Word Problems in Fraction

Fraction Word Problems

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Word problems in fraction involves the interpretation real-life scenarios expressed via words or sentences in mathematical questions where you use addition, subtraction, multiplication, and division (with fractions) to find answers.

In order to find answers to word problems in fraction, we may have to convert mixed fraction, find common denominators through LCM, alongside applying the rules associated with the multiplication and division of fractions.

Please read on LCM here.

 

An important step towards solving word problems in fraction is by reading carefully to understand the question, and identifying operations (like "sum and altogether for addition", "difference and how much more for subtraction"; while also using visuals to understand parts of a whole or groups.

Please read on expressing one quantity as a fraction of another here.

 

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Worked Examples on Word Problems in Fraction 

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Example 1

• A boy spends 1/3 of her money on rice and 3/8 of her money on beans. What fraction of her money is left?

Solution 

Since this is a fraction, the total money owned by the girl is a whole number, and that's 1.

Fraction spent on rice = 1/3

Fraction spent on beans = 3/8

Total money = 1

Fraction of money left = Total money - money spent on rice + beans.

1 - 1/3 + 3/8

The LCM of 3 and 8 is 24

• 7/24

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Example 2

• A fruit grower uses 1/3 of his land for bananas, 3/8 for pineapples, 1/6 for mangoes and the remainder for oranges. What is the fraction of the oranges?

Solution 

Since this is a fraction, the total land equals to a  a whole number, and that's 1.

Fraction of oranges = Total land - fractions for bananas + pineapples+ mangoes.

3¹/24₈ = 1/8

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Example 3

• A farmer harvested 10 1/2 basket of tomatoes from his farm. He gave 1/10 of the basket as tithe, used 4/21 of the remaining at home and sold the rest. What fraction of the tomatoes did he use? What fraction of the tomatoes did he sell?

Solution

Total harvest by the farmer = 10 1/2 basket of tomatoes = 21/2 baskets of tomatoes 

Tithe = 1/10

Basket of tomatoes given a tithe = total harvest × tithe fraction

21/2 × 1/10

21/20 or 1 1/20 basket of tomatoes given as tithe.

Basket of tomatoes left after tithe = total basket of harvest - total basket of tithe

21/2 - 21/20

LCM of 2 and 20 is 20

189/20 basket of tomatoes left after tithe

Basket of tomatoes used at home = Basket of tomatoes left after tithe x fraction of tomatoes used at home

189/20 × 4/21

756/420

9/5 basket of tomatoes used at home

Fraction of tomatoes sold = Basket of tomatoes left after tithe - basket of tomatoes used at home 

189/20 - 9/5

LCM of 20 and 5 is 20

• 153/20 or 7 13/20 basket of tomatoes sold.

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Example 4

• 1/5 of a the timetable for a class is given to English and 1/8 to Mathematics. What fraction is left for other subjects?

Solution 

Since this is a fraction, the timetable for all subjects is a whole number, and that's 1.

Fraction given to English= 1/5

Fraction given to Mathematics = 1/8

Timetable for all subjects = 1

Fraction left for other subjects = Time table for all subjects - fractions on English + Mathematics 

1 - 1/5 + 1/8

The LCM of 5 and 8 is 40

• 27/40 or 1 13/40

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Example 5

• During a week, a student spends 1/3 of her time in bed, 5/24 of her time in lessons, and 1/8 of her time doing homework. What fraction of her time is left for doing other things?

Solution 

Since this is a fraction, the total time the student have got in a week is a whole number, and that's 1.

Fraction spent in bed= 1/3

Fraction spent in lessons = 5/24

Fraction spent on doing homework= 1/8

Total time in a week = 1

Fraction left for doing other things = Total time in a week - fractions spent in bed + lessons + doing other things.

1 - 1/3 + 5/24 +1/8

The LCM of 3, 8 and 24 is 24

• 8¹/24₃ = 1/3

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Example 6

• A girl spends 1/4 of her pocked money on monday and 3/8 on wednesday. What fraction of her money is left?

Solution 

Since this is a fraction, the total money owned by the girl is a whole number, and that's 1.

Fraction spent on rice = 1/4

Fraction spent on beans = 3/8

Total money = 1

Fraction of money left = Total money - fractions of money spent on rice + beans.

1 - 1/4 + 3/8

The LCM of 4 and 8 is 8

• 3/8

Please read on the multiplication and division of fractions here.

Please read on the use of BODMAS in mathematics here.

 

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Assignment on Word Problems in Fraction

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• Find the product of 3 1/4 and 2 2/5.

• Find the value of 6 2/3 divided by 1 7/9.

• What is three-quarters of 3 3/7?

• Does 4 1/2 divided into 1 4/5 mean 4 1/2 ÷ 1 4/5 or 1 4/5 ÷ 4 1/2?

• Find the values of 4 1/2 ÷ 1 4/5 and 1 4/5 ÷ 4 1/2 and say which one is 4 1/2 divided into 1 4/5.

• The mass of each book of an encyclopaedia set is 1 3/4 kg. There are 20 books in the encyclopaedia set. Find the total mass of the encyclopaedia set.

• A tank holds 15 litres of water. The capacity of a cup is 3/10 of a litre. How many cups of water does the tank hold?

• LP records turn round 33 1/3 times every minute. If one side of an LP plays for 24 minutes, how many times does it turn round?

Please read on word problems leading to algebraic equation here.

Please read on mathematics week 7 topic for jss1 first term here.

Please read on mathematics scheme of work for jss1 first term here.