Class 7 Maths Part 2 Chapter 7: Finding the Unknown Notes

This chapter in five lines

Finding the Unknown is about equations: two expressions joined by an equals sign, such as 2n + 1 = 99. You solve one by doing the same operation on both sides, the way a balanced scale stays level when equal weights come off both pans, or by moving a term across with the opposite operation. Equations turn word problems into simple steps, and the chapter ends with bijaganita, the algebra of Brahmagupta and Bhaskaracharya.

Mind map of Part 2 Chapter 7: what an equation is, keeping the balance, moving terms across, solving problems, mistakes to avoid, and bijaganita — The whole chapter on one page

What is this chapter about?

Earlier you used letter-numbers such as n to describe a pattern: position n of a matchstick pattern needs 2n + 1 sticks. This chapter asks the question the other way round. If Jasmine has exactly 99 sticks, which position can she build? To answer it we write 2n + 1 = 99 and look for the n that makes it true. Such statements are equations, and finding the unknown is called solving them.

Unknown weights and balances

The chapter starts with hanging scales and pan balances. The number on a hanging scale is the total weight, and a level bar means both sides weigh the same. On a pan balance, five sacks balance two sacks and 21 kg of weights. Take two sacks off each pan and the scale stays level, so three sacks weigh 21 kg and one sack weighs 7 kg. This idea, removing equal amounts from both sides, is the key to every equation in the chapter.

On a balance, 5 sacks equal 2 sacks and 21 kg; taking 2 sacks off each pan leaves 3 sacks = 21 kg, so one sack is 7 kg — Keeping the scale balanced

An equation has a left hand side (LHS) and a right hand side (RHS), joined by the equals sign. Its solution is the value of the letter-number that makes the two sides equal.

The equation 2n + 1 = 99 with its LHS, RHS, letter-number and equals sign labelled — Parts of an equation

Solving equations systematically

You can guess and test values, which is the trial and error method, but that can be slow. A surer way uses one fact: if you add, subtract, multiply or divide both sides by the same number, the equation stays true. For 5x − 4 = 7, add 4 to both sides to get 5x = 11, then divide both sides by 5 to get x = 11/5. Put the answer back to check it. If the unknown is on both sides, as in 6y + 7 = 4y + 21, first subtract 4y from both sides.

A faster way to write the same steps is to move a term across the equals sign with the opposite operation: + 7 on one side becomes − 7 on the other, a factor 2 becomes ÷ 2, and a divisor 15 becomes × 15. Read more in solving simple equations.

Three rules for moving a term to the other side of an equation, with examples — Moving a term across

Solving problems with equations

Equations help with real questions. Name the unknown with a letter, write what the problem says as an equation, solve it and answer the question asked. Ranjana’s tile pattern uses 3k + 1 tiles at Step k, so 100 tiles fit Step 33. Madhubanti can spend ₹500 on snacks at ₹25 a plate plus ₹50 delivery, so 25p + 50 = 500 and 18 people can come: her family of 5 and 13 friends. Two friends who save at different rates have equal savings after 7 months. You can also go backwards and build equations that have a chosen solution. See word problems on equations.

A bar of ₹500 split into 18 plates at ₹25, for 5 family members and 13 friends, and ₹50 delivery — Madhubanti’s party

Mind the mistake

The chapter shows worked solutions with slips in them for you to find. The usual ones are keeping the sign of a term that moves across, dividing only one term of a side, dividing the wrong way round, and sign slips when multiplying out a bracket.

A pinch of history

In India, algebra was called bijaganita. Brahmagupta wrote rules for working with unknowns in 628 CE, and his rule for Ax + B = Cx + D gives x = (D − B) ÷ (A − C) at once. The ideas travelled into Arabic and later to Europe, where Al-Khwarizmi’s book title al-jabr gave us the word algebra. Bhaskaracharya’s Bijaganita (1150 CE) has a famous problem about the price of a horse. Read bijaganita: algebra in ancient India. Answers to every question, including the puzzles, machines and the path from Start to End, are in the NCERT solutions for Part 2 Chapter 7.

