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 = πr2
- 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 = 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’.
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 + 2x2 + 5x3 + … is a polynomial.