Samacheer Kalvi Class 5 Maths Solutions Term 2 Chapter 2 Numbers InText Questions

Tamilnadu Samacheer Kalvi 5th Maths Solutions Term 2 Chapter 2 Numbers InText Questions

Try These (Text Book Page No. 5)

 

Question 1. Complete the square values for the numbers from 1 to 10.
Answer:
\( 1^2 = 1 \times 1 = 1 \)
\( 2^2 = 2 \times 2 = 4 \)
\( 3^2 = 3 \times 3 = 9 \)
\( 4^2 = 4 \times 4 = 16 \)
\( 5^2 = 5 \times 5 = 25 \)
\( 6^2 = 6 \times 6 = 36 \)
\( 7^2 = 7 \times 7 = 49 \)
\( 8^2 = 8 \times 8 = 64 \)
\( 9^2 = 9 \times 9 = 81 \)
\( 10^2 = 10 \times 10 = 100 \)
In simple words: To find the square of a number, you multiply the number by itself. For example, the square of 1 is \( 1 \times 1 = 1 \), and the square of 7 is \( 7 \times 7 = 49 \).

🎯 Exam Tip: Knowing the squares of numbers up to 10 by heart helps in quick calculations and solving problems faster.

Activity (Text Book Page No. 6)

A. Count and Write the number of boxes:

 

Question 1. \( 1^2 \)
Answer: 1
In simple words: One square means one group of one box. So, \( 1 \times 1 = 1 \) box.

🎯 Exam Tip: Visualize square numbers as actual square shapes to understand why they are called "squares."

 

Question 2. \( 2^2 \)
Answer: 4
In simple words: Two squared means two rows of two boxes each. So, \( 2 \times 2 = 4 \) boxes.

🎯 Exam Tip: Practice drawing these square patterns to reinforce the concept of squaring a number.

 

Question 3. \( 3^2 \)
Answer: 9
In simple words: Three squared means three rows of three boxes each. So, \( 3 \times 3 = 9 \) boxes.

🎯 Exam Tip: Remember that the base number tells you how many rows and columns are in the square arrangement.

 

Question 4. \( 4^2 \)
Answer: 16
In simple words: Four squared means four rows of four boxes each. So, \( 4 \times 4 = 16 \) boxes.

🎯 Exam Tip: Understanding the visual representation of square numbers helps in understanding multiplication arrays.

B. Circle and colour the square numbers:

 

Question 5. In the multiplication table below, identify and mark the square numbers.

Answer: The square numbers in the table are those where a number is multiplied by itself (e.g., \( 1 \times 1 = 1 \), \( 2 \times 2 = 4 \), etc.).
The square numbers in the table are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
In simple words: Look for numbers in the table where the row number and column number are the same. The answer at that spot is a square number, like 5 in the row for 5 and column for 5 gives 25.

🎯 Exam Tip: Square numbers always form a diagonal pattern in a multiplication table when the rows and columns are numbered the same.

Work Sheet (Text Book Page No. 7)

I. Answer the following:

 

Question 1. The square number of 2 is
Answer: The square number of 2 is 4, because \( 2 \times 2 = 4 \).
In simple words: To find the square of 2, just multiply 2 by itself. This gives 4.

🎯 Exam Tip: Always remember that "square of a number" means multiplying the number by itself, not by 2.

 

Question 2. The square number of 5 is
Answer: The square number of 5 is 25, because \( 5 \times 5 = 25 \).
In simple words: When you square 5, you get 25.

🎯 Exam Tip: Square numbers are important for understanding areas of squares and other geometric concepts.

 

Question 3. These number of boxes is equal to one square number, The number is
Answer: The number of boxes represents a square number. If there are 9 boxes, the number is 9. This means it is the square of 3, as \( 3 \times 3 = 9 \).
In simple words: If you have 9 boxes arranged in a square, the number that was squared is 3.

🎯 Exam Tip: To find the number that was squared to get a square number, think of its square root.

 

Question 4. Which of the following number is a square number?
(a) 23
(b) 54
(c) 36
(d) 45
Answer: (c) 36
In simple words: We know that \( 6 \times 6 = 36 \). So, 36 is a square number. The other numbers (23, 54, 45) cannot be made by multiplying a whole number by itself.

🎯 Exam Tip: To check if a number is a square number, try to find two identical whole numbers that multiply together to give that number.

 

Question 5. What is the next square number after 49?
(a) 95
(b) 64
(c) 45
Answer: (b) 64
In simple words: We know that \( 7 \times 7 = 49 \). The next whole number after 7 is 8. So, the next square number is \( 8 \times 8 = 64 \).

🎯 Exam Tip: To find the next square number in a sequence, find the square root of the given number, add 1, and then square that new number.

Find the Factors:

 

Question 6. Find the factors of 18.
Answer: The factors of 18 are the numbers that divide 18 evenly without leaving a remainder. We can find them by listing multiplication pairs that result in 18.
\( 1 \times 18 = 18 \)
\( 2 \times 9 = 18 \)
\( 3 \times 6 = 18 \)
So, the factors of 18 are 1, 2, 3, 6, 9, and 18.
In simple words: Factors are numbers that fit perfectly into another number. For 18, the numbers are 1, 2, 3, 6, 9, and 18.

🎯 Exam Tip: Always start with 1 and the number itself, then systematically check other small numbers to find all factor pairs.

