Q1: What does Ameena ask Sarita to do in the mind-reading game? (a) Think of a number, multiply it by 10, and subtract 20 (b) Think of a number, multiply it by 4, and add 5 (c) Think of a number, multiply it by 5, and subtract 10 (d) Think of a number, divide it by 4, and add 5
Solution:
Ans: (b) Ameena asks Sarita to think of a number, multiply it by 4, and add 5 to the product, resulting in a final answer of 65.
Q2: In the equation 4x + 5 = 65, what does the term LHS refer to? (a) 65 (b) 4x + 5 (c) 4x (d) x
Solution:
Ans: (b) LHS stands for left-hand side of the equation. In 4x + 5 = 65, the left-hand side is 4x + 5, which is on the left of the equal sign.
Q3: Which of the following is NOT an equation? (a) 4x + 5 = 65 (b) 65 = 4x + 5 (c) 4x + 5 > 65 (d) 10y - 20 = 50
Solution:
Ans: (c) An equation must have an equality sign. 4x + 5 > 65 uses a greater than sign, not an equality sign, so it is not an equation.
Q4: What number did Balu think of in Appu's game? (a) 15 (b) 5 (c) 10 (d) 7
Solution:
Ans: (d) Appu accurately guesses that Balu's number was 7 after Balu multiplied it by 10 and subtracted 20 to get a result of 50.
Q5: When transposing a term from one side of an equation to the other, what happens to its sign? (a) It remains the same (b) It changes to the opposite sign (c) It becomes zero (d) It doubles in value
Solution:
Ans: (b) When transposing, the sign of the term changes: a positive term becomes negative and a negative term becomes positive when moved to the other side.
Fill in the Blanks
Q1: An equation is like a balance _____ where both sides have equal value.
Solution:
Ans: scale
Q2: The part on the right of the equal sign is called the _____.
Solution:
Ans: RHS
Q3: Any value of the variable that makes the equation true is called a _____ of the equation.
Solution:
Ans: solution
Q4: In Ameena's example, the equation formed is 4x + 5 = 65, and solving it gives x = _____.
Solution:
Ans: 15
Q5: To convert the statement "A number increased by 5 is 12" into an equation, we write x + 5 = _____.
Solution:
Ans: 12
True or False
Q1: An equation remains true if the LHS and RHS are interchanged.
Solution:
Ans: True An equation maintains its validity when LHS and RHS are swapped. For example, 4x + 5 = 65 is the same as 65 = 4x + 5.
Q2: If different operations are applied to each side of an equation, the equality still holds.
Solution:
Ans: False Applying different operations to each side breaks the equality. For example, adding 2 to one side and 3 to the other destroys the balance.
Q3: Ameena correctly guesses that Sarita's number was 15 when the final answer was 65.
Solution:
Ans: True Ameena quickly and accurately guesses that the number Sarita thought of was 15, which when multiplied by 4 and added to 5 gives 65.
Q4: An equation must always have the variable only on the left-hand side.
Solution:
Ans: False Both sides of an equation can contain the variable. For example, 4x + 5 = 6x - 25 has the variable on both sides.
Q5: To solve 25y = 125, we divide both sides by 25 to get y = 5.
Solution:
Ans: True Dividing both sides of the equation 25y = 125 by 25 gives y = 5, which is the correct solution to this equation.
Match the Following
Column A
Column B
1. The sum of four times x and 12 is 38
A. x - 3 = 7
2. A number decreased by 3 is equal to 7
B. x + 5 = 12
3. If you subtract 4 from 6 times a number, you get 8
C. (n/4) + 7 = 10
4. A number increased by 5 is 12
D. 4x + 12 = 38
5. One fourth of a number plus 7 is 10
E. 6z - 4 = 8
Solution:
Ans:
1 - D: Four times x is 4x, and its sum with 12 equals 38, forming the equation 4x + 12 = 38.
2 - A: A number decreased by 3 means subtracting 3 from x, which equals 7, giving the equation x - 3 = 7.
3 - E: Six times a number z is 6z, and subtracting 4 from it gives 8, forming the equation 6z - 4 = 8.
4 - B: A number increased by 5 means adding 5 to x, which equals 12, resulting in the equation x + 5 = 12.
5 - C: One fourth of n is n/4, and adding 7 to it equals 10, forming the equation (n/4) + 7 = 10.
Short Answer Questions
Q1: Explain what an equation is and give one example from the mind-reading game.
Solution:
Ans: An equation is like a balance scale with an equal sign in the middle, showing that the value on the left side is the same as the value on the right side. The left part is the LHS and the right part is the RHS. In Ameena's game, when Sarita multiplied her number by 4 and added 5 to get 65, the equation formed was 4x + 5 = 65.
Q2: How do you form an equation from a statement? Describe the steps with an example.
Solution:
Ans: To form an equation from a statement, first identify the unknown quantity and represent it with a variable. Then translate words into mathematical operations such as addition, subtraction, multiplication, or division. Next, combine the variable and operations using the equal sign where equality is indicated. For example, "A number increased by 5 is 12" becomes x + 5 = 12.
Q3: What is transposing in equations and how does it help in solving them?
Solution:
Ans: Transposing means moving a term from one side of an equation to the other side. When a term is transposed, its sign changes: positive becomes negative and negative becomes positive. This method helps collect all variable terms on one side and constants on the other side. For example, in x + 11 = 35, transposing 11 to the right gives x = 35 - 11, making x = 24.
Q4: Solve the problem: Shikha's mother's age is 5 years more than three times Shikha's age. If the mother is 44 years old, find Shikha's age.
Solution:
Ans: Let Shikha's age be y years. Mother's age is three times Shikha's age plus 5, which is 3y + 5. Given that mother is 44 years old, the equation is 3y + 5 = 44. Transposing 5 to the right gives 3y = 39. Dividing both sides by 3 gives y = 13. Therefore, Shikha's age is 13 years.
Q5: How can you check if a given value is a solution to an equation? Explain with an example.
Solution:
Ans: To check if a value is a solution, substitute it into the equation and verify if both sides are equal. For example, to check if n = 1 is a solution of n + 5 = 19, substitute n = 1 to get 1 + 5 = 6. Since 6 does not equal 19, n = 1 is not a solution. Any value making both sides equal is the correct solution.
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