# NCERT Solution Class 6 Maths Chapter -11 Algebra

**Exercise 1**

**Question 1: Let the side of an equilateral triangle be m. Show the perimeter of the triangle with the help of m.**

** Answer**

Perimeter = sum of three sides

= m+m+m

= 3m

**Question 2:Let the side of a regular hexagon be denoted by m. Show the perimeter of the hexagon with the help of m.**

**(All sides are equal in regular hexagon)**

** **

** Answer**

Side of regular hexagon = m

Perimeter = sum of all sides

= 6m

**Question 3: In the given figure a cube, 3 – D cube is shown. It has six identical squares as all the sides are equal so same six faces. Let the length of a side of cube be given by m. Find formula for total length of the cube.**

**Answer**

Length of an edge = m

Number of edges = 12

Total length of the edges = total number of edges × Length of each edge

= 12m

**Question 4 : Diameter of a circle is a line which passes through the centre and joins two points of circle. (In the given figure XY is a diameter of circle; c is centre.) Express the diameter of the circle (d) in form of its radius(r).**

**Answer**

d = twice the radius

= 2r

**Exercise 2**

**Question 1: Make as many expressions with no. as you can from three numbers 2, 6 and 9. Each no. should be used only once. Use only addition, multiplication and subtraction.**

** Answer:** We can make many expressions using 2, 6 and 9 as given below.

9+ (6 – 2)

9 + (6 × 2)

(6 – 2) + 9

(6 + 2) × 9

(2 + 9) – 6

(2 × 9) × 6

**Question 2: Which of these expressions are formed with numbers only?**

y + 6

(8 × 10) – 6p

9 (15 – 7) + 6 × 4

9n

11

7 – 7m

(2 × 40) – (4 × 20) – 25 + q

**Answer:** From above expressions given, it can be observed that option (c) and (e) are formed by using numbers only.

**Question 3: Identify the operations and tell how the expressions have been formed.**

** a + 2, a – 2, b + 13, b – 13**

** 7t, t/7, 15t**

** 4x + 13, 4x – 13**

** 8c, -8c + 2, -8m – 2**

**Answer**

1. Addition: 2 is added to a

Subtraction: 2 is subtracted from a

Addition: 13 is added to b

Subtraction: 13 is subtracted from b

2. Multiplication: t is multiplied with 7

Division: t is divided by 7

Multiplication: t is multiplied with 15

3.Multiplication and addition: 4 is multiplied with x and result is added to 13.

Multiplication and subtraction: 4 is multiplied with x and 13 is subtracted from the result.

4. Multiplication: 8 is multiplied with c

Multiplication and addition: -8 is multiplied by c and add 2 to the result.

Multiplication and subtraction: c is multiplied with -8 and 2 is subtracted from the result.

**Question 4: Give expressions for the below:**

**3 added to m**

** 3 subtracted from m**

** m multiplied by 8**

** n divided by 8**

** 9 subtracted from –n**

** –m multiplied by 6**

** –n divided by 6**

** n multiplied by -9**

** Answer**

** m + 3**

m – 3

8m

n/8

–n – 9

-6m

–n/6

-9n

**Question 5 : Give expressions for the following cases**

**15 added to 3p**

** 15 subtracted from 3p**

** 7 times x to which 6 is added**

** 7 times x from which 6 is subtracted**

** z is multiplied by -9**

** z is multiplied by -5 and then 3 is added to the result**

** q is multiplied by 8 and the result is subtracted from 12**

** q is multiplied by -8 and the result is added to 12
Answer:**

3p + 15

3p – 15

7x + 6

7x – 6

-9z

-5z + 3

12 – 8q

-8q + 12

**Question 6:**

** (a) Form expressions with s and 5. Use only one operation in the expressions. Every expression should have s in it.**

** (b) Form expressions with t, 3 and 8. Every expression should have t. Use only two operations. These two operations should be different.**

**Answer**

**(a)** s + 5

s – 5

5s

^{s}⁄_{5} ^{5}⁄_{s
}5 – s

**(b)** 3t + 8

3t – 8

8t + 3

8t – 3 etc..