WORKSHEET ON WORD PROBLEMS ON RATIONAL NUMBERS

Problem 1 :

John reads ⅓ part of a book in 1 hour. How much part of the book will he read in 2⅕ hours?

Problem 2 : 

A teacher wants to give pizza to her students and each student can eat ¼ of a pizza. If there are 25 students in her class, how many pizzas does she need?

Problem 3 : 

Mason made ¾ of a pound of trail mix. If he puts ⅜ of a pound into each bag, how many bags can Mason fill?

Problem 4 :

A shop keeper sold 7¾ kg, 2½ kg and 3⅗ kg of sugar to three customers in a day. Find the total weight of sugar sold on that day.

Problem 5 :

John bought 25 kg of Rice and he used 1¾ kg on the first day, 4½ kg on the second day. Find the remaining quantity of rice left.

Problem 6 :

In Science class, Jeslyn watched an insect crawl 3⅙inches in one minute.The next minute the insect crawled 2¾ inches. How far did the insect crawl in total?

Problem 7 :

Three places are on a straight line as shown in the picture below.

The distance from A to C is 7 miles and the distance from B to C is ⅖ of the diatance from A to C. Find the distance from A to B.

Problem 8 :

Alex had $450, he spent two-fifth of the money for clothes and and one-third of the rest for food. After spending money for clothes and food, how much does he have left?

Problem 9 :

There are 15000 books in a library. One-fifth of the book are English, two-third of the books are French and the rest are Spanish. Find the number of spanish books in the library.

Problem 10 :

Pipe A can fill a tank in 10 minutes and pipe B can fill the same tank in 8 minutes. How long will it take to fill the tank, if both the pipes are opened together?

Answers

1. Answer :

The part of the book read by John in 1 hour is ⅓.

The part of the book read by him in 2⅕ hours :

= 2⅕ x ⅓

= ¹¹⁄₅ x ⅓

= ¹¹⁄₁₅

2. Answer :

To find the number of pizzas needed, we have to multiply the number of students in the class by the amount of pizza given to each student and the number of students.

= 25 ⋅ ¼ 

= ²⁵⁄₄

= 6¼

So, the teacher needs 6¼ pizzas.

3. Answer :

To find the number of bags, we have to divide ¾ by ⅜. 

= ¾ ÷ ⅜

Change the division to multiplication by taking reciprocal of ⅜.

= ¾ ⋅ ⁸⁄₃

Simplify.

= ¹⁄₁ ⋅ ²⁄₁

= 2   

So, the Mason can fill the trail mix in 2 bags.

4. Answer :

To find the total weight of sugar on that day, we have to add the above quantities.

Total weight of sugar :

= 7¾ + 2½ + 3⅗

Convert the mixed numbers to improper fractions. 

= ³¹⁄₄ + ⁵⁄₂ + ¹⁸⁄₅

Least common multiple of (4, 2, 5) = 20.

Make each denominator as 20 by multiplying each fraction by an appropriate number. 

= ⁽³¹ˣ⁵⁾⁄₍₄ₓ₅₎ + ⁽⁵ˣ¹⁰⁾⁄₍₂ₓ₁₀₎ + ⁽¹⁸ˣ⁴⁾⁄₍₅ₓ₄₎

  = ¹⁵⁵⁄₂₀ + ⁵⁰⁄₂₀ + ⁷²⁄₂₀

  = ⁽¹⁵⁵ ⁺ ⁵⁰ ⁺ ⁷²⁾⁄₂₀

= ²⁷⁷⁄₂₀

= 13¹⁷⁄₂₀

The total weight of sugar sold on that day is 13¹⁷⁄₂₀ kg.

5. Answer :

Rice used on first day = 1¾ kg

Rice used on second day = 4½ kg

Quantity of rice used on first day and second day :

= 1¾ + 4½

Convert the mixed numbers to improper fractions.

= ⁷⁄₄ + ⁹⁄₂

Least common multiple of (4, 2) = 4.

Make the second denominator as 4 by multiplying the numerator and denominator of the second fraction by 2.

