Fraction Word Problems

Word Problems in Fraction

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Fraction word problems in mathematics involves the use of real-world instances expressed through words, and will often be solved through the application of an appropriate operation such as addition, subtraction, multiplication, or division.

A good understanding and interpretation of word problems in fraction is crucial crucial for students. Also, an adequate understanding on the concept of fraction is also important. For instance, we may have proper, improper or mixed fractions in our word problems.

Please read on LCM here.

• In proper fractions, the numerator is less than the denominator.

• In improper fractions, the numerator is greater than the denominator.

• A mixed fraction contains a whole number and a fraction together.

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 man goes in a journey. He does 1/6 of it on a bicycle, 4/5 on a lorry and walks the rest. What fraction of the journey does he walk?

Solution 

Since this is a fraction, the total journey travelled will be a whole number, and that's 1.

Fraction travelled on bicycle= 1/6

Fraction travelled on lorry= 4/5

Total journey travelled = 1

Fraction of journey walked = Total journey - fractions of journey travelled by bicycle + lorry.

1 - 1/6 + 4/5

The LCM of 5 and 6 is 30

• 1/30

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Example 2

• A boy plays football for 1 3/4 hours, listens to the radio for 3/4 hour and the spend 1 1/4 hours doing his homework. How how time does he spend altogether doing these things.

Solution

Since the term "altogether" is used, we'll simply add the hours spent on football, radio and homework.

1 3/4 + 3/4 + 1 1/4

Convert the mixed fractions to improper fraction 

7/4 + 3/4 + 5/4

LCM of 4, 4 and 4 is 4

• 15/4 or 3 3/4 hours is spent altogether by the boy.

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Example 3

• By how much is the sum of 2 4/5 and 4 1/2 less than 8 1/10.

Solution

From the question, "sum" means to add while "less than" implies minus or subtraction.

8 1/10 - 2 4/5 + 4 1/2

Convert the mixed fractions to improper fraction 

81/10 - 14/5 + 9/2

LCM of 2, 5 and 10 is 10

• 8⁴/10₅ = 4/5

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Example 4

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

Solution

Since there a 20 books in the encyclopedia, we'll simply multiply the mass of each book by 20 to get the total mass of the encyclopedia.

1 3/4 × 20

7/4₁ × 20⁵

• 35kg

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Example 5

• In a school, 9/10 of students play sports, 2/3 of these play football. What fraction of the students play football.

Solution 

To get the fraction of students that play sports (9/10), we will simply the fraction of the specific students who play football (2/3).

9/10 × 2/3 = 18³/30₅

• 3/5

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Example 6

• 4/9 of the spectators of a football match are males. If 200 of them are females, how many spectators are there in the competition?

Solution

Since there is a fraction of males, to get the fraction of females, we'll simply subtract it from 1.

1 - 4/9

The LCM of 9 and 1 is 9

5/9 equals the fraction of females.

From the question, 5/9 of the total spectators (T) equals 200 females; therefore, the total spectators equals 5/9T = 200

5/9T = 200

Make T the subject of the formula.

T = 200 ÷ 5/9

T = 200⁴⁰ × 9/5₁

40 × 9 = 360

• Total spectators in competition = 360

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Example 7

In mathematics test, Uche got 5/6, while Danladi got 1/2 of Uche's score and Kim got 3/2 of Danladi's score.

• Calculate Danladi's score in the test in fraction.

• What is the difference between Kim's score and Danladi's score expressed in fraction.

Solution 

Danladi got half of Uche's score. That is 1/2 × 5/6

1/2 × 5/6 = 5/12

Danladi's score is 5/12 in fraction.

Kim got 3/2 of Danladi's score

3¹/2 × 5/12₄ = 5/8

Kim's score is 5/8 in fraction

Difference between Kim's score and Danladi's score 

5/8 - 5/12

LCM of 8 and 12 is 24

5/24

• Difference between Kim's score and Danladi's score in fraction is 5/24

Please read on word problems in fraction (1) here.

Please read on word problems leading to algebraic expressions here.

 

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Assignment on Word Problems in Fraction

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• One lecture at an evening course lasts 1 1/2 hours. If the course lasts 30 hours altogether, how many lectures are there?

• Some shop-soiled goods are sold for 2/5 of their original price. What will the selling price be of a T-shirt originally costing N850?

• In a school, 9/10 of the students play sports. 2/3 of these play football. What fraction of the students play football?

• It takes 1 3/4 m of cloth to make a skirt. How many skirts can be made from 10 1/2 m of cloth?

• A ball always bounces to 3/5 of the height from which it falls. If it falls from a height of 1m, how high will it rise after the second bounce?

• A farmer uses 9/16 of a field for growing cassava. He uses 2/7 of the remainder for growing corn. What fraction of the field does he use for growing corn?

• Three sisters share some money. The oldest gets 9/11 of the money. The next girl gets 7/12 of the remainder. What fraction of the money does the youngest girl get?

Please read on the addition and subtraction of fractions 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.