Why letters appear in arithmetic
One rule beats a long list
Meera is four years older than Arun. When Arun is 7 she is 11; when he is 12 she is 16.
📚 Chapter Learning Kit
Expressions using Letter-Numbers · Class 7 Mathematics · Ganita Prakash
English 3 topics 105 leveled MCQs 51 flashcards 5 games Free
Shared by a Veda teacher · Generated with Veda AI · Oct 2026
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The whole idea, one bite at a time
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
What x actually stands for
The letter is a number
Let x be Arun age in years. Then Meera age is x + 4.
Substituting a value
Asking the rule a question
Replacing the letter by a number is called substituting.
Why 3 times m is written 3m
The sign that goes missing
Three times m could be written 3 x m, but algebra writes 3m.
Why the sign is dropped
A clash of symbols
The letter x is a common name for an unfixed number, and the multiplication sign looks almost the same.
So 3m is not 3 + m
Only multiplication loses its sign
Addition and subtraction keep their signs, so three more than m stays 3 + m.
📖 Smart notes
What you'll study, topic by topic
1
Letter-numbers, and the relations they record
A letter in an expression stands for a number that has not been fixed, so one line can answer every case of a situation at once. Substituting replaces the letter by a number. Always say what the letter counts, and read t…
- A letter stands for a number, not for a person, a word or a unit.
- One expression covers every case, because its letter is not fixed.
- Substituting means replacing the letter by a number and changing nothing else.
~35 min · full explanation, examples & memory tricks in the app
2
The missing sign, and collecting like terms
Algebra leaves the multiplication sign out, so three times m is written 3m and the number in front is the coefficient. Terms carrying exactly the same letter part are like terms and may be collected by adding their coeff…
- A missing operation sign between a number and a letter means multiply.
- The sign is dropped because it looks too much like the letter x.
- Addition and subtraction keep their signs, so 3m is not 3 + m.
~40 min · full explanation, examples & memory tricks in the app
3
Picking patterns, and revealing the relationship
Find the constant step of a pattern first, and say why that step happens. Turn the step into the term holding the letter. The leftover constant comes from the ends of the arrangement. A rule read off the numbers alone is…
- A matchstick row needs 4 sticks for one square and 3 for each after.
- So n squares need 3n + 1 sticks, and ten squares need 31.
- The constant always comes from the ends of the arrangement.
~45 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
105 questions laddered from warm-up to topper-level, each with an explanation. A taste:
An expression is written with a letter in it so that one rule can cover every case instead of just one. In such an expression the letter stands for
Beginner
A a number that has not been fixed
B a person or an object
C a unit of measurement
D the answer to the whole question asked
Show answer & explanation
a number that has not been fixed
It is a number we have not yet named.
A letter in an expression is given a value, and the letter is rubbed out and the number written in its place. Doing that is called
Beginner
A substituting
B simplifying the expression
C evaluating the letter
D cancelling
Show answer & explanation
substituting
Nothing else in the expression changes.
Arun is x years old and Meera was born four years before him, so her age has to be written with the same letter. Meera being four years older is
Beginner
A 4x
B x - 4
C 4 - x
D x + 4
Show answer & explanation
x + 4
More means added.
Substituting x = 7 into x + 4 gives
Beginner
A 28
B 11
C 3
D 47
Show answer & explanation
11
Seven and four make eleven.
🃏 Flashcards
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