solving multi step problems with fractions and mixed numbers worksheet

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

Problem 3 :

A ream of paper weighs 12 ½  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  2 ½  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  1 ¼  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  37 ½  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 2 ½  liters. 

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

=  31  ⋅  2 ½

=  31  ⋅ 5/2

=  155/2

=  77 ½

So, the family would require  77 ½  liters of milk for 31 days. 

Answer (3) : 

Weight of 1 ream of paper  =   12 ½  kg

Because one ream is equal to 20 quire, we have 

Weight of 20 quire paper  =   12 ½  kg

Weight of 1 quire paper  =  ( 12 ½ )  ÷ 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

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

( 2 ½ )  ⋅ 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  1 ¼  kg.

Number of packets is 7.

Then, the total weight is

=  7  ⋅ ( 1 ¼ ) kg

=  7  ⋅ (5/4) kg

=  35/4 kg -----(1)

Second Kind :

Weight of each packet  is 3 /4  kg.

Number of packets is 9.

=  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  37 ½  liters. 

Number of half liter bottles can be filled is 

=  ( 37 ½ )   ÷ (1/2)

=  (75/2)  ÷  (1/2)

=  (75/2)  ⋅ (2/1)

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

(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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Fraction Multi-Step Word Problems Worksheet

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Fractions — Multi-Step Problems (Year 6)

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This multi-step problems worksheet is a great way to help children consolidate their knowledge of fraction calculations. They must complete all the activities including filling the gaps in addition pyramids and solving multi-step problems based on common everyday scenarios.

Answers are included.

• Key Stage: Key Stage 2
• Subject: Maths
• Topic: Fraction Calculations
• Topic Group: Fractions, Decimals and Percentages
• Year(s): Year 6
• Media Type: PDF
• Resource Type: Worksheet
• Last Updated: 23/11/2023
• Resource Code: M2WAT14778
• Curriculum Point(s): Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions.

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