Samacheer Kalvi Class 5 Maths Solutions Term 3 Chapter 4 Algebra Exercise 4.2

Tamilnadu Samacheer Kalvi 5th Maths Solutions Term 3 Chapter 4 Algebra Ex 4.2

Question 1. Say whether true or false
(i) (23 + 4) = (4 + 23)
Answer: True
In simple words: The sum of 23 and 4 is 27. The sum of 4 and 23 is also 27. Since both sides are equal, the statement is true. This shows that the order in which we add numbers does not change the total.

🎯 Exam Tip: When checking true/false statements, perform the operations on both sides of the equation or inequality to confirm the result.

Question 1.
(ii) (9 + 4) > 12
Answer: True
In simple words: When we add 9 and 4, we get 13. Since 13 is a number greater than 12, the statement is correct.

🎯 Exam Tip: Always calculate the values on both sides of an inequality before comparing them. The greater than (>) symbol means the left side must be larger than the right side.

Question 1.
(iii) (9 + 4) < 12
Answer: False
In simple words: Adding 9 and 4 gives 13. The statement says 13 is less than 12, which is not correct.

🎯 Exam Tip: Understand the difference between less than (<) and greater than (>) symbols clearly. Misinterpreting them is a common mistake.

Question 1.
(iv) 11 > 121
Answer: False
In simple words: The number 11 is smaller than 121. So, the statement that 11 is greater than 121 is wrong.

🎯 Exam Tip: When comparing numbers, look at their place values. A number with more digits or a larger digit in the highest place value is generally larger.

Question 1.
(v) 142 < 142
Answer: False
In simple words: The number 142 is exactly the same as 142. It cannot be less than itself.

🎯 Exam Tip: A number is only less than itself if the condition allows for equality, like "less than or equal to" (\(\le\)). When it's strictly "less than" (\(<\)), it must be different.

Question 1.
(vi) 112 = 112
Answer: True
In simple words: The number 112 is equal to 112. This statement is correct because both sides have the exact same value.

🎯 Exam Tip: The equal sign (\(=\)) indicates that the value on the left side is exactly the same as the value on the right side.

Question 1.
(vii) (6 × 5) = (32 - 2)
Answer: True
In simple words: Multiplying 6 by 5 gives 30. Subtracting 2 from 32 also gives 30. Since both results are 30, the statement is true. Always finish both calculations first.

🎯 Exam Tip: For expressions involving multiple operations, perform all calculations on both sides of the equals sign before making a comparison.

Question 1.
(viii) \( \frac { 49 }{ 7 } > 7 \)
Answer: False
In simple words: When we divide 49 by 7, the answer is 7. The statement says 7 is greater than 7, which is incorrect because 7 is equal to 7.

🎯 Exam Tip: Pay very close attention to the specific comparison symbol used. `>` means "strictly greater than," not "greater than or equal to."

Question 1.
(ix) (4 × 3) = (3 × 4)
Answer: True
In simple words: Multiplying 4 by 3 gives 12. Multiplying 3 by 4 also gives 12. This shows that the order of numbers does not change the result in multiplication.

🎯 Exam Tip: This property is called the commutative property of multiplication. It's a fundamental concept in algebra.

Question 1.
(x) (21 + 0) = 21
Answer: True
In simple words: When you add zero to any number, the number itself stays the same. So, 21 plus 0 is indeed 21.

🎯 Exam Tip: Zero is called the "additive identity" because adding it to any number does not change the number's identity.

Question 2. Fill in the blanks with the right symbol (<, > or =).
(i) (54 ÷ 9) ____ (8 - 3)
Answer:
\( 54 \div 9 = 6 \)
\( 8 - 3 = 5 \)
\( 6 > 5 \)
So, \( (54 \div 9) > (8 - 3) \)
In simple words: First, 54 divided by 9 equals 6. Then, 8 minus 3 equals 5. Since 6 is bigger than 5, we use the `>` sign.

🎯 Exam Tip: When filling in comparison symbols, always calculate the numerical value of both expressions fully before deciding which symbol to use.

Question 2.
(ii) (6 + 2) ____ (4 × 2)
Answer:
\( 6 + 2 = 8 \)
\( 4 \times 2 = 8 \)
So, \( (6 + 2) = (4 \times 2) \)
In simple words: Adding 6 and 2 gives 8. Multiplying 4 by 2 also gives 8. Since both sides are equal, we put the `=` sign in the blank.

