R d sharma mathematics solutions class 6 Solutions for Chapter 8 introduction to algebra

Write the following using numbers, literals and signs of basic operations. State what each letter represents:

(i) The diameter of a circle is twice its radius.

(ii) The area of a rectangle is the product of its length and breadth.

(iii) The selling price equals the sum of the cost price and the profit.

(iv) The total amount equals the sum of the principal and the interest.

(v) The perimeter of a rectangle is two times the sum of its length and breadth.

(vi) The perimeter of a square is four times its side.

Write the following using numbers, literals and signs of basic operations:

(i) The sum of 6 and x.

(ii) 3 more than a number y.

(iii) One-third of a number x.

(iv) One-half of the sum of number x and y.

(v) Number y less than a number 7.

(vi) 7 taken away from x.

(vii) 2 less than the quotient of x and y.

(viii) 4 times x taken away from one-third of y.

(ix) Quotient of x by 3 is multiplied by y.

Think of a number. Multiply by 5. Add 6 to the result. Subtract y from this result. What is the result?

The number of rooms on the ground floor of a building is 12 less than the twice of the number ofrooms on first floor. If the first floor has x rooms, how many rooms does the ground floor has?

Binny spend Rs a daily and saves Rs b per week. What is her income for two weeks?

Rahul scores 80 marks in English and x marks in Hindi. What is his total score in the two subjects?

Rohit covers x centimetres in one step. How much distance does he cover in y steps?

One apple weighs 75 grams and one orange weighs 40 grams. Determine the weight of x apples and y oranges.

One pencil costs Rs 2 and one fountain pen costs Rs 15. What is the cost of x pencils and y fountainpens?

Write each of the following products in exponential form:

(i) a × a × a × a × ……….15 times

(ii) 8 × b × b × b × a × a × a × a

(iii) 5 × a × a × a × b × b × c × c × c

(iv) 7 × a × a × a …….. 8 times × b × b × b × …… 5 times

(v) 4 × a × a × …… 5 times × b × b × ……. 12 times × c × c …… 15 times

Write each of the following in the product form:

Write down each of the following in exponential form:

The number of bacteria in a culture is x now. It becomes square of itself after one week. What will be its number after two weeks?

The area of a rectangle is given by the product of its length and breadth. The length of a rectangle is twothird of its breadth. Find its area if its breadth is x cm.

If there are x rows of chairs and each row contains x2 chairs. Determine the total number of chairs.