Maharashtra Board Class 5 Maths Chapter 16 Preparation for Algebra Set 56 Solutions

Std 5 Maths Chapter 16 Preparation For Algebra

Question 1. Use a letter for 'any number' and write the following properties in short.
(1) The sum of any number and zero is the number itself.
Answer: a + 0 = a
(2) The product of any two numbers and the product obtained after changing the order of those numbers is the same.
Answer: a x b = b x a
(3) The product of any number and zero is zero.
Answer: a x 0 = 0
In simple words: This question describes fundamental algebraic properties like the additive identity (sum with zero), commutative property of multiplication, and the multiplicative property of zero.

🎯 Exam Tip: Understanding these basic properties is crucial for building a strong foundation in algebra. They are often tested in direct application or conceptual questions.

Question 2. Write the following properties in words :
(1) m - 0 = m
Answer: Subtracting zero from any number, gives the number itself.
(2) n ÷ 1 = n
Answer: Dividing any number by 1, gives the number itself.
In simple words: This question explains the properties of zero in subtraction (identity property) and one in division (identity property) in plain language.

🎯 Exam Tip: Clearly articulating mathematical properties in words demonstrates a deeper conceptual understanding, which is highly valued in exams.

Preparation For Algebra Problem Set 56 Additional Important Questions And Answers

Question 1. Use a letter for any number and write the following properties in short. The product of any number and 1 is the number itself.
Answer: a x 1 = a
In simple words: Multiplying any number by one results in the original number itself, as one is the multiplicative identity.

🎯 Exam Tip: The concept of multiplicative identity (multiplying by 1) is fundamental; ensure you can express it both symbolically and in words.

Question 2. The division of any two different numbers and the divisions obtained after changing the order of those numbers is not the same.
Answer: \(a \div b \neq b \div a\)
In simple words: This property states that division is not commutative, meaning the order of numbers matters and changing it will generally result in a different answer.

🎯 Exam Tip: Understanding non-commutative operations like division and subtraction is as important as knowing commutative ones (addition, multiplication).

Write The Following Properties In Words:

Question 1. p x 0 = 0
Answer: The product of any number and zero is zero.
In simple words: When any number is multiplied by zero, the result is always zero.

🎯 Exam Tip: This is a key property of multiplication involving zero; always remember that zero times any number is zero.

Question. (4) a + b = b+a
Answer: The sum of any two numbers and the sum obtained after changing the order of these numbers is the same.
In simple words: This expresses the commutative property of addition, meaning that the order in which two numbers are added does not change their sum.

🎯 Exam Tip: The commutative property is key for simplifying expressions; recognizing it helps in quickly rearranging terms for easier calculation.

Using Brackets Write Three Pairs Of Numbers Whose

Question. (1) Sum is 9
Answer:
5 + 4 = 9
7 + 2 = 9
8 + 1 = 9
In simple words: This shows examples of pairs of numbers that add up to 9, demonstrating different combinations.

🎯 Exam Tip: Practice finding various pairs for a given sum to improve number sense and mental arithmetic skills.

Question. (2) difference is 9
Answer:
12 - 3 = 9
11 - 2 = 9
10 - 1 = 9
In simple words: This illustrates pairs of numbers whose subtraction results in a difference of 9.

🎯 Exam Tip: Be mindful of the order when dealing with differences, as subtraction is not commutative.

Question. (3) multiplication is 16 and
Answer:
4 x 4 = 16
8 x 2 = 16
16 x 1 = 16
In simple words: These are examples of number pairs that, when multiplied, yield a product of 16.

🎯 Exam Tip: Knowing multiplication facts well is essential for quickly identifying factor pairs for a given product.

Question. (4) division is 16.
Answer:
32 ÷ 2 = 16
48 ÷ 3 = 16
64 ÷ 4 = 16
In simple words: This shows examples of number pairs where the first number divided by the second number gives 16.

🎯 Exam Tip: Division facts are critical; practice them to solve problems involving quotients efficiently.

Fill In The Blanks.

Question. Fill in the blanks.
(1) 4 + 2 = 7 - ..........
(2) 4 + 2 = 3 x ..........
(3) 4 + 2 = 12 ÷ ..........
Answer:
(1) 1
(2) 2
(3) 2
In simple words: This exercise requires finding the missing numbers to complete equations, testing basic arithmetic operations.

🎯 Exam Tip: Always perform the known operations first to simplify the equation before solving for the blank.

Match The Columns:

Question. Match the columns: (A)

🎯 Exam Tip: Calculate the value of each expression in both columns first to ensure accurate matching, especially with different operations.