= ⁷⁄₄ + ⁽⁹ˣ²⁾⁄₍₂ₓ₂₎

= ⁷⁄₄ + ¹⁸⁄₄

= ⁽⁷ ⁺ ¹⁸⁾⁄₄

= ²⁵⁄₄

Remaining quantity of rice left :

= ²⁵⁄₁ - ²⁵⁄₄

= ⁽²⁵ˣ⁴⁾⁄₍₁ₓ₄₎ - ²⁵⁄₄

= ¹⁰⁰⁄₄ - ²⁵⁄₄

= ⁽¹⁰⁰ ⁻ ²⁵⁾⁄₄

= ⁷⁵⁄₄

= 18¾

Remaining quantity of rice is 18¾ kg.

6. Answer :

Total distance crawled by the insect :

= 3⅙ + 2¾

Convert the mixed numbers to improper fractions.

= ¹⁹⁄₆ + ¹¹⁄₄

Least common multiple of (6, 4) = 12.

Make each denominator as 12 by multiplying each fraction by an appropriate number.

= ⁽¹⁹ˣ²⁾⁄₍₆ₓ₂₎ + ⁽¹¹ˣ³⁾⁄₍₄ₓ₃₎

= ³⁸⁄₁₂ + ³³⁄₁₂

= ⁽³⁸ ⁺ ³³⁾⁄₁₂

= ⁷¹⁄₁₂

= 5¹¹⁄₁₂ inches.

7. Answer :

Distance from A to B :

= Distance (AC) - Distance (BC)

= 7 - ⅖ of distance (AC)

= 7 - ⅖(7)

= 7 - ¹⁴⁄₅

= ⁷⁄₁ - ¹⁴⁄₅

= ⁽⁷ˣ⁵⁾⁄₍₁ₓ₅₎ - ¹⁴⁄₅

= ³⁵⁄₅ - ¹⁴⁄₅

= ⁽³⁵ ⁻ ¹⁴⁾⁄₅

= ²¹⁄₅

= 4¹⁄₅ miles

8. Answer :

Amount of mone spent for clothes :

= ⅖ ⋅ $450

= $180

After spending for clothes, remaining amount of money :

= $450 - $180

= $270

Amount of mone spent for food :

= ⅓ ⋅ $270

= $90

After spending for clothes and food, amount of money Alex has left :

= $450 - ($180 + $90)

= $450 - $270

= $180

9. Answer :

Fraction of books which are English and French :

= ⅓ + ⅖

Least common multiple of (3, 5) = 15.

Make each denominator as 15 by multiplying each fraction by an appropriate number.

= ⁽¹ˣ⁵⁾⁄₍₃ₓ₅₎ + ⁽²ˣ³⁾⁄₍₅ₓ₃₎

= ⁵⁄₁₅ + ⁶⁄₁₅

= ⁽⁵ ⁺ ⁶⁾⁄₁₅

= ¹¹⁄₁₅

Fraction of books which are Spanish :

= ⁴⁄₁₅

Number of Spanish books in the library :

= ⁴⁄₁₅ ⋅ 15000

= 4 ⋅ 1000

= 4000

10. Answer :

Part of the tank filled by pipe A in 1 minute :

= ⅒

Part of the tank filled by pipe B in 1 minute :

= ⅛

Part of the tank filled in 1 minute, if both the pipes are opened together :

= ⅒ + ⅛

Least common multiple of (10, 8) = 40.

Make each denominator as 40 by multiplying each fraction by an appropriate number.

= ⁽¹ˣ⁴⁾⁄₍₁₀ₓ₄₎ + ⁽¹ˣ⁵⁾⁄₍₈ₓ₅₎

= ⁴⁄₄₀ + ⁵⁄₄₀

= ⁽⁴ ⁺ ⁵⁾⁄₄₀

= ⁹⁄₄₀

Time taken to fill the tank, if both the pipes are opened together :

= ⁴⁰⁄₉

= 4⁴⁄₉ minutes

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