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 divide 25 by ¼.

= 25 ÷ ¼ 

Change the division to multiplication by taking reciprocal of ¼.

= 25 ⋅ ⁴⁄₁

= 25 ⋅ 4

= 100

So, the teacher needs 100 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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