# DAV Class 6 Maths Chapter 6 Worksheet 1 Solutions

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:

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:

(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:

1. Area of a rectangle A = l × b
2. Volume of a cuboid V = l × b × h
3. Perimeter of a rectangle P = 2 [l + b]
4. Area of a circle = πr2
5. 5 less than x = x – 5
6. 6 times of x is added to 5 times of y = 6x + 5y

Operations:

• 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 = x3
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 5x3
(5x)3 = 5x × 5x × 5x and
5x3 = 5 × x × x × x

Powers of the same base are added in multiplication.
Example:
1. x5 × x3 = x5 + 3 = x3
2. y7 × y– 4 = y7 – 4 = y3

Powers of the same base are subtracted in division.
Example:
1. p4 ÷ p3 = p4 – 3
= p1 = p

2. x5 ÷ x– 2 = x5 – (- 2)
= x5 + 2 = x7

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: 3x2, 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’.