 

Question 7. Find the factors of 20.
Answer: The factors of 20 are the numbers that divide 20 evenly. We list the multiplication pairs that give 20.
\( 1 \times 20 = 20 \)
\( 2 \times 10 = 20 \)
\( 4 \times 5 = 20 \)
So, the factors of 20 are 1, 2, 4, 5, 10, and 20.
In simple words: The numbers that divide 20 exactly are 1, 2, 4, 5, 10, and 20.

🎯 Exam Tip: Once you find a factor, its pair (the result of dividing the number by that factor) is also a factor. For example, if 2 is a factor of 20, then \( 20 \div 2 = 10 \) means 10 is also a factor.

 

Question 8. Find the factors of 24.
Answer: The factors of 24 are found by listing all the pairs of whole numbers that multiply to make 24.
\( 1 \times 24 = 24 \)
\( 2 \times 12 = 24 \)
\( 3 \times 8 = 24 \)
\( 4 \times 6 = 24 \)
So, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
In simple words: The numbers that can divide 24 without any remainder are 1, 2, 3, 4, 6, 8, 12, and 24.

🎯 Exam Tip: You can stop checking for factors when the smaller number in your pair starts to repeat or goes past the square root of the number.

 

Question 9. Find the factors of 42.
Answer: To find the factors of 42, we look for all pairs of numbers that multiply to 42.
\( 1 \times 42 = 42 \)
\( 2 \times 21 = 42 \)
\( 3 \times 14 = 42 \)
\( 6 \times 7 = 42 \)
So, the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
In simple words: The factors of 42 are all the numbers that can be multiplied together to get 42, which are 1, 2, 3, 6, 7, 14, 21, and 42.

🎯 Exam Tip: It is helpful to test for divisibility by prime numbers first (2, 3, 5, 7, etc.) to quickly find factors.

Activity (Text Book Page No. 9)

 

Question 10. Tick the factors of the following numbers.

Answer: The table above shows which numbers are factors for each given number. A checkmark means it is a factor. For example, 1, 2, and 4 are factors of 316. This helps in understanding divisibility rules.
In simple words: The checkmarks in the table show which numbers can divide the main number without a remainder.

🎯 Exam Tip: Learn divisibility rules for 2, 3, 4, 5, 6, 8, and 10 to quickly identify factors without performing long division.

Try These (Text Book Page No. 11)

 

Question 11. Complete the sequence: 5, 10, 15, _____, _____, _____, _____
Answer: The given sequence shows multiples of 5, which means each number is 5 more than the previous one. To complete the sequence, we add 5 to the last given number repeatedly.
5, 10, 15, 20, 25, 30, 35, 40
In simple words: This is a list where each number is 5 more than the one before it. We just need to keep adding 5.

🎯 Exam Tip: For number sequences, first identify the pattern (e.g., adding, subtracting, multiplying, or dividing by a constant number).

Try These (Text Book Page No. 12)

Find L.C.M

 

Question 12. Find the L.C.M of 10 and 15.
Answer: To find the Least Common Multiple (LCM) of 10 and 15, we list their multiples until we find the first common one.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, ...
The common multiples of 10 and 15 are 30, 60, 90, ...
The smallest common multiple (LCM) of 10 and 15 is 30.
In simple words: The LCM is the smallest number that both 10 and 15 can divide into evenly. We list multiples of both and find the first number that appears in both lists.

🎯 Exam Tip: Always list out at least the first few multiples for both numbers to correctly identify the least common multiple.

 

Question 13. Find the L.C.M of 8 and 6.
Answer: To find the LCM of 8 and 6, we write down their multiples.
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, ...
The common multiples of 6 and 8 are 24, 48.
The smallest common multiple (LCM) of 6 and 8 is 24.
In simple words: The smallest number that both 8 and 6 can divide into is 24. We find this by looking at their multiplication tables.

🎯 Exam Tip: When finding LCM by listing multiples, stop as soon as you find the first common multiple, as that is the least one.

 

Question 14. Find the L.C.M of 4 and 10.
Answer: We list the multiples of 4 and 10 to find their Least Common Multiple.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, ...
Multiples of 10: 10, 20, 30, 40, 50, 60, ...
The common multiples of 4 and 10 are 20, 40, ...
The smallest common multiple (LCM) of 4 and 10 is 20.
In simple words: The lowest number that both 4 and 10 can be divided into exactly is 20.

🎯 Exam Tip: LCM is often used when adding or subtracting fractions with different denominators, as you need a common denominator.

 

Question 15. Find the L.C.M of 6 and 16.
Answer: To find the LCM of 6 and 16, we list their multiples.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, ...
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, ...
The common multiples of 6 and 16 are 48, 96, ...
The smallest common multiple (LCM) of 6 and 16 is 48.
In simple words: The smallest number that is a multiple of both 6 and 16 is 48.

🎯 Exam Tip: For larger numbers, prime factorization can be a more efficient method to find the LCM than listing all multiples.

Think it (Text Book Page No. 12)

 

Question 16. Can we say the highest common multiples for two numbers?
Answer: No, we cannot determine a "highest common multiple" for two numbers. Multiples of any number go on infinitely (e.g., multiples of 2 are 2, 4, 6, 8...). Therefore, common multiples would also go on infinitely, meaning there's no single highest one. We only talk about the Least Common Multiple (LCM) and Highest Common Factor (HCF).
In simple words: Multiples never end, so there can't be a "highest" common one. Only the "lowest" common multiple (LCM) makes sense.

🎯 Exam Tip: Understand the difference between factors (which are limited) and multiples (which are infinite) to correctly apply terms like HCF and LCM.