CBSE Class 5 Mathematics Unitary Worksheets Worksheet

UNITARY METHOD

Question 1. The method used for finding the price of one/the value of one is called ________ method.
Answer: unitary
In simple words: The unitary method finds the value of a single unit first, then finds the value of the required quantity.

Exam Tip: Always remember that to find more, we multiply; to find one, we divide.

Write statements and solve the following problems: (Revision Notebook)

Question 1. If the total wages of 36 workers in factory is Rs. 1836 per day, what will be the wages of 44 such workers in the factory for one day?
Answer:
Wages of 36 workers = Rs. 1836
Wages of 1 worker = \(\frac{1836}{36} =\) Rs. 51
Wages of 44 workers = \(51 \times 44 =\) Rs. 2244
In simple words: First divide the total wages by 36 to get one worker's daily wage, then multiply by 44.

Exam Tip: Show the division and multiplication steps clearly to avoid calculation errors.

Question 2. There are 322 pens in 23 boxes. How many pens are there in 24 boxes?
Answer:
Number of pens in 23 boxes = 322
Number of pens in 1 box = \(\frac{322}{23} =\) 14 pens
Number of pens in 24 boxes = \(14 \times 24 =\) 336 pens
In simple words: Find the number of pens in a single box by dividing 322 by 23, then multiply by 24.

Exam Tip: Verify the division \(322 \div 23\) by multiplying 14 by 23.

Question 3. The price of a dozen exercise books is Rs. 72. Find the cost of 18 exercise books.
Answer:
Note: 1 dozen = 12 exercise books.
Cost of 12 exercise books = Rs. 72
Cost of 1 exercise book = \(\frac{72}{12} =\) Rs. 6
Cost of 18 exercise books = \(6 \times 18 =\) Rs. 108
In simple words: Convert dozen to 12 items, find the price of one book, and multiply by 18.

Question 4. An aeroplane flies 4800 km in 4 hours. How far does it travel in 3 hours?
Answer:
Distance travelled in 4 hours = 4800 km
Distance travelled in 1 hour = \(\frac{4800}{4} =\) 1200 km
Distance travelled in 3 hours = \(1200 \times 3 =\) 3600 km
In simple words: Calculate the distance covered in 1 hour by dividing 4800 by 4, then multiply by 3.

Exam Tip: Include units like km and hours in every statement.

Question 5. The price of a dozen exercise books is Rs. 392. Find the cost of 20 kg of wheat?
Answer:
Note: The source text contains a minor mismatch between "exercise books" and "wheat", but following standard unitary method structure based on the immediate preceding numbers (assuming 14 kg of wheat costs Rs. 392 as seen in standard worksheets):
Cost of 14 kg of wheat = Rs. 392
Cost of 1 kg of wheat = \(\frac{392}{14} =\) Rs. 28
Cost of 20 kg of wheat = \(28 \times 20 =\) Rs. 560
In simple words: Divide the total cost by 14 to find the price of 1 kg, then multiply by 20.

Exam Tip: Read the quantities carefully and set up the ratio properly.

Question 6. 18 buses carry 936 passengers. How many passengers will 25 buses carry?
Answer:
Passengers carried by 18 buses = 936
Passengers carried by 1 bus = \(\frac{936}{18} =\) 52 passengers
Passengers carried by 25 buses = \(52 \times 25 =\) 1300 passengers
In simple words: Find passengers per bus by dividing 936 by 18, then multiply by 25.

Exam Tip: Double-check multiplication with 25 by multiplying by 100 and dividing by 4.

Question 7. The cost of 12 m of cloth is Rs. 480. Find the cost of 8 m of cloth.
Answer:
Cost of 12 m of cloth = Rs. 480
Cost of 1 m of cloth = \(\frac{480}{12} =\) Rs. 40
Cost of 8 m of cloth = \(40 \times 8 =\) Rs. 320
In simple words: Find the cost of 1 metre of cloth, then multiply by 8.

Exam Tip: Keep units consistent in your statements.

Question 8. The weight of 25 bags of sugar is 625 kg. Find the weight of 100 bags of sugar.
Answer:
Weight of 25 bags = 625 kg
Weight of 1 bag = \(\frac{625}{25} =\) 25 kg
Weight of 100 bags = \(25 \times 100 =\) 2500 kg
In simple words: Divide 625 by 25 to find the weight of 1 bag, then multiply by 100.

Exam Tip: Notice that 100 is 4 times 25, so you can also multiply 625 directly by 4.

Question 9. The train fare from Chennai to Mumbai for 6 persons is Rs. 1122. What is the fare for 10 persons?
Answer:
Fare for 6 persons = Rs. 1122
Fare for 1 person = \(\frac{1122}{6} =\) Rs. 187
Fare for 10 persons = \(187 \times 10 =\) Rs. 1870
In simple words: Find the fare for 1 person by dividing 1122 by 6, then multiply by 10.

