Algebra class 6 Questions
Until ex 11.3
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Answer:
Step-by-step explanation:
CBSE Class –VI Mathematics
NCERT Solutions
Chaper 11 Algebra (Ex. 11.2)
Question 1. The side of an equilateral triangle is shown by l. Express the perimeter of the equilateral triangle using l.
Answer: Side of equilateral triangle = l
Therefore, Perimeter of equilateral triangle = 3 x side = 3l
Question 2. The side of a regular hexagon is denoted by l. Express the perimeter of the hexagon using l. (Hint: A regular hexagon has all its six sides in equal length)
Answer: Side of hexagon = l
Therefore, Perimeter of Hexagon = 6 x side = 6l
Question 3. A cube is a three-dimensional figure. It has six faces and all of them are identical squares. The length of an edge of the cube is given by l. find the formula for the total length of the edges of a cube.
Answer: Length of one edge of cube = l
Number of edges in a cube = 12
Therefore, total length = 12×l=12l
Question 4. The diameter of a circle is a line, which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure AB is a diameter of the circle; C is its centre). Express the diameter of the circle (d) in terms of its radius (r).
Answer: Since, length of diameter is double the length of radius.
Therefore, d=2r (Here r is the radius of the circle)
Question 5. To find sum of three numbers 14, 27 and 13. We can have two ways.
(a) We may first add 14 and 27 to get 41 and then add 13 to it to get the total sum 54, or
(b) We may add 27 and 13 to get 40 and then add 14 to get the sum 54. Thus
(14 + 27) + 13 = 14 + (27 + 13)
This can be done for any three numbers. This property is known as the associativity of addition of numbers. Express this property which we have already studied in the chapter on Whole Numebrs, in a general way, by using variables a,b and c.
Answer: (a+b)+c=a+(b+c)
CBSE Class –VI Mathematics
NCERT Solutions
Chaper 11 Algebra (Ex. 11.3)
Question 1. Make up as many expressions with numbers (no variables) as you can from three numbers 5, 7 and 8. Every number should be used not more than once. Use only addition, subtraction and multiplication.
(Hint: Three possible expressions are 5 + (8 – 7), 5 – (8 – 7), (5 x 8) + 7 make the other expressions)
Answer:
(a) (8 x 5) – 7
(b) (8 + 5) – 7
(c) (8 x 7) – 5
(d) (8 + 7) – 5
(e) 5 x (7 + 8)
(f) 5 + (7 x 8)
(g) 5 + (8 – 7)
(h) 5 – (7 + 8)
Question 2. Which out of the following are expressions with numbers only:
(a) y+3
(b) (7×20)−8z
(c) 5(21−7)+7×2
(d) 5
(e) 3x
(f) 5−5n
(g) (7×20)−(5×10)−45+p
Answer: (c) and (d)
Question 3. Identify the operations (addition, subtraction, division, multiplication) in forming the following expressions and tell how the expressions have been formed:
(a) z+1,z−1,y+17,y−17
(b) 17y,y17,5z
(c) 2y+17,2y−17
(d) 7m,−7m+3,−7m−3
Answer:
(a) z+1→ Addition
z−1→ Subtraction
y+17→ Addition
y−17→ Subtraction
(b) 17y→ Multiplication
y17→ Division
5z→ Multiplication
(c) 2y+17→ Multiplication and Addition
2y−17→ Multiplication and Subtraction
(d) 7m→ Multiplication
−7m+3→ Multiplication and Addition
−7m−3→ Multiplication and Subtraction
Question 4. Give expressions for the following cases:
(a) 7 added to p.
(b) 7 subtracted from p.
(c) p multiplied by 7.
(d) p divided by 7.
(e) 7 subtracted from −m.
(f) −p multiplied by 5.
(g) −p divided by 5.
(h) p multiplied by −5.
Answer:
(a) p+7
(b) p−7
(c) 7p
(d) p7
(e) −m−7
(f) −5p
(g) −p5
(h) −5p
Question 5. Give expression in the following cases:
(a)11 added to 2m.
(b)11 subtracted from 2m.
(c) 5 times y to which 3 is added.
(d) 5 times y from which 3 is subtracted.
(e) y is multiplied by −8.
(f) y is multiplied by −8 and then 5 is added to the result.
(g) y is multiplied by 5 and result is subtracted from 16.
(h) y is multiplied by −5 and the result is added to 16.
Answer:
(a) 2m+11
(b) 2m−11
(c) 5y+3
(d) 5y−3
(e) −8y
(f) −8y+5
(g) 16−5y
(h) −5y+16
Question 7. (a) From expressions using t and 4. Use not more than one number operation. Every expression must have t in it.
(b) Form expressions using y, 2 and 7. Every expression must have y in it. Use only two number operations. These should be different.
Answer:
(a) t+4,t−4,4−t,4t,t4,4t
(b) 2y+7,2y−7,7y+2,7y−2 and so on
Answer:
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