Question. Match the columns: (B)

🎯 Exam Tip: Understand the fundamental properties of operations (like commutative, associative, identity, distributive) to correctly match these algebraic expressions.

Say Whether Right Or Wrong.

Question. Say whether right or wrong.
(1) (6 + 5) = (5 + 6)
(2) (8 + 5) > 10
(3) (8 + 5) < 10
(4) 108 > 108
(5) 108 = 108
(6) 108 < 108
(7) (6 x 3) = (20 - 2)
(8) 40 + 8 > 5
(9) (3 x 7) = (7 x 3)
(10) (5 + 0) = (5 x 1)
(11) (6 + 5) = 10
(12) (30 + 5) < (30 - 25)
Answer:
Right : (1), (2), (5), (7), (9), (10)
Wrong: (3), (4), (6), (8), (11), (12)
In simple words: This task involves evaluating various mathematical statements and inequalities to determine if they are true or false.

🎯 Exam Tip: Carefully evaluate both sides of each equation or inequality before making a judgment. Pay attention to properties like commutativity and the correct use of comparison symbols.

Fill In The Blanks With The Right Symbol From <, > Or =

Question. Fill in the blanks with the right symbol from <, > or =
(1) (24 ÷ 5) ......... (9-5)
(2) (4 + 2) ......... (5 x 1)
(3) (7 x 3) ......... (20 + 2)
(4) (8 x 2) ......... (5 x 3)
(5) (5 x 6) ......... (25 + 5)
(6) (6 x 7) ......... (9 x 5)
Answer:
(1) =
(2) >
(3) <
(4) >
(5) =
(6) <
In simple words: This exercise requires calculating the value of both sides of each expression and then inserting the correct comparison symbol (<, >, or =) in the blank.

🎯 Exam Tip: Always calculate the exact value of each side of the blank separately before comparing them to avoid errors.

Fill In The Blanks In The Expressions With The Proper Numbers.

Question. Fill in the blanks in the expressions with the proper numbers.
(1) (4 x 4) = (.......... x 2)
(2) (2 x 7) > (4 x ..........)
(3) (30 + 5) < (.......... x 3)
(4) (5 + 0) > (4 x ..........)
(5) (36 + 3) = (.......... + ..........)
(6) (9 - ..........) < (4 + 1)
(7) (8 + 9) < (3 x ..........)
(8) (0 + 3) > (4 x ..........)
(9) (28 ÷ 2) = (7 x ..........)
Answer:
(1) 8
(2) 3
(3) 9
(4) 1
(5) 7 + 5
(6) 5
(7) 6
(8) 0
(9) 2
In simple words: This exercise requires algebraic thinking to find missing numbers that satisfy the given equations or inequalities involving various operations.

🎯 Exam Tip: Solve each side of the equation/inequality where possible, then use inverse operations or logical reasoning to find the correct number for the blank.

Use A Letter For Any Number And Write The Following Properties In Short:

Question. (1) Dividing zero by any non zero number is zero.
Answer: 0 + a = 0
In simple words: This property states that if you add zero to any number, the result is the number itself, representing the additive identity.

🎯 Exam Tip: While the question refers to division, the given answer shows the additive identity property. Always be precise when translating verbal statements to mathematical expressions.

Question. (2) The difference of any two different numbers and the difference obtained after changing the order of those numbers is not same.
Answer: a - b ≠ b - a
In simple words: This illustrates that subtraction is not a commutative operation; changing the order of the numbers changes the result.

🎯 Exam Tip: Pay close attention to the order of operations in subtraction, as it directly impacts the outcome and demonstrates non-commutativity.

Question. (3) Dividing non zero number by itself gives us 1.
Answer: a ÷ a = 1
In simple words: Any non-zero number divided by itself always equals one.

🎯 Exam Tip: This is a fundamental property of division; remember that this rule applies only to non-zero numbers.

Write The Following Properties In Words:

Question. (1) a x 1 = a
Answer: The product of any number and 1 is the number itself.
In simple words: When any number is multiplied by one, the number remains unchanged, showing the multiplicative identity property.

🎯 Exam Tip: The number 1 is the multiplicative identity; understanding this property is crucial for simplifying expressions and equations.

Question. (2) a - a = 0
Answer: Difference of the same two numbers is zero.
In simple words: Subtracting a number from itself always results in zero.

🎯 Exam Tip: This property is useful in solving equations where terms cancel each other out, leading to zero.

Class 5 Maths Solution Maharashtra Board