Exam Tip: Multiplying by 10 simply appends a zero to the number.

Question 10. 12 kg of potatoes cost Rs. 84. How much will Mr. Bhaskar have to pay if he wants only 5 kg potatoes?
Answer:
Cost of 12 kg of potatoes = Rs. 84
Cost of 1 kg of potatoes = \(\frac{84}{12} =\) Rs. 7
Cost of 5 kg of potatoes = \(7 \times 5 =\) Rs. 35
In simple words: Find the cost of 1 kg by dividing 84 by 12, then multiply by 5.

Question 11. The rent of a house is Rs. 18,000 per year. What is the rent for 8 months?
Answer:
Note: 1 year = 12 months.
Rent for 12 months = Rs. 18,000
Rent for 1 month = \(\frac{18000}{12} =\) Rs. 1500
Rent for 8 months = \(1500 \times 8 =\) Rs. 12,000
In simple words: Convert the year into 12 months, find the monthly rent, and multiply by 8.

Exam Tip: Always convert time units to a common base (months) before applying the unitary method.

Which is a better buy? (Revision Notebook)

Question 1. 6 batteries for Rs. 96 or 12 batteries for Rs. 180
Answer:
Price of 1 battery in first option = \(\frac{96}{6} =\) Rs. 16
Price of 1 battery in second option = \(\frac{180}{12} =\) Rs. 15
Since Rs. 15 is less than Rs. 16, 12 batteries for Rs. 180 is a better buy.
In simple words: Find the unit price of each option and choose the one with the lower unit price.

Exam Tip: A better buy always means getting a lower price per single item.

Question 2. 8 staplers for Rs. 120 or 4 staplers for Rs. 80
Answer:
Price of 1 stapler in first option = \(\frac{120}{8} =\) Rs. 15
Price of 1 stapler in second option = \(\frac{80}{4} =\) Rs. 20
Since Rs. 15 is less than Rs. 20, 8 staplers for Rs. 120 is a better buy.
In simple words: Compare the unit cost of both options; the lower cost per item wins.

Exam Tip: Calculate unit price carefully by dividing total cost by quantity.

Question 3. 5 calculators for Rs. 6000 or 6 calculators for Rs. 7080
Answer:
Price of 1 calculator in first option = \(\frac{6000}{5} =\) Rs. 1200
Price of 1 calculator in second option = \(\frac{7080}{6} =\) Rs. 1180
Since Rs. 1180 is less than Rs. 1200, 6 calculators for Rs. 7080 is a better buy.
In simple words: Find the cost of one calculator for each deal to find which is cheaper.

Exam Tip: Perform division accurately with large numbers.

Question 4. 18 pens for Rs. 684 or 30 pens for Rs. 960
Answer:
Price of 1 pen in first option = \(\frac{684}{18} =\) Rs. 38
Price of 1 pen in second option = \(\frac{960}{30} =\) Rs. 32
Since Rs. 32 is less than Rs. 38, 30 pens for Rs. 960 is a better buy.
In simple words: Compare unit prices: Rs. 38 per pen versus Rs. 32 per pen.

Exam Tip: Cancel out zeros in fractions like \(960 \div 30\) to make division easier (\(96 \div 3\)).

FACTORS AND MULTIPLES AND DIVISIBILITY TESTS

Question 1. Factors: 1 is a factor of every number.
Answer: 1
In simple words: 1 divides every whole number completely.

Exam Tip: Remember that 1 is a universal factor.

Question 2. The biggest greatest factor of a number is the number itself.
Answer: the number itself
In simple words: A number cannot have a factor larger than itself.

Exam Tip: Every non-zero number's greatest factor is the number itself.

Question 3. 1 is the only number which has only one factor.
Answer: 1
In simple words: 1 has only one factor, which is 1 itself.

Exam Tip: 1 is neither prime nor composite because of this unique property.

Question 4. A factor of a number is less than or equal to a number.
Answer: less than
In simple words: Factors are smaller than or equal to the given number.

Exam Tip: Contrast this with multiples, which are greater than or equal to the number.

Question 5. A number has limited number of factors.
Answer: finite / limited
In simple words: You can count all the factors of any given number.

Exam Tip: Factors are countable, unlike multiples.

Question 6. Multiples: 1. A number is a multiple of itself.
Answer: multiple
In simple words: Every number is 1 times itself, making it its own multiple.

Exam Tip: The first multiple of any number is the number itself.

Question 7. Every number is a multiple of 1.
Answer: multiple
In simple words: Multiplying 1 by any number gives that number.

Exam Tip: 1 is a factor of every number, and every number is a multiple of 1.

Question 8. Every multiple of a number is greater than or equal to the number itself.
Answer: greater than
In simple words: Multiples grow larger or stay equal (when multiplied by 1).

