In mathematics, memorizing all concepts formulas and learning how to frame the formula is very important. By using the process of framing linear equations and algebraic expressions, we will frame the formula & express the relation between the unknown quantities. For more details go with the Evaluation of Subject by Substitution along with the worksheet on Framing the Formula.
Activity sheet on framing the formula will aid students during the practice of math formula sheet on how to frame a formula or equation using the translation of mathematical statements with symbols and literals. Practice well with the detailed questions and answers given in the framing a formula worksheet pdf and excel in solving all maths concepts.
Do Check:
Printable Activity Sheet on Framing the Formula | Framing Algebraic Expressions Worksheet Pdf
I. Express the following as an equation.
Sita’s father’s age is 10 years more than 5 times Sita’s age. Father’s age is 50 years.
Solution:
Given that, Father’s age is 50 years
Let’s Sita’s age be x years
Five times her age = 5x
Father’s age = 10 + 5x
Now, apply the given value
50 years = 10 + 5x
Hence, 10 + 5x = 50 is the resultant.
II. A rectangular box is of height h cm. Its length is 2 times its height and the breadth is 8 cm less than the length. Express the length, breadth, and height.
Solution:
Let the length, breadth, and height of the rectangle be L, B, H.
Given that length of the rectangle is 2 times the height. ie., length L = 2h
The breadth of the rectangle is 8 cm less than the length
Hence, B = 8 – L but L = 2h
Therefore, breadth of the rectangle in terms of height = 2h – 8.
III. Change the given statements using expression into statements in regular language.
(a) Price of a DVD is Rs. 2P and the price of a CD is Rs. P
(b) Arun’s age is x years. His sister’s age is ( 2x + 4 ) years.
Solution:
(a) In regular language, we write it as:
The price of a DVD is two times the price of a CD.
(b) In ordinary language, we state the expression as:
Arun’s sister’s age is 4 years more than two times his age.
IV. Frame a formula for each of the following statements:
(i) The selling price ‛a’ of an article is (1 – \(\frac { 1 }{ 20 } \)) times its marked price ‛b’ after a discount of 30%.
(ii) The length ‘L’ of the diagonal of a rectangle is √5 times the length of an edge measuring ‘a’.
Solution:
(i) a = (1 – \(\frac { 1 }{ 20 } \))b
(ii) L = √5a
V. Banana cost x rupees per dozen and apples cost y rupees per score. Write a formula to get the total cost c in rupees 40 bananas and 20 apples
Solution:
Given cost of 12 bananas = x rupees (1 dozen=12)
cost of 1 banana = \(\frac { x }{ 12 } \) rupees
cost of 40 bananas = \(\frac { 40x }{ 12 } \) rupees
Give cost of 20 apples = y rupees (1 score=20)
cost of 1 apple = \(\frac { y }{ 20 } \) rupees
cost of 20 apples = \(\frac { 20y }{ 20 } \) rupees
Total Cost = \(\frac { 40x }{ 12 } \) + \(\frac { 20y }{ 20 } \)
= \(\frac { 10x }{ 3 } \) + y
= \(\frac { (10x+3y) }{ 3 } \)
According to the given context C = \(\frac { (10x+3y) }{ 3 } \)
VI. Establish an equation for each of the following statements.
(a) One-sixth of a number x exceeds One-seventh of the number by 4.
(b) A mother is 40 years older than her daughter. After 2 years from now, the age of the mother will become 2 times her daughter’s age. Find the present age ‘y’ years of the daughter.
Solution:
(a) \(\frac { x }{ 6 } \) – \(\frac { x }{ 7 } \) = 4
(b) 40 + y + 2 = 2( y + 2)
VII. Make a formula for the statement: “The number of diagonals, d, that can be drawn from one vertex of an n sided polygon to all the other vertices is equal to the number of sides of the polygon more than 5”
Solution:
Given that the number of sides of the polygon = n
Number of sides of the polygon more 5 = n+5
As per the statement, the formula is d = n+5