CBSE Class 6 Mathematics Algebra Assignment Set 03

VI - Mathematics Assignment No-03 - Algebra

Q1. Ajay think of a number, add 4 to it and the result is 10. Express in algebraic form. (Take number as \(x\))
Answer: Let the number be \(x\).
Adding 4 to the number gives \(x + 4\).
The result is equal to 10.
Algebraic expression / equation = \(x + 4 = 10\)
In simple words: Translate the sentence word-for-word into math symbols using \(x\) for the unknown number.

Exam Tip: Identify key action words like "add" to determine the correct arithmetic operation (+).

Q2. Anika think of two numbers, their difference is multiplied by 3, the result is 24. Form algebraic expression
Answer: Let the numbers be \(x\) and \(y\).
Their difference is \(x - y\).
Multiplying the difference by 3 gives \(3(x - y)\).
The result is 24, so the equation is \(3(x - y) = 24\).
In simple words: Write the difference inside parentheses first, then multiply the whole expression by 3.

Exam Tip: Whenever a phrase like "sum of" or "difference of" is multiplied by a number, always enclose the sum or difference in parentheses.

Q3. A number is 5 more than \(3x\). Express this number by an algebraic expression.
Answer: The given term is \(3x\).
"5 more than" means we need to add 5 to the given term.
Algebraic expression = \(3x + 5\)
In simple words: The phrase "more than" translates to addition (+) in algebra.

Exam Tip: "5 more than \(3x\)" means \(3x + 5\), not \(5 + 3x\) (though both are mathematically equivalent due to commutative property, the former matches the reading order).

Q4. Form an equation for the given statement,
(i) When 14 is added to a number, the result is 70.
Answer: Let the number be \(x\).
Equation = \(x + 14 = 70\)
In simple words: Add 14 to \(x\) and set it equal to 70.

Exam Tip: Use any variable like \(x\) or \(y\) when the number is not specified.

(ii) The difference of a number with 3 is 10
Answer: Let the number be \(x\).
Equation = \(x - 3 = 10\)
In simple words: Subtract 3 from the number and equate to 10.

Exam Tip: "Difference of a number with 3" means \(x - 3\).

(iii) Five times a number is 25
Answer: Let the number be \(x\).
Equation = \(5x = 25\)
In simple words: Multiply 5 by the number \(x\).

Exam Tip: "Five times" translates directly to multiplication, written compactly as \(5x\).

(iv) A number divided by 3 gives 15
Answer: Let the number be \(x\).
Equation = \(\frac{x}{3} = 15\)
In simple words: Divide the unknown number by 3 and put equal to 15.

Exam Tip: Division can be represented using a fraction bar like \(\frac{x}{3}\).

(v) Three is added to two times of a number gives 13.
Answer: Let the number be \(x\).
Two times of the number = \(2x\)
Three added to it = \(2x + 3\)
Equation = \(2x + 3 = 13\) (or \(3 + 2x = 13\))
In simple words: Form the term \(2x\), add 3, and equate to 13.

Exam Tip: Read carefully to combine operations in the correct sequence.

Q5. Replace * by a number to make a true statement
(i) \(* + 5 = 15\)
Answer: \(* = 15 - 5 = 10\)
In simple words: Find the missing addend by subtracting 5 from 15.

Exam Tip: Move the number to the other side by changing its sign.

(ii) \(* - 3 = 12\)
Answer: \(* = 12 + 3 = 15\)
In simple words: Add 3 to 12 to find the missing minuend.

(iii) \(* \div 4 = 12\)
Answer: \(* = 12 \times 4 = 48\)
In simple words: Multiply 12 by 4 to find the dividend.

Exam Tip: Inverse of division is multiplication.

(iv) \(\frac{*}{3} = 5\)
Answer: \(* = 5 \times 3 = 15\)
In simple words: Multiply 5 by 3.

Exam Tip: A fraction indicates division, so multiply both sides by the denominator.

(v) \(8 \times * = 48\)
Answer: \(* = \frac{48}{8} = 6\)
In simple words: Divide 48 by 8.

Exam Tip: Use division to find a missing factor in multiplication.

Q6. Pick out one value from the two values given in the bracket to make a true statement
(i) \(x + 5 = 10\) ; \((5, 6)\)
Answer: Substitute \(x = 5\): \(5 + 5 = 10\) (True)
Substitute \(x = 6\): \(6 + 5 = 11 \neq 10\) (False)
Correct value = 5
In simple words: Test each given number in the equation until the left side equals the right side.