Question 9. There is no limit to the multiples you can get of a particular number.
Answer: infinite / unlimited
In simple words: Multiples go on forever.

Exam Tip: Multiples are infinite, while factors are finite.

Fill in the blanks:

Question a. The first 5 multiples of 13 are ________
Answer: 13, 26, 39, 52, 65
In simple words: Multiply 13 by 1, 2, 3, 4, and 5.

Exam Tip: List multiples sequentially by adding the number repeatedly.

Question b. Write all the factors of 60 ________
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
In simple words: Find all pairs of numbers that multiply to give 60.

Exam Tip: Write factor pairs (like \(1 \times 60\), \(2 \times 30\), etc.) so you do not miss any factor.

Question c. Two numbers are said to be co-prime numbers if their common factor is 1 only.
Answer: co-prime
In simple words: Co-prime numbers share no common factors other than 1.

Exam Tip: Consecutive numbers are always co-prime.

Question d. Numbers having more than two factors are called composite numbers.
Answer: composite
In simple words: Composite numbers have 3 or more factors.

Question e. Prime numbers have only two factors.
Answer: two (1 and the number itself)
In simple words: Prime numbers can only be divided by 1 and themselves.

Exam Tip: 2 is the only even prime number.

Question f. 1 is neither a prime number nor a composite number.
Answer: 1
In simple words: Because 1 has only one factor, it doesn't fit the definition of prime or composite.

Exam Tip: Remember this exception whenever classifying numbers.

Question g. The least composite number is 4
Answer: 4
In simple words: 4 has factors 1, 2, and 4, making it the smallest composite number.

Exam Tip: Do not confuse composite numbers with odd numbers.

Question h. The only even prime number is 2
Answer: 2
In simple words: All other even numbers can be divided by 2, so they are composite.

Exam Tip: 2 is unique as both even and prime.

Question i. A number to be divisible by 10 should have 0 at its place.
Answer: 0
In simple words: Any number ending in 0 is divisible by 10.

Exam Tip: Check the units digit for divisibility rules.

Question j. A number to be divisible by 5 should have 0 or 5 at its place.
Answer: 0, 5
In simple words: Numbers ending in 0 or 5 are always multiples of 5.

Exam Tip: Divisibility by 5 requires the last digit to be 0 or 5.

Fill in the blanks:

Question 1. The least prime number is 2
Answer: 2
In simple words: Counting primes starts from 2.

Exam Tip: 2 is the starting point for prime numbers.

Question 2. All prime numbers are odd numbers except number 2.
Answer: odd
In simple words: Every prime number except 2 is an odd number.

Exam Tip: No even number greater than 2 can be prime.

Question 3. The only even prime number is 2
Answer: 2
In simple words: 2 is even and prime.

Exam Tip: Frequently asked conceptual question in tests.

Question 4. The least composite number is 4
Answer: 4
In simple words: Numbers 1, 2, and 3 are not composite; 4 is the first.

Exam Tip: 4 has three factors: 1, 2, and 4.

Question 5. The greatest one digit prime number is 7
Answer: 7
In simple words: Single-digit primes are 2, 3, 5, 7, making 7 the largest.

Exam Tip: 9 is composite (\(3 \times 3\)), so 7 is the maximum single-digit prime.

Question 6. The greatest one digit composite number is 9
Answer: 9
In simple words: Single-digit numbers 4, 6, 8, 9 are composite, and 9 is the largest.

Exam Tip: 9 has factors 1, 3, and 9.

Question 7. The greatest prime number between 1 and 100 is 97
Answer: 97
In simple words: 97 cannot be divided by any number other than 1 and itself.

Exam Tip: Memorize 97 as the largest two-digit prime number.

Question 8. 1 is neither a prime number nor a composite number.
Answer: 1
In simple words: 1 stands alone without prime or composite classification.

Exam Tip: A classic rule to remember for classification questions.

Question 9. Every even number is a composite number except number 2.
Answer: 2
In simple words: All even numbers above 2 can be divided by 2, making them composite.

Exam Tip: 2 is the lone even exception.

Question 10. The least odd prime is 3
Answer: 3
In simple words: The first odd prime number after 2 is 3.

Question 11. There are 4 one digit prime numbers.
Answer: 4
In simple words: The single-digit primes are 2, 3, 5, and 7 (total 4).

Exam Tip: Count them carefully: 2, 3, 5, 7.

Question 12. There are 25 prime numbers between 1 and 100.
Answer: 25
In simple words: There are exactly 25 prime numbers between 1 and 100.

Exam Tip: Standard mathematical fact useful for quick answers.

Question 13. Numbers which have only 2 factors are called prime numbers.
Answer: prime
In simple words: Numbers with exactly two factors (1 and itself) are prime.

Exam Tip: Prime numbers have precisely two distinct factors.