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?

**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 **==> 5**x**/8

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

Number of mangoes remained = 300

Total no.of mangoes = 5**x**/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 = 2 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 **x **be the number of friends that Richard has

**x**/8 = 6 ==> **x **= 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 **x ** = 100 ==> (5/2) x **x **= 100 ==> (5**x**/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 = 1 ¼ kg

Number of packets in Type B = 9

Weight of each packet = ¾ kg

Weight of packet A = 7 x 1 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 **X ** = 18 ==> **X** = 18 x (3/2) ==> **X **= 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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