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?
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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