CBSE Class 6 Mathematics Algebra Assignment Set 01

Fill in the blanks:

Question 1. The __________ can take different values.
Answer: variable
In simple words: A variable is a quantity that can change or take various numerical values.

Exam Tip: Remember that letters like \(x\), \(y\), or \(z\) used in algebra represent variables.

Question 2. The value of the variable in an equation which satisfies the equation is called a __________ to the equation.
Answer: solution (or root)
In simple words: The solution is the specific number that makes both sides of the equation equal.

Exam Tip: Always substitute the value back into the equation to verify if it satisfies the condition.

Question 3. An equation has __________ sides, LHS and RHS, between them is the equal (=) sign.
Answer: two
In simple words: An equation is separated into two parts: a Left Hand Side and a Right Hand Side.

Exam Tip: LHS stands for Left Hand Side and RHS stands for Right Hand Side.

Question 4. The LHS of an equation is equal to its RHS only for a __________ of the variable in the equation.
Answer: particular value
In simple words: Unlike an identity, an equation holds true only for specific values of the variable.

Exam Tip: Equations are strict condition checkers for specific variable values.

Question 5. The value of a variable is not __________.
Answer: fixed
In simple words: Variables do not have a single permanent value; their value depends on the problem.

Exam Tip: Contrast variables with constants, which always maintain a fixed numerical value.

Question 6. An equation is expressed by saying that an expression with a variable is equal to a ___________.
Answer: constant (or another expression)
In simple words: An equation sets an algebraic expression equal to a specific value or another expression.

Exam Tip: The presence of the equals sign (=) is what defines an equation.

Question 7. The word ‘_________’ means something that can vary, i.e. change.
Answer: variable
In simple words: The term variable literally comes from the ability to vary.

Question 8. An ________ is a condition on a variable.
Answer: equation
In simple words: An equation restricts the variable to only take values that satisfy the equality.
Exam Tip: Think of an equation as a balanced weighing scale where the pointer rests only under a condition.

Do as directed:

Question 9. Write each of the following phrases using numbers, literals or variables and the basic operations:
(i) 5 times x.
Answer: \(5x\)
In simple words: Times means multiplication, so 5 times x is written as \(5x\).

Exam Tip: In algebra, multiplication between a number and a variable is written without any multiplication sign.

Question 9(ii). The product of 7 and x.
Answer: \(7x\)
In simple words: Product means the result of multiplying numbers and variables together.

Exam Tip: "Product of 7 and x" and "7 times x" mean the exact same thing.

Question 9(iii). Multiply x by 7.
Answer: \(7x\)
In simple words: Multiplying \(x\) by 7 gives \(7x\).

Exam Tip: Always write the numerical coefficient before the variable literal.

Question 9(iv). 3 taken away from the quotient of x by 2y.
Answer: \(\frac{x}{2y} - 3\)
In simple words: First divide \(x\) by \(2y\), then subtract 3 from that result.

Exam Tip: "Taken away from" means subtraction where the term following it is subtracted from the preceding expression.

Question 10. Write each of the following phrases using numbers, literals or variables and the basic operations:
(i) a times b.
Answer: \(ab\)
In simple words: Multiply variable \(a\) by variable \(b\).

Question 10(ii). 3 times x added to y.
Answer: \(y + 3x\) (or \(3x + y\))
In simple words: Add \(3x\) to \(y\).
Exam Tip: Addition is commutative, so both \(3x + y\) and \(y + 3x\) are correct.

Question 10(iii). Quotient of z by 6 is multiplied by y.
Answer: \(\frac{z}{6} \times y\) or \(\frac{zy}{6}\)
In simple words: Divide \(z\) by 6, then multiply the fraction by \(y\).

Exam Tip: The word "quotient" denotes division.

Question 10(iv). 4 times the sum of x and y.
Answer: \(4(x + y)\)
In simple words: First add \(x\) and \(y\) inside parentheses, then multiply the sum by 4.

Exam Tip: Whenever "sum of" or "difference of" is followed by a multiplication factor, brackets are mandatory.

Question 10(v). 3 times x is subtracted from y.
Answer: \(y - 3x\)
In simple words: Subtract \(3x\) starting from \(y\).

Exam Tip: "Subtracted from y" means \(y\) comes first in the subtraction expression.

Question 10(vi). Quotient of x by y added to the product of x and y.
Answer: \(\frac{x}{y} + xy\)
In simple words: Add the division of \(x\) by \(y\) to the product \(xy\).

Exam Tip: Break complex statements into parts (quotient part + product part) and connect them with the appropriate operation sign.

Question 10(vii). 5 more than thrice a number x.
Answer: \(3x + 5\)
In simple words: Thrice \(x\) is \(3x\), and 5 more means adding 5 to it.

Exam Tip: "More than" translates to addition.

Question 10(viii). 3 times x added to 7 times y.
Answer: \(3x + 7y\)
In simple words: Combine \(3x\) and \(7y\) with an addition sign.

Exam Tip: Identify each term separately before combining them.

Question 10(ix). Quotient of x by 4 is added to y.
Answer: \(y + \frac{x}{4}\) (or \(\frac{x}{4} + y\))
In simple words: Add \(\frac{x}{4}\) to \(y\).

Exam Tip: Quotient means numerator divided by denominator.

