CBSE Class 6 Mathematics Algebra Assignment Set 05

VI - Mathematics Assignment No-01 - Algebra

Question 1. Write the following using numbers, literal numbers and basic arithmetic operations.
(a) The sum of the numbers 5 and x
Answer: \(5 + x\)
In simple words: Addition of 5 and the variable x is written as \(5 + x\).

Exam Tip: The word 'sum' indicates addition (+).

Question 1(b). 4 less than the number x
Answer: \(x - 4\)
In simple words: Subtracting 4 from x gives \(x - 4\).

Exam Tip: 'Less than' means subtraction where the amount is taken away from the given variable.

Question 1(c). 5 more than the number y
Answer: \(y + 5\)
In simple words: Adding 5 to y gives \(y + 5\).

Exam Tip: 'More than' means addition (+).

Question 1(d). Two-fifth of a number x
Answer: \(\frac{2}{5}x\)
In simple words: Multiply the fraction \(\frac{2}{5}\) by x.

Exam Tip: Fractional parts like 'two-fifth' are written as coefficients multiplying the variable.

Question 1(e). One-third of the sum of the numbers x and y
Answer: \(\frac{1}{3}(x + y)\)
In simple words: First find the sum \(x + y\), then multiply by \(\frac{1}{3}\).

Exam Tip: Always use parentheses when applying an operation to a sum or difference.

Question 1(f). 3 less than the quotient of x and y
Answer: \(\frac{x}{y} - 3\)
In simple words: Divide x by y to get the quotient, then subtract 3.

Exam Tip: 'Quotient' means division (\(\frac{x}{y}\)).

Question 1(g). 4 more than thrice a number x
Answer: \(3x + 4\)
In simple words: Thrice x is \(3x\), and 4 more than that is \(3x + 4\).

Exam Tip: 'Thrice' means multiplication by 3.

Question 1(h). Number x multiplied by itself
Answer: \(x^2\)
In simple words: Multiplying x by x gives \(x \times x = x^2\).

Exam Tip: Repeated multiplication of the same variable results in exponents.

Question 1(i). 5 times a number x
Answer: \(5x\)
In simple words: Multiply 5 by x.

Exam Tip: 'Times' indicates multiplication.

Question 1(j). Number y less than a number 5
Answer: \(5 - y\)
In simple words: Subtract y from 5.

Exam Tip: Pay close attention to the order of subtraction in phrases like 'less than'.

Question 2. (i) Write a number which is 5 more than x.
Answer: \(5 + x\)
In simple words: Add 5 to x.

Exam Tip: 'More than' translates directly to addition.

Question 2. (ii) A number 3 less than x, write the number.
Answer: \(x - 3\)
In simple words: Subtract 3 from x.

Exam Tip: 'Less than x' means x comes first, followed by minus 3.

Question 2. (iii) If 5 is added to x, it becomes y, write y in terms of x.
Answer: \(y = 5 + x\)
In simple words: Equate y to the sum of 5 and x.

Question 3. Write the following statements using numbers, literal numbers and operations. State what each letter represents?
(i) The selling price of an item is equal to the sum of the cost price of the item and the profit earned.
Answer: \(S.P. = C.P. + Profit\)
Let S represent Selling Price, C represent Cost Price, and P represent Profit.
In simple words: Selling price is found by adding cost price and profit together.

Exam Tip: Define all variables clearly when converting word formulas into algebraic equations.

Question 3. (ii) The profit on an item is the difference between selling price and cost price.
Answer: \(Profit = S.P. - C.P.\)
Let S represent Selling Price, C represent Cost Price, and P represent Profit.
In simple words: Profit is calculated by subtracting cost price from selling price.

Exam Tip: 'Difference' means subtraction.

Question 3. (iii) Amount is equal to the sum of principal and interest.
Answer: \(A = P + I\)
Let A represent Amount, P represent Principal, and I represent Interest.
In simple words: Total amount is principal plus interest.

Exam Tip: Standard financial formula representation in algebra.

Question 4. Write the number which is 5 times the product of x and y.
Answer: \(5xy\)
In simple words: The product of x and y is \(xy\), and 5 times that is \(5xy\).

Exam Tip: Product terms are written together without multiplication signs.

Question 5. Write the number which is 5 more than \(\frac{1}{3}\text{rd}\) of the number x.
Answer: \(\frac{1}{3}x + 5\)
In simple words: One-third of x is \(\frac{1}{3}x\), and 5 more than that is \(\frac{1}{3}x + 5\).

Exam Tip: Combine fractional terms and addition correctly.

Question 6. Write the following using numbers, literals and signs of basic operation: Quotient of x by y added to the product of x and y.
Answer: \(\frac{x}{y} + xy\)
In simple words: Quotient is \(\frac{x}{y}\), product is \(xy\), add them together.

Exam Tip: Break complex statements into smaller parts (quotient part + product part).

Question 7. Write the following statement, using numbers, literals and signs of basic operations: '8 times a number x is y less than a number z'
Answer: \(8x = z - y\)
In simple words: 8 times x equals z minus y.

Exam Tip: 'Is' translates to the equals sign (\(=\)).

Question 8. Write the following in exponential form:
(i) \(a \times a \times a \times \dots\) 15 times
Answer: \(a^{15}\)
In simple words: Multiplying a by itself 15 times gives \(a^{15}\).

Exam Tip: The count of repetitions becomes the exponent.

Question 8. (ii) \(5 \times x \times x \times x \times y \times y \times y\)
Answer: \(5x^3y^3\)
In simple words: Combine coefficient 5, \(x \times x \times x\) as \(x^3\), and \(y \times y \times y\) as \(y^3\).

Exam Tip: Group like variables together when writing in exponential form.

Question 9. Ram scores 60 marks in mathematics and x marks in English. What is his total score in the two subjects?
Answer: \((x + 60) \text{ marks}\)
In simple words: Add mathematics marks and English marks together.

Exam Tip: Always include units like 'marks' in the final answer when specified in word problems.

Question 10. Write \(9x^2y^2z^2\) in product form.
Answer: \(9 \times x \times x \times y \times y \times z \times z\)
In simple words: Expand each squared variable into individual multiplications.

Exam Tip: Product form breaks down exponents into explicit multiplication factors.