Maharashtra Board Class 5 Maths Chapter 16 Preparation for Algebra Set 54 Solutions

Question 1. Using brackets, write three pairs of numbers whose sum is 13. Use them to write three equalities.
Answer: (7 + 6), (8 + 5), (9 + 4). since 7 + 6 = 13, 8 + 5 = 13, 9 + 4 = 13. (7 + 6) = (8 + 5), (7 + 6) = (9 + 4) or (8 + 5) = (9 + 4).
In simple words: To find pairs of numbers that sum to 13, identify two numbers that add up to 13 and write them using brackets. Then, use these pairs to create equality statements showing their sum is 13.

🎯 Exam Tip: Clearly show the pairs of numbers in brackets and then write the equality statements to demonstrate the sum. Ensure all parts of the question are addressed.

Question 2. Find four pairs of numbers, one for each of addition, subtraction, multiplication and division that make the number 18. Write the equalities for each of them.
Answer: (9 + 9), (20 - 2), (9 x 2), (36 ÷ 2). since 9 + 9 = 18, 20 - 2 = 18, 9 x 2 = 18 and 36 ÷ 2 = 18, so (9 + 9) = (20 - 2) = (9 x 2) = (36 ÷ 2).
In simple words: For each of the four operations - addition, subtraction, multiplication, and division - find a pair of numbers that result in 18 and express this relationship as an equality.

🎯 Exam Tip: Remember to use different pairs of numbers for each operation to clearly demonstrate understanding of all four basic arithmetic functions achieving the target number.

Inequality

The values of \( 7 + 5 \) and \( 7 \times 5 \) are 12 and 35 respectively. It means that they are not equal. To represent 'not equal', the symbol '≠' is used.

To show that \( (7 + 5) \) and \( (7 \times 5) \) are not equal, we write \( (7 + 5) \neq (7 \times 5) \) in short.

This kind of representation is called an 'inequality'.

\( (9 - 5) \neq (15 \div 3) \) means that the expressions \( (9 - 5) \) and \( (15 \div 3) \) are not equal.

If two expressions are not equal, one of them is greater or smaller than the other.

To show greater or lesser values, we use the symbols '<' and '>'. Therefore, these symbols can also be used to show inequalities.

The value of \( (9 - 5) \) is 4 and the value of \( (15 \div 3) \) is 5. \( 4 < 5 \), so the relation between \( (9 - 5) \) and \( (15 \div 3) \) can be shown as \( (9 - 5) < (15 \div 3) \) or \( (15 \div 3) > (9 - 5) \).

Question. Fill in the boxes between the expressions with <, = or > as required.

(1) \( (9 + 8) \text{ [ ] } (30 \div 2) \)
9 + 8 = 17,
30 ÷ 2 = 15
17 > 15
Therefore \( (9 + 8) \text{ [ > ] } (30 \div 2) \)
Answer: \( (9 + 8) \text{ [ > ] } (30 \div 2) \)

(2) \( (16 \times 3) \text{ [ ] } (4 \times 12) \)
16 × 3 = 48,
4 × 12 = 48,
48 = 48
Therefore \( (16 \times 3) \text{ [ = ] } (4 \times 12) \)
Answer: \( (16 \times 3) \text{ [ = ] } (4 \times 12) \)

(3) \( (16 - 5) \text{ [ ] } (2 \times 7) \)
16 - 5 = 11,
2 × 7 = 14,
11 < 14
Therefore \( (16 - 5) \text{ [ < ] } (2 \times 7) \)
Answer: \( (16 - 5) \text{ [ < ] } (2 \times 7) \)
In simple words: For each pair of expressions, calculate their values and then use the appropriate symbol (>, <, or =) to show their relationship.

🎯 Exam Tip: Always perform the calculations for both sides of an expression before attempting to determine the correct relational symbol.

Question. Write a number in the box that will make this statement correct.

(1) \( (7 \times 2) = ( \text{ [ ] } - 6) \)
The value of the expression \( 7 \times 2 \) is 14, so the number in the box has to be one that gives 14 when 6 is subtracted from it. Subtracting 6 from 20 gives us 14.
Therefore \( (7 \times 2) = ( \text{ [ 20 ] } - 6) \)
Answer: \( (7 \times 2) = ( \text{ [ 20 ] } - 6) \)

(2) \( (24 \div 3) < (5 + \text{ [ ] }) \)
The value of the expression \( 24 \div 3 \) is 8, so the number in the box has to be such that when it is added to 5, the sum is greater than 8.
Now, \( 5 + 1 = 6 \), \( 5 + 2 = 7 \), \( 5 + 3 = 8 \). So the number in the box has to be greater than 3.
Therefore, writing any number like 4, 5, 6 ... onwards will do. It means that this problem has several answers. \( (24 \div 3) < (5 + \text{ [ 4 ] } ) \) is one among many answers. Even if that is true, writing only one answer will be enough to complete this statement.
Answer: \( (24 \div 3) < (5 + \text{ [ 4 ] } ) \) (or any number greater than 3)
In simple words: For each inequality, determine the missing number that makes the statement true by balancing the equation or satisfying the inequality.

🎯 Exam Tip: When filling in a box for an inequality, remember there might be multiple correct answers. Provide any valid number that satisfies the condition.

Preparation For Algebra Problem Set 54 Additional Important Questions And Answers

Question 1. Fill in the blanks.
(1) \( 7 + 3 = \text{ ......................} \)
(2) \( 7 + 3 = \text{ ...................... x ......................} \)
(3) \( 7 + 3 = \text{ ...................... + ......................} \)
Answer:
(1) \( 7 + 3 = 10 \) and \( 12 - 2 = 10 \) or \( 15 - 5 = 10 \)
(2) \( 7 + 3 = 10 \) and \( 10 \times 1 = 10 \) or \( 5 \times 2 = 10 \)
(3) \( 7 + 3 = 10 \) and \( 20 + 2 = 10 \) or \( 30 + 3 = 10 \)
In simple words: Understand that the expression 7 + 3 equals 10, then find different mathematical operations (subtraction, multiplication, addition) that also result in 10 to fill the blanks.

🎯 Exam Tip: Focus on understanding that the given expression (7+3=10) is the target value. Find various equivalent expressions using different operations to correctly fill the blanks.

Question 2. Write the proper number in the box.

(1) \( 7 + 8 = 10 + \text{ [ ] } \)
Answer: \( 7 + 8 = 15 \) so, \( 10 + \text{ [ ] } = 15 \). \( \therefore \text{ [ ] } = 15 - 10 = 5 \)

(2) \( 7 + 8 = 20 - \text{ [ ] } \)
Answer: \( 7 + 8 = 15 \) so, \( 20 - \text{ [ ] } = 15 \). \( \therefore \text{ [ ] } = 20 - 15 = 5 \)

(3) \( 7 + 8 = 30 + \text{ [ ] } \)
Answer: \( 7 + 8 = 15 \) so, \( 30 + \text{ [ ] } = 15 \). \( \therefore \text{ [ ] } = 30 + 15 = 2 \)

(4) \( 7 + 8 = 5 \times \text{ [ ] } \)
Answer: \( 7 + 8 = 15 \) so, \( 5 \times \text{ [ ] } = 15 \). \( \therefore \text{ [ ] } = 15 + 5 = 3 \)
In simple words: Calculate the value of 7 + 8, which is 15. Then, for each sub-part, find the missing number in the box that makes the equation true.

🎯 Exam Tip: First, solve the known side of the equation (7+8). Then, use basic arithmetic operations to isolate the unknown variable in the box for the other side of the equation.