled in 18 minutes. How many minutes will it require to fill the whole tank?  

Solution :

Let "X" be the time taken to fill the whole tank.

Time taken to fill  2/3 
part of the tank = 18 minutes 

(2/3) x  =  18 ==> X = 18 x (3/2) ==> = 9 x 3 

  =  27 minutes 

After having gone through the stuff given above, we hope that the students would have understood "Solving Multistep Problems with Fractions and Mixed Numbers". 

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