On the webpage, "Solving multistep problems with fractions and mixed numbers" we are going to see how to solve word problems with fraction.

**Steps to be followed while solving multi step problems with fractions and mixed numbers ****:**

(i) First read the given problem carefully.

(ii) Understand practical situation.

(iii) If we have to find the value of anything then we have to keep it as x.

We can not imagine the subject Math without the term "Fraction". Because, we solve many problems with it. So, we must be aware of the operations which we often do in fractions.

**Operations with fractions :**

- When we need to add or subtract two or more fractions first we need to consider the denominators. If the denominators are same, we can put only one denominator and we can add or subtract the numerator.
- If we have different denominators, we should take L.C.M.Then we can add or subtract.
- For multiplying two fractions we do not have to consider the denominators. We should multiply numerator with numerator and denominator with denominator.
- For dividing two fractions, we have to keep the first fraction as it is change the division sign as multiplication and we have to write the second fraction as its reciprocal.

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

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

**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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