Timeline of bijaganita from the Bakhshali Manuscript to Bhaskaracharya, with the spread of algebra through Arabic and Latin — How algebra grew

Key terms

Term	Meaning
Equation	A statement that two algebraic expressions are equal, written with an equals sign between them, such as 3x + 4 = 7 or 2z + 4 = 5z − 14.
Letter-number (unknown)	A letter such as x, n or y that stands for a number we do not know yet.
LHS and RHS	The left hand side and the right hand side of an equation: what is written before and after the equals sign.
Solution	The value of the unknown that makes the LHS equal to the RHS. The solution of 2n + 1 = 99 is n = 49.
Trial and error	Solving by trying one value after another until the two sides match. It works, but it can take many tries.
Same operation on both sides	Adding, subtracting, multiplying or dividing both sides by the same number keeps an equation true (division by zero is not allowed).
Inverse operations	Operations that undo each other: addition and subtraction, and multiplication and division.
Moving a term across	Shifting a term to the other side with the inverse operation: + 7 becomes − 7, a factor 2 becomes ÷ 2, and a divisor 15 becomes × 15. It is often called transposing.
Additive inverse	The number that adds to a given number to make 0. The additive inverse of 7 is −7, and of −5 it is 5.
Checking a solution	Putting the value back into the equation to see that the LHS and the RHS come out equal.
Bijaganita	The old Indian name for algebra. Bija means seed: the answer hides inside the unknown, as a tree hides inside a seed.
Brahmagupta’s rule	For an equation Ax + B = Cx + D, the solution is x = (D − B) ÷ (A − C).

Topics in this chapter

Quick revision

An equation says two expressions are equal; solving it means finding the value of the unknown that makes LHS = RHS.
A level scale shows two equal sides, and taking equal weights off both pans keeps it level: 5 sacks = 2 sacks + 21 kg gives 3 sacks = 21 kg, so one sack is 7 kg.
Matchstick triangles need 2n + 1 sticks at position n, so 99 sticks give 2n + 1 = 99 and n = 49; 200 sticks is impossible, as 2n + 1 is always odd.
Trial and error works but is slow; doing the same operation on both sides is a sure method.
Undo additions and subtractions first, then multiplications and divisions: 5x − 4 = 7 gives 5x = 11, then x = 11/5.
Moving a term across: an added term is subtracted on the other side, a factor divides the other side, and a divisor multiplies it.
With unknowns on both sides, first gather them on one side: 6y + 7 = 4y + 21 gives 2y + 7 = 21, so y = 7.
Always check the answer by putting it back into the equation.
For a word problem: name the unknown, write the equation, solve it, and answer the question asked; 25p + 50 = 500 gives p = 18, so Madhubanti can invite 13 friends.
Starting from a solution, you can build new equations by doing the same operation on both sides, as in the chains from y + 1 = 6 and 3y = 15.
Common mistakes: keeping a term’s sign when it moves, dividing only one term, and sign slips with brackets.
Bijaganita grew in India with Aryabhata (499 CE), Brahmagupta (628 CE) and Bhaskaracharya (1150 CE); through Al-Khwarizmi’s al-jabr it gave the world the word algebra.

NCERT solutions for this chapter Every exercise question of this chapter, answered step by step.

Practice

Which of these is an equation?
1. (a) 3x + 4
2. (b) 3x + 4 = 7
3. (c) 5y
4. (d) x + y + 2
Show answer

Answer: (b) 3x + 4 = 7
What is the solution of 2n + 1 = 99?
1. (a) n = 50
2. (b) n = 49
3. (c) n = 98
4. (d) n = 100
Show answer

Answer: (b) n = 49
When + 7 on the left side is moved to the right side, it becomes:
1. (a) + 7
2. (b) − 7
3. (c) × 7
4. (d) ÷ 7
Show answer

Answer: (b) − 7
Solve 3u − 7 = 2u + 3.
1. (a) u = 4
2. (b) u = −10
3. (c) u = 10
4. (d) u = 1
Show answer

Answer: (c) u = 10
Ramesh has 30 more marbles than Suresh, and they have 60 together. How many does Suresh have?
1. (a) 30
2. (b) 15
3. (c) 45
4. (d) 20
Show answer

Answer: (b) 15
Who gave the rule x = (D − B) ÷ (A − C) for Ax + B = Cx + D?
1. (a) Al-Khwarizmi
2. (b) Brahmagupta
3. (c) Euclid
4. (d) Pythagoras
Show answer

Answer: (b) Brahmagupta

Questions students ask

What are the main topics of Class 7 Maths Part 2 Chapter 7?

Unknown weights on scales and patterns of matchsticks; what an equation is; solving equations by trial and error and then systematically, by doing the same operation on both sides or moving terms across; solving word problems with equations; building equations from a given solution; spotting mistakes in solutions; and the history of bijaganita, or algebra, in India.

Is Finding the Unknown in the new Ganita Prakash Part 2 book?

Yes. It is Chapter 7, the last chapter of Ganita Prakash, the Class 7 Maths textbook Part 2 (2026-27), on pages 164 to 190. It comes after Constructions and Tilings and uses the letter-numbers of earlier chapters to find unknown values.

What is the easiest way to solve an equation?

Get the unknown alone on one side. Undo what has been added or subtracted, then undo what has been multiplied or divided, doing the same to both sides each time. Then put your answer back into the equation to check that both sides match.

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