Exam Tip: Substitution is the safest way to verify solutions in linear equations.

(ii) \(3x = 30\) ; \((10, 11)\)
Answer: Substitute \(x = 10\): \(3(10) = 30\) (True)
Substitute \(x = 11\): \(3(11) = 33 \neq 30\) (False)
Correct value = 10
In simple words: Check which number when multiplied by 3 gives 30.

Exam Tip: Remember that \(3x\) means \(3 \times x\).

(iii) \(\frac{x}{2} = 10\) ; \((20, 30)\)
Answer: Substitute \(x = 20\): \(\frac{20}{2} = 10\) (True)
Substitute \(x = 30\): \(\frac{30}{2} = 15 \neq 10\) (False)
Correct value = 20
In simple words: Half of 20 is 10, so 20 is the correct value.

Exam Tip: Test by reversing the operation: \(10 \times 2 = 20\).

(iv) \(x - 3 = 10\) ; \((13, 23)\)
Answer: Substitute \(x = 13\): \(13 - 3 = 10\) (True)
Substitute \(x = 23\): \(23 - 3 = 20 \neq 10\) (False)
Correct value = 13
In simple words: 13 minus 3 gives 10.

Exam Tip: You can also solve \(x = 10 + 3 = 13\) directly.

(v) \(3x + 5 = 5\) ; \((0, 10)\)
Answer: Substitute \(x = 0\): \(3(0) + 5 = 0 + 5 = 5\) (True)
Substitute \(x = 10\): \(3(10) + 5 = 35 \neq 5\) (False)
Correct value = 0
In simple words: Putting 0 for \(x\) leaves just 5.

Exam Tip: Any number multiplied by 0 is 0.

Q7. Fill the gap:
Answer:

In simple words: Add 5 to each given value of \(n\) in the table.

Exam Tip: Be careful with negative numbers when adding positive integers.

Q8. Solve the following equations for \(x\):
(i) \(x + 8 = 10\)
Answer:
\(x = 10 - 8\)
\(x = 2\)
In simple words: Subtract 8 from 10 to isolate \(x\).

Exam Tip: Transposing a term changes its sign from positive to negative.

(ii) \(x - 3 = 13\)
Answer:
\(x = 13 + 3\)
\(x = 16\)
In simple words: Add 3 to 13 to find \(x\).

Exam Tip: Transposing a negative term makes it positive.

(iii) \(x \times 5 = 50\)
Answer:
\(x = \frac{50}{5}\)
\(x = 10\)
In simple words: Divide 50 by 5.

Exam Tip: Multiplication on one side becomes division on the other side.

(iv) \(x \div 5 = 30\)
Answer:
\(x = 30 \times 5\)
\(x = 150\)
In simple words: Multiply 30 by 5.

Exam Tip: Division on one side becomes multiplication on the other side.

(v) \(4x = 20\)
Answer:
\(x = \frac{20}{4}\)
\(x = 5\)
In simple words: Divide 20 by 4.

Exam Tip: Coefficient of \(x\) goes to the denominator when transposed.

Q9. A Cuboid is a three dimensional object, (Look at your pencil box which is a cuboid), having length 'l', width 'b' and height 'h'. Calculate the total length of edges of the cuboid.
Answer: A cuboid has 12 edges in total:
- 4 edges of length \(l\)
- 4 edges of width \(b\)
- 4 edges of height \(h\)
Total length of edges = \(4l + 4b + 4h\)
In simple words: Add up the lengths of all 12 edges of a cuboid.

Exam Tip: A cuboid has 4 lengths, 4 breadths, and 4 heights.

Q10. Nisha scored one-half the total marks scored by Sita and Geeta in Maths. If Seeta and Geeta scored \(x\) and \(3y\) marks respectively, express, by an algebraic expression, the marks scored by Nisha.
Answer: Marks scored by Sita = \(x\)
Marks scored by Geeta = \(3y\)
Total marks scored by Sita and Geeta = \(x + 3y\)
Nisha's marks = One-half of total marks = \(\frac{1}{2}(x + 3y)\)
In simple words: Add Sita and Geeta's marks and divide the sum by 2.

Exam Tip: "One-half" means multiplying by \(\frac{1}{2}\) or dividing by 2.