🎯 Exam Tip: The equals sign is used when two different mathematical expressions or operations yield the exact same numerical result.

Question 2.
(iii) (10 × 2) ____ (15 + 20)
Answer:
\( 10 \times 2 = 20 \)
\( 15 + 20 = 35 \)
\( 20 < 35 \)
So, \( (10 \times 2) < (15 + 20) \)
In simple words: 10 times 2 is 20. 15 plus 20 is 35. Since 20 is a smaller number than 35, we use the `<` sign.

🎯 Exam Tip: Always double-check your calculations before comparing numbers. A small mistake in addition or multiplication can lead to selecting the wrong comparison symbol.

Question 3. Fill in the blanks in the expressions with the suitable number.
(i) (1 × 9) = (___ × 1)
Answer:
\( (1 \times 9) = (9 \times 1) \)
In simple words: The left side is 1 multiplied by 9, which is 9. To make the right side equal to 9, the blank must be 9, because 9 multiplied by 1 is also 9. This uses the swapping property of multiplication.

🎯 Exam Tip: This question tests the commutative property of multiplication, which states that changing the order of factors does not change the product.

Question 3.
(ii) (6 × 3) > (8 × ___ )
Answer:
\( 6 \times 3 = 18 \)
We need \( 8 \times \text{number} < 18 \). If the blank is 2, then \( 8 \times 2 = 16 \).
Since \( 18 > 16 \), the suitable number is 2.
So, \( (6 \times 3) > (8 \times 2) \)
In simple words: 6 times 3 is 18. We need to find a number that, when multiplied by 8, gives a result smaller than 18. The number 2 works, because 8 times 2 is 16, and 18 is bigger than 16.

🎯 Exam Tip: For inequality problems with a blank, calculate the known side first. Then, find a number for the blank that makes the inequality true by testing small, logical values.

Question 3.
(iii) (36 ÷ 6) < (___ × 7)
Answer:
\( 36 \div 6 = 6 \)
We need \( \text{number} \times 7 > 6 \). If the blank is 1, then \( 1 \times 7 = 7 \).
Since \( 6 < 7 \), the suitable number is 1.
So, \( (36 \div 6) < (1 \times 7) \)
In simple words: 36 divided by 6 is 6. We need to find a number that, when multiplied by 7, gives a result larger than 6. The number 1 works, because 1 times 7 is 7, and 6 is smaller than 7.

🎯 Exam Tip: When solving inequalities with a blank, determine what value the blank must make the expression on that side to satisfy the comparison with the known side.

Question 3.
(iv) (0 + 2) > (7 × ______)
Answer:
\( 0 + 2 = 2 \)
We need \( 7 \times \text{number} < 2 \). If the blank is 0, then \( 7 \times 0 = 0 \).
Since \( 2 > 0 \), the suitable number is 0.
So, \( (0 + 2) > (7 \times 0) \)
In simple words: 0 plus 2 is 2. We need to find a number that, when multiplied by 7, gives a result smaller than 2. The number 0 works, because 7 times 0 is 0, and 2 is bigger than 0.

🎯 Exam Tip: Remember the multiplication property of zero: any number multiplied by zero always results in zero. This is crucial for solving such problems.

Question 3.
(v) (42 ÷ 7) = (4 + ______)
Answer:
\( 42 \div 7 = 6 \)
We need \( 4 + \text{number} = 6 \). If the blank is 2, then \( 4 + 2 = 6 \).
So, \( (42 \div 7) = (4 + 2) \)
In simple words: First, 42 divided by 7 equals 6. To make the other side equal to 6, we need to find what number added to 4 makes 6. That number is 2.

🎯 Exam Tip: To solve equations with a missing number, first simplify the side that has all known values. Then, work out what value the blank needs to be to make the other side equal.

Question 3.
(vi) (6 – ____) < (1 + 2)
Answer:
\( 1 + 2 = 3 \)
We need \( 6 - \text{number} < 3 \). If the blank is 4, then \( 6 - 4 = 2 \).
Since \( 2 < 3 \), the suitable number is 4.
So, \( (6 - 4) < (1 + 2) \)
In simple words: First, 1 plus 2 is 3. We need to subtract a number from 6 so that the answer is smaller than 3. If we subtract 4 from 6, we get 2, which is smaller than 3. So, the missing number is 4.

🎯 Exam Tip: For inequalities, think about what values would make the statement true. Sometimes there can be more than one correct number, but usually, the simplest whole number is expected.