SOLVING MULTI STEP PROBLEMS WITH FRACTIONS AND MIXED NUMBERS WORKSHEET

Problem 1 :

A fruit merchant bought mangoes in bulk. He sold 5/8 of the mangoes. 1/16 of the mangoes were spoiled. 300 mangoes remained with him. How many mangoes did he buy?

Problem 2 :

A family requires 2½ liters of milk per day.How much milk would family require in a month of 31 days?  

Problem 3 :

A ream of paper weighs 12½ kg What is the weight per quire, if 20 quire make one ream? 

Problem 4 :

It was Richard's birthday. He distributed 6 kg of sweets among her friends. If he gave 1/8 kg of sweet to each. How many friends were there?  

Problem 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 total expenses does each of 5 students pay?

Problem 6 :

I have 2½ times money that David has. If I have $100, how much money does David have? 

Problem 7 :

In a basket there are two kinds of sweet packets. There are 7 packets of the first kind each weighing 1¼ kg and 9 packets of the second kind each weighing 3/4 kg . What is the total weight of the sweets in the basket?

Problem 8 :

How many half-liter bottles can be filled from a can containing 37½ liters of milk? 

Problem 9 :

A gentleman bought 200 liters of milk for a function. 4/5 of it was used for preparing candies. 3/4 of the remaining milk was used for preparing coffee. How much of the milk is remaining?  

Problem 10 :

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

Detailed Answer Key

Answer (1) :

Let x be the number of mangoes that the merchant bought.

Number of mangoes sold is 

=  (5/8) ⋅ x

=  5x / 8

Number of mangoes spoiled is

=  (1/16) ⋅ x

=  x / 16

Number of mangoes remaining is 300. 

Then, we have 

x - (5x/8 + x/16)  =  300

x - (10x/16 + x/16)  =  300

x - 11x/16  =  300

16x/16 - 11x/16  =  300

(16x - 11x) / 16  =  300

5x / 16  =  300

Multiply each side by 16.

5x  =  4800

Divide each side by 5

x  =  960

So, the number of mangoes bought by the merchant is 960.

Answer (2) :

Milk required per day is 2½ liters. 

Then, number of liters of milk required for 31 days is

=  31 ⋅ 2½

=  31 ⋅ 5/2

=  155/2

=  77½

So, the family would require 77½ liters of milk for 31 days. 

Answer (3) : 

Weight of 1 ream of paper  =  12½ kg

Because one ream is equal to 20 quire, we have 

Weight of 20 quire paper  =  12½ kg

Weight of 1 quire paper  =  (12½) ÷ 20 kg

Weight of 1 quire paper  =   (25/2) ÷ 20 kg

Weight of 1 quire paper  =   25/(2 ⋅ 20) kg

Weight of 1 quire paper  =   25/40 kg

Weight of 1 quire paper  =   5/8 kg

Answer (4) :

Total quantity of sweet distributed is 6 kg. 

If each friend receives 1/8 kg, then the number of friends is 

=  6 ÷ (1/8)

=  6 ⋅ 8

=  48

So, 48 friends were there.

Answer (5) : 

Let x be the total expense 

Given : One student agreed to bear half of the expenses.

So, the remaining expenses is x/2. 

Given : The remaining expenses is shared by 5 students equally.

Then, the share of each student is 

=  (x/2) ÷ 5

=  x / 10

=  (1/10) ⋅ x

So, 1/10 of the total expenses is shared by each of 5 students. 

Answer (6) :

Let x be the money that David has. 

Then, we have

(2½) ⋅ x  =  100

(5/2) ⋅ x  =  100

5x / 2  =  100

Multiply each side by 2. 

5x  =  200

Divide each side by 5.

x  =  40

So, David has $40. 

Answer  (7) : 

First Kind :

Weight of each packet is 1¼ kg.

Number of packets is 7.

Then, the total weight is

=  7 ⋅ (1¼) kg

=  7 ⋅ (5/4) kg

=  35/4 kg -----(1)

Second Kind :

Weight of each packet  is 3/4 kg.

Number of packets is 9.

Then, the total weight is

=  9 ⋅ (3/4) kg

=  27/4 kg -----(2)

Weight (1st kind) + Weight (2nd kind)  =  35/4 + 27/4 

Weight (1st kind) + Weight (2nd kind)  =  (35 + 27) / 4

Weight (1st kind) + Weight (2nd kind)  =  62 / 4

Weight (1st kind) + Weight (2nd kind)  =  15 1/2

So, the total weight of sweets in the basket is 15 1/2 kg.

Answer (8) : 

Total quantity of milk is 37½ liters. 

Number of half liter bottles can be filled is 

=  (37½) ÷ (1/2)

=  (75/2) ÷ (1/2)

=  (75/2) ⋅ (2/1)

=  75

So, 75 half-liter bottles can be filled. 

Answer (9) : 

Total quantity of milk is 200 liters.   fraction word problems 9

Milk used for preparing candies is 

=  (4/5) ⋅ 200

=  160 liters

Remaining milk (after milk used for preparing sweets) is

=  200 - 160

=  40 liters

Given : 3/4 of the remaining milk was used for preparing coffee. 

So, the quantity of milk was used for preparing coffee is 

=  (3/4) ⋅ 40

=  30 liters

Milk used for preparing candies and coffee  is

=  160 + 30

=  190 liters

Remaining quantity of milk (after milk used for preparing sweets and coffee) is

=  200 - 190

=  10 liters

Answer (10) : 

Let x be the capacity of the whole tank. 

Given : Two third of a tank can be filled in 18 minutes

Then, we have

(2/3) ⋅ x -----> 18 minutes

x -----> 18 ⋅ (3/2) minutes

x -----> 27 minutes 

So, it will take 27 minutes to fill the whole tank. 

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