The DAV Class 6 Maths Solutions and **DAV Class 6 Maths Chapter 6 Worksheet 1 **Solutions of Introduction to Algebra offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 6 WS 1 Solutions

Question 1.

Write the number which is:

(a) 5 more than x

Solution:

x + 5

(b) 3 less than y

Solution:

y – 3

(c) 2 times z

Solution:

2z

(d) One third of x

Solution:

\(\frac{1}{3}\) x

(e) 4 more than sum of a and b

Solution:

a + b + 4

Question 2.

Write the following expressions using numbers, literal numbers and arithmetic operations:

(a) x added to y

Solution:

x + y

(b) m increased by 2 ____

Solution:

m + 2

(c) Sum of x, y and z ___

Solution:

x + y + z

(d) 2 times p added to 3 times q ____

Solution:

2p + 3q

(e) One third the sum of a and b ____

Solution:

\(\frac{1}{3}\) (a + b)

(f) 4 less than x ____

Solution:

x – 4

(g) x less than 4 ____

Solution:

4 – x

(h) p taken away from twice q ____

Solution:

2q – p

(j) 3 times x ____

Solution:

3x

(j) One-fifth of y added to x ____

Solution:

\(\frac{1}{5}\) y + x

(k) 5 times the sum of x and y ____

Solution:

5 (x + y)

(l) a divided by 6 ____

Solution:

a ÷ 6

(m) Quotient of x by 5 ____

Solution:

x ÷ 5

(n) Half the sum of p and q ____

Solution:

\(\frac{1}{2}\) (p + q)

Question 3.

Write the following expressions in words:

(a) x + 5

Solution:

5 added to x

(b) y – 3

Solution:

3 less than y

(c) \(\frac{2}{3}\) x

Solution:

Two-third of x

(d) 4z

Solution:

4 times z

(e) \(\frac{x}{y}\)

Solution:

x divided by y

(f) 2a + 3b

Solution:

twice a added to three times b

Question 4.

There are 38 students in a class. If x more students joined the class, how many students are there in the class?

Solution:

Number of students in the class = 38

x more students also joined the class

Total number of students in the class = x + 38 or 38 + x.

Question 5.

Three sides of a triangle are x cm, y cm and z cm. Find the perimeter of the triangle.

Solution:

Perimeter of the triangle = x cm + y cm + 2 cm

= (x + y + z) cm

Question 6.

Cost of one pen is ₹ 8. Find the cost of y pens.

Solution:

Cost of 1 pen = ₹ 8

∴ Cost of y pens = ₹ 8 × y = ₹ 8y

Question 7.

Neha has 7 more toffees than Megha. If Megha has x toffees, how many toffees does Neha have?

Solution:

Megha has x toffees

∴ Neha has 7 more toffees than Megha = x + 7.

Question 8.

Anshul is 2 years old. How old was he 3 years ago?

Solution:

Anshul’s age before 3 years was z – 3 years.

### DAV Class 6 Maths Chapter 6 Worksheet 1 Notes

Algebra is a branch of mathematics in which numbers are used by letters which are called ‘literal numbers’.

Examples:

- Area of a rectangle A = l × b
- Volume of a cuboid V = l × b × h
- Perimeter of a rectangle P = 2 [l + b]
- Area of a circle = πr
^{2} - 5 less than x = x – 5
- 6 times of x is added to 5 times of y = 6x + 5y

**Operations:**

1. Addition:

- x + y = y + x
- x + 0 = 0 + x = x
- x +(y + z) = (x + y) + z

2. Subtraction:

- x – y ≠ y – x
- x – 0 = x ≠ 0 – x

3. Multiplication:

- x × y = y × x or xy = yx
- x (y + z) = xy + xz
- x × 1 = 1 × x = x
- x × 0 = 0 × x = 0
- x × 7 is written as 7x and not x7

4. Division:

- x ÷ y ≠ y ÷ x
- x ÷ x = 1
- x ÷ 1 = x

Powers of literal numbers:

x × x × x = x^{3}

Here, x is multiplied by itself 3 times. So x is the base and 3 is the iwer of x.

Difference between (5x)^{3} and 5x^{3}

(5x)^{3} = 5x × 5x × 5x and

5x^{3} = 5 × x × x × x

Powers of the same base are added in multiplication.

Example:

1. x^{5} × x^{3} = x^{5 + 3} = x^{3}

2. y^{7} × y^{– 4} = y^{7 – 4} = y^{3}

Powers of the same base are subtracted in division.

Example:

1. p^{4} ÷ p^{3} = p^{4 – 3}

= p^{1} = p

2. x^{5} ÷ x^{– 2} = x^{5 – (- 2)}

= x^{5 + 2} = x^{7}

Constant and variable terms:

The quantity which (loes not change its value is called constant.

Example:

1. Perimeter of a square = 4x here 4 is constant

2. Number of hours in a day i.e. 24 is constant

The quantity which changes its value is called variable.

Example:

Sides of a rectangle, radius of a circle and volume of a sphere are all variables.

Coefficient of a term: In xy, x is the coefficient of y and y is the coefficient of x.

In 4x, 4 is the coefficient of x.

**Like terms and unlike terms:**

The terms having the same variables are called like terms.

Example:

3x, – x, – 2x are all ‘like terms’ having different coefficients but same power of x.

The terms having different variable are called ‘unlike terms’.

Example: 3x^{2}, 7y, – \(\frac{1}{2}\) z, 5x are all different variables.

**Types of algebraic expressions:**

1. Monomial:

The expression having oniy one term is called ‘Monomial’.

Example: 3x, 5y, z, 2 etc.

2. Binomial:

The expression having only two terms are called ‘Binomials’.

Example: 2x + 3y, 2x + 3, 7 + 5y etc.

3. Trinomial:

The expression having three terms is called ‘Trinornial’.

Example: 2x + 3y + 5z, x + y + 7, 2a + b – 7c are all ‘Trinoinials’.

4. Quadrinomial:

The expression having four terms is called ‘Quadrinomial’.

Example: 2x + y + z – 5, a + 2b + 3z + 7, p + q + r + 5 are all Quadrinomial.

5. Polynomial:

The expression having many terms is called ‘Polynomial’.

Example: 1 + x + 2x^{2} + 5x^{3} + … is a polynomial.