Question 10(x). Eight times a number p is x less than a number y.
Answer: \(8p = y - x\)
In simple words: \(8p\) equals \(y\) decreased by \(x\).

Exam Tip: "Is" translates to an equals sign (=), and "x less than y" means \(y - x\).

Question 11. Think of a number. Multiply it by 5. Add 6 to the result. Subtract y from this result. What is the result?
Answer: Let the thought number be \(x\).
Step 1: Multiply the number by 5 = \(5x\)
Step 2: Add 6 to the result = \(5x + 6$
Step 3: Subtract \(y\) from this result = \(5x + 6 - y$
Result = \(5x + 6 - y\)
In simple words: Follow each instruction sequentially: multiply by 5, add 6, and subtract \(y\).

Exam Tip: Proceed step-by-step from the initial variable to build the final expression.

Question 12. The number of rooms on the ground floor of a building is 12 less than the twice of the number of rooms on first floor. If the first floor has x rooms, how many rooms does the ground floor have?
Answer: Number of rooms on the first floor = \(x$
Twice the number of rooms on the first floor = \(2x$
Number of rooms on the ground floor = \(2x - 12\)
In simple words: Double the first floor rooms and subtract 12 to find the ground floor rooms.

Exam Tip: "12 less than twice x" means start with \(2x\) and subtract 12.

Question 13. Binny spends Rs. a daily and saves Rs. b per week. What is her income for two weeks?
Answer: Daily spending = Rs. \(a$
Spending in one week (7 days) = Rs. \(7a$
Weekly savings = Rs. \(b$
Total income in one week = Weekly spending + Weekly savings = Rs. \((7a + b)$
Total income for two weeks = \(2 \times (7a + b) = 14a + 2b\)
In simple words: Calculate weekly income by adding weekly spending and savings, then multiply by 2 for two weeks.

Exam Tip: Be careful with units: convert daily spending to weekly spending by multiplying by 7 before adding savings.

Question 14. Rahul scores 80 marks in English and x marks in Hindi. What is his total score in the two subjects?
Answer: Marks in English = 80
Marks in Hindi = \(x$
Total score = \(80 + x\)
In simple words: Add the marks of both subjects together.

Exam Tip: The sum of a constant and a variable cannot be simplified further, so leave it as \(80 + x\).

Question 15. One pencil costs Rs. 2 and one fountain pen costs Rs. 15. What is the cost of x pencils and y fountain pens?
Answer: Cost of 1 pencil = Rs. 2
Cost of \(x\) pencils = Rs. \(2x$
Cost of 1 fountain pen = Rs. 15
Cost of \(y\) fountain pens = Rs. \(15y$
Total cost = Rs. \(2x + 15y\)
In simple words: Multiply the quantity of each item by its unit cost and add them together.

Exam Tip: Always multiply individual item counts by their respective unit prices.

Question 16. Rohit covers x centimeters in one step. How much distance does he cover in y steps?
Answer: Distance covered in 1 step = \(x\) cm
Total distance covered in \(y\) steps = \(xy\) cm
In simple words: Multiply the distance of one step by the total number of steps taken.

Question 17. One apple weighs 75 grams and one orange weighs 40 grams. Determine the weight of x apples and y oranges.
Answer: Weight of 1 apple = 75 grams
Weight of \(x\) apples = \(75x\) grams
Weight of 1 orange = 40 grams
Weight of \(y\) oranges = \(40y\) grams
Total weight = \(75x + 40y\) grams
In simple words: Multiply the weight of each fruit by its quantity and sum the totals.
Exam Tip: Keep track of the units (grams) for clarity.

Question 18. A rectangular box has height h cm. Its length is 5 times the height and breadth is 10 cm less than the length. Express the length and the breadth of the box in terms of the height.
Answer: Height of the box = \(h\) cm
Length = 5 times height = \(5h\) cm
Breadth = 10 cm less than length = \(5h - 10\) cm
In simple words: Length is \(5h\), and breadth is 10 less than that length, making it \(5h - 10\).

Exam Tip: Express all dimensions step by step using the primary variable \(h\).

Question 19. Pick out the solution from the values given in the bracket next to each equation.
(a) \(p - 5 = 5\) \quad \((0, 10, 5)\)
Answer:
For \(p = 0\): \(0 - 5 = -5 \neq 5\)
For \(p = 10\): \(10 - 5 = 5\) (Satisfied)
For \(p = 5\): \(5 - 5 = 0 \neq 5\)
Solution: \(p = 10\)
In simple words: Test each number from the bracket until you find the one that makes the equation true.

Exam Tip: Show substitution for all test values to prove your final choice.

Question 19(b). \(\frac{q}{2} = 7\) \quad \((7, 2, 10, 14)\)
Answer:
For \(q = 7\): \(\frac{7}{2} \neq 7\)
For \(q = 2\): \(\frac{2}{2} = 1 \neq 7\)
For \(q = 10\): \(\frac{10}{2} = 5 \neq 7\)
For \(q = 14\): \(\frac{14}{2} = 7\) (Satisfied)
Solution: \(q = 14\)
In simple words: Substitute each candidate value into \(\frac{q}{2}\) to see which equals 7.

Question 20. Complete the entries in the third column of the table.
Answer:

Exam Tip: Verify equality by checking if LHS equals RHS after substitution.