**Solving Multi Step Problems with Fractions and Mixed Numbers Worksheet :**

Worksheet given in this section will be much useful for the students who would like to practice solving multi step problems with fractions and mixed numbers.

**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 ?

**Solution :**

**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.

**Problem 2 :**

A family requires 2 1/2 liters of milk per day.How much milk would family require in a month of 31 days ?

**Solution :**

Milk required per day is 2 1/2 liters.

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

= 31 ⋅ 2 1/2

= 31 ⋅ 5/2

= 155/2

= 77 1/2

So, the family would require 77 1/2 liters of milk for 31 days.

**Problem 3 :**

A ream of paper weighs 12 1/2 kg What is the weight per quire, if 20 quire make one ream ?

**Solution : **

Weight of 1 ream of paper = 12 1/2 kg

Because one ream is equal to 20 quire, we have

Weight of 20 quire paper = 12 1/2 kg

Weight of 1 quire paper = (12 1/2) ÷ 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

**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 ?

**Solution :**

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.

**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 ?

**Solution : **

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.

**Problem 6 :**

I have 2 1/2 times money that David has. If i have $100, how much money does David have ?

**Solution :**

Let x be the money that David has.

Then, we have

(2 1/2) ⋅ 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.

**Problem 7 :**

In a basket there are two kinds of sweet packets. There are 7 packets of the first kind each weighing 1 1/4 kg and 9 packets of the second kind each weighing 3/4 kg . What is the total weight of the sweets in the basket ?

**Solution : **

**First Kind : **

Weight of each packet is 1 1/4 kg.

Number of packets is 7.

Then, the total weight is

= 7 ⋅ (1 1/4) 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.

**Problem 8 :**

How many half-liter bottles can be filled from a can containing 37 1/2 liters of milk ?

**Solution : **

Total quantity of milk is 37 1/2 liters.

Number of half liter bottles can be filled is

= (37 1/2) ÷ (1/2)

= (75/2) ÷ (1/2)

= (75/2) ⋅ (2/1)

= 75

So, 75 half-liter bottles can be filled.

**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 ?

**Solution : **

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

**Problem 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 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.

After having gone through the stuff given above, we hope that the students would have understood, how to solve multi step problems with fractions and mixed numbers.

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