What is financial infrastructure?

The network of banks, payment systems and stock markets that helps manage money

What are the main things a bank does?

Holds deposits and lends money as loans

How do banks make money?

They pay lower interest on deposits and charge higher interest on loans

Earning interest on previous interest as well as on the original amount

What is a letter-number?

A letter used to represent a number, such as \(a\) standing for Aftab's age.

If Shabnam is 3 years older than Aftab, write Shabnam's age.

If Aftab's age is \(a\), then Shabnam's age is \(s = a + 3\).

Find Shabnam's age when Aftab is 23.

Substitute \(a = 23\): \(s = 23 + 3 = 26\) years.

What does substitution mean?

Replacing a letter-number with a number to compute the expression's value.

Why are algebraic expressions useful?

One expression captures infinitely many cases, helping to predict values and justify patterns.

What is a constant in an expression like 3n + 4?

The fixed number \(4\), which does not change with \(n\).

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Expressions Using Letter-Numbers — Class 7 Mathematics

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Mathematics · 15 chapters

Summary, key terms, important questions and a practice quiz with AI diagnosis for each.

Chapter 4: Expressions Using Letter-Numbers

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Summary

This chapter introduces algebra by using letters to stand for numbers. A letter such as \(a\) or \(s\) used to represent a number is called a letter-number (a variable). For example, if Aftab's age is \(a\) and Shabnam is 3 years older, then Shabnam's age is \(s = a + 3\); substituting \(a = 23\) gives \(s = 26\). Expressions containing letter-numbers, like \(a + 3\) or \(2n - 1\), are called algebraic expressions, and replacing the letter by a number to compute a value is called substitution. You learn to translate word relationships into expressions, to read patterns in sequences (the \(n\)th multiple of 4 is \(4n\); the \(n\)th even number is \(2n\); the \(n\)th odd number is \(2n-1\)), and to use these generalisations to explain why a pattern holds. The power of letter-numbers is that one short expression captures infinitely many cases at once, making it possible both to predict values and to justify mathematical claims — a major step beyond arithmetic.

Letter-numbers (variables)Writing algebraic expressionsSubstitution and evaluating expressionsPatterns and the nth termGeneralisation using algebra

Key terms

Letter-number (variable)

A letter used to represent a number, e.g. \(a\) for Aftab's age.

Algebraic expression

A mathematical expression containing one or more letter-numbers, e.g. \(a + 3\).

Substitution

Replacing a letter-number by a particular number to find the value of an expression.

Generalisation

A statement that captures a pattern for all cases, written using letter-numbers.

\(n\)th term

An expression in \(n\) giving the value at position \(n\) of a sequence, e.g. \(4n\).

Constant

A fixed number in an expression whose value does not change.

Important questions

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TermLetter-number (variable)

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Practice quiz

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Class 7 Maths — Expressions Using Letter-Numbers (Practice Quiz)

10 Qs · ~10 min