4. Expressions using Letter-Numbers

6 topics57 min

Chapter 4 of NCERT Mathematics for Class 7: Expressions using Letter-Numbers. Three sections — From numbers to letter-numbers, Notation and simplest form and Algebra as a language for patterns. Six videos, 57 min in all.

Worked answers to the 24 exercise questions in this chapter →

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Part 1

From numbers to letter-numbers

10 minA letter-number stands for any number, not one numberAlgebra does not add a new kind of number to arithmetic. It adds a new kind of name — one that refuses to say which number it is.10 min · 12 partsहिंदी9 minWhy every rule of arithmetic carries over to algebraA chapter about letters stops, one page in, to revise arithmetic with no letters in it anywhere. There is a reason for that.9 min · 11 partsहिंदी

Part 2

Notation and simplest form

9 minThe dropped multiplication sign, and what it silently means4n is not a new object. It is 4 × n with a symbol the reader is expected to put back, every single time.9 min · 11 partsहिंदी10 minCollecting like terms, and what "simplest form" is forSimplifying is not tidying up. Two expressions are equal here only if they agree for every replacement of their letters.10 min · 11 partsहिंदी

Part 3

Algebra as a language for patterns

9 minTurning a pattern into a formula that predictsA formula is worth writing only if it answers cases nobody checked. So the method never starts with symbols.9 min · 11 partsहिंदी9 minWhy a formula says in one line what words take a paragraph to sayAlgebra is shorter than ordinary language for the same reason it is stronger. A sentence speaks about one square; a letter speaks about all of them.9 min · 11 partsहिंदी

What you will be able to do

  • State what a letter-number is and why the chapter calls it that
  • Rewrite a subtraction as the addition of a negative term, and say why that makes the expression easier to read
  • Rewrite 4 × n in the chapter's shortened form and back again
  • Simplify an expression by collecting terms that carry the same letter-number
  • Describe a growing pattern in words before writing any symbols
  • State a pattern noticed in a grid of numbers, in words

What this chapter assumes you already know

  • Reading an arithmetic expression as a sum of its terms, and evaluating one
  • The idea that a relationship between two quantities can be stated in words ("3 more than", "twice as many as")
  • Perimeter of a square and of simple regular figures, and the word regular as it was used in Class 6
  • Multiplication tables and the idea of a multiple
  • Negative numbers: adding a negative is the same as subtracting
  • Multiplication before addition when both appear without brackets
  • Multiples and multiplication tables; the position of a term in a sequence
  • Multiplication is done before addition unless brackets say otherwise

It builds directly on Writing a situation as an expression before computing it and Every expression can be rewritten as a sum of terms.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "The letter is a secret number I have to find."
  • "a always means the same thing."
  • "a stands for absolutely any number at all."
  • "s = a + 3 and a = s – 3 are two different facts."
  • "An expression with letters cannot be a number."
  • "Two quantities need one letter each only if they are unrelated."
  • "Algebra has its own rules, which is why it is hard."
  • "You can only rearrange an expression once you know what the numbers are."