Schooling · Class 7 · Mathematics · Finding the Unknown · Chapter on a page
CBSE Class 7 · Mathematics · NCERT Ganita Prakash-II
Finding the Unknown: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- An equation is a statement that two…
- The unknown is the letter in the…
- Whatever you do to one side of an…
- To isolate the unknown, undo the…
- A solution is the value of the…
- You can always check your answer by…
- Formulas and facts
- If x + a = b
- If x − a = b
- If a × x = b
- If x ÷ a = b
- Checking
- Watch out for
- Doing an operation on one side only
- Using the wrong opposite operation…
- Forgetting to check the answer
- Writing the equation the wrong way…
- Mixing up the unknown with the…
What this chapter is about
This chapter teaches you how to find a number that you do not know yet. We call this number the unknown. In mathematics, we use letters like x, y or n to stand for the unknown. The job is to figure out what value the letter must have so that a given statement becomes true.
Key ideas
- An equation is a statement that two things are equal. For example, x + 4 = 10 says that some number plus 4 equals 10.
- The unknown is the letter in the equation. Our goal is to find what number it stands for.
- Whatever you do to one side of an equation, you must do the same to the other side. This keeps the two sides equal.
- To isolate the unknown, undo the operation that is done to it. If something is added, subtract it from both sides. If something is multiplied, divide both sides by that number.
- A solution is the value of the unknown that makes the equation true.
- You can always check your answer by substituting it back into the original equation.
Formulas and facts to remember
- If x + a = b, then x = b − a. (Subtract the added number from both sides.)
- If x − a = b, then x = b + a. (Add back what was subtracted.)
- If a × x = b, then x = b ÷ a. (Divide both sides by the multiplier.)
- If x ÷ a = b, then x = b × a. (Multiply both sides by the divisor.)
- Checking: Put the answer back into the equation. Left side should equal right side.
Common mistakes
- Doing an operation on one side only → Always do the same operation on both sides to keep the equation balanced.
- Using the wrong opposite operation, such as adding when you should subtract → Remember: addition undoes subtraction, multiplication undoes division.
- Forgetting to check the answer → Substitute your answer back into the original equation to be sure it works.
- Writing the equation the wrong way round, like 15 − x = 32 instead of x − 15 = 32 → Read the problem carefully to see what is happening to the unknown.
- Mixing up the unknown with the answer too soon → Keep the letter until you finish solving; only then state the value.
Quick revision
- An equation says two expressions are equal; solve it to find the unknown.
- Undo addition by subtracting, and undo subtraction by adding.
- Undo multiplication by dividing, and undo division by multiplying.
- Always perform the same step on both sides.
- Check your answer by substituting it back.