ML Aggarwal CBSE Solutions Class 6 Math 12th Chapter Algebra Exercise 12.3
Ex 12.3
(1) Form four expressions with numbers 7, 5 and 8 (no variable) using operations of addition, subtraction or multiplication with the condition that every number should be used but not more than once.
Solution: The expressions formed from the given numbers satisfying the given conditions are:
7 x 5 + 8, 5 x 8 – 7, (7 + 5) + 8, 5 x (7 + 8).
In fact, we can form more expressions satisfying the given conditions.
(2) Which out of the following are expressions with numbers only?
(i) 2y + 3
(ii) (7 x 20) – 8z
(iii) 5 x (21 – 7) + 9 x 2
(iv) 5 x 11n
(v) (5 x 4) – 45 + p
(vi) 3 x (11 + 7) – 24 ÷ 3.
Solution: (iii) 5 x (21 – 7) + 9 x 2 & (vi) 3 x (11 + 7) – 24 ÷ 3 are expressions with numbers only.
(3) (i) x + 5
Solution: addition; 5 added to x
(ii) y – 7
Solution: subtraction; 7 subtracted from y
(iii) 3z
Solution: multiplication; z multiplied by 3
(iv) p/5
Solution: division, p divided by 5
(v) 2x + 17
Solution: multiplication and addition, first x multiplied by 2 and then 17 added to the product
(vi) 3y – 5
Solution: multiplication and subtraction, first y multiplied by 3 and then 5 subtracted from the product.
(vii) -7m + 2/3
Solution: multiplication and addition, first m multiplied by -7 and then 2/3 added to the product.
(viii) x/3 – 15
Solution: division and subtraction, first x divided by 3 and then 15 subtracted from the quotient.
(4) Write expressions for the following:
(i) 7 added to p
Ans. p + 7
(ii) p subtracted from 7
Ans. 7 – p
(iii) p multiplied by 7
Ans. 7 x p = 7p
(iv) p divided by 7
Ans. p / 7
(v) 7 divided by p
Ans. 7 / p
(vi) 7 subtracted from –m
Ans. –m – 7
(vii) p multiplied by -5
Ans. -5 x p = -5p
(viii) –p divided by 5
Ans. –p / 5
(5) Write expressions:
(i) 11 added to 2m
Ans. 2m + 11
(ii) 11 subtracted from 2m
Ans. 2m – 11
(iii) 3 added to 5 times y
Ans. 5y + 3
(iv) 3 subtracted from 5 times y
Ans. 5y – 3
(v) y is multiplied by -8 and then 5 is added to the result
Ans. -8y + 5
(vi) y is multiplied by 5 and then the result is subtracted from 16
Ans. 16 – 5y
(6) Write the following in mathematical form using signs and symbols
(i) 6 more than thrice a number x
Solution: 3x + 6
(ii) 7 taken away from y
Solution: y – 7
(iii) 3 less than quotient of x by y.
Solution: x/y – 3
(7) Form six expressions using t and 4 . Use not more than one number operation and every expression must have t in it.
Solution: t + 4. T – 4, 4t, t/4, 4/t, 4 – t
(8) Form expressions using y, 2 and 7. Use only two different number operations and every expression must have y in it.
Solution: 2y + 7, 2y – 7, 7y + 2, 7y – 2, y/2 + 7, y/2 – 7….
(9) A student scored x marks in English but the teacher deducted 5 marks for bad handwriting. What was the students final score in English?
Solution: students scored x marks
Deducted score for bad handwriting x – 5
Then, Students final score = x – 5
(10) Raju’s father’s age is 2 years more than 3 times Raju’s age. If Raju’s present age is y years, then what is his father’s age?
Solution: Raju’s present age = y years.
3 time of Raju’s age = 3y
According to the questions, it is said that his father is 2 years more than 3 times of Rajus age.
Then, his father age = 3y + 2
(11) Mohini is x years old. Express the following in algebraic form:
(i) three times Mohini’s age next year
(ii) four times Mohini’s age 3 years ago.
(iii) the present age of Mohini’s uncle, if his uncle is 5 times as old as Mohini will be two years from now.
(iv) the present age of Mohini’s cousin, if her cousin is two years less than one-third of Mohini’s age 5 years ago.
Solution: (i) 3 (x + 1) years
(ii) 4 (x – 3) years.
(iii) 5 (x + 2) years.
(iv) (1/3(x – 5) -2) years
(12) A cuboidal box has height h cm. Its length is 5 times the height and breadth is 10 cm less than the length. Express the length and the breadth of the box in terms of the height.
Solution: Cuboidal box height – h cm
Questions said, length is 5 times the height. So length is = 5h
Breadth is 10 cm less than the length.
So, the breadth is 5h – 10
(13) A bus travels at v km per hour. It is going from Delhi to Jaipur. After the bus has travelled 5 hours, Jaipur is still 20 km away. What is the distance from Delhi to Jaipur?
Solution: Bus speed = v km/hr
It has travelled 5 hours. Then distance covered = 5v
Jaipur is still 20 km away, after travelled 5 hours.
∴ Total distance from Delhi to Jaipur = 5v + 20
(14) Solution:
(i) The cost of a book is 3 times the cost of a notebook.
(ii) The cost of oil per litre is 5 times the cost of rice per kg.
(iii) The speed of a bus is 10 km per hour more than the speed of a truck.
(iv) Tony puts q marbels on the table. He has 8q marbels in his box.
(v) Our class has n students. The school has 20n students.
(vi) Raju’s uncle is 4 times older than Raju and his aunt is 3 years younger than his uncle.
(vii) The total number of dots is 5 times the number of rows.