Algebraic Expressions

In math, a letter is an empty box that stands for a number we have not fixed yet. If one pencil costs 500 won, the price of a pencils is simply 500a, so one expression covers any amount. Shorthand rules, like writing 3 × a as 3a or a ÷ b as a fraction, keep expressions tidy. Here you drop numbers into the box and watch how a value like 2x + 3 changes.

Letters are Empty Boxes

x value4

👀 Why Use Letters?

①Letters generalize "some number"

②x = 3 → 2x+3 = 9; x = 5 → 13

③The structure stays the same even when numbers change

Multiplication-Sign Conventions

🔍 Notation Rules

①Letter × letter, number × letter → drop ×

②Numbers come before letters: 3x (not x3)

③Alphabetical order: ab (not ba)

④Coefficient 1 is dropped: 1×x = x, -1×x = -x

⑤Division written as a fraction: a÷b = a/b

Evaluating Expressions

Substitution

Replacing a letter with a number

When x = 3, 2x + 1 = 2×3 + 1 = 7

Value of an Expression

Result after substitution

Reinsert × when substituting and calculate

💡 Cautions When Substituting

①Always use parentheses for negatives: x = -2 → 2×(-2) + 1

②Use parentheses for fractions

③Powers of negatives: x² → (-2)² = 4

Work It Out

Example 1

Write the cost of a pencils at 500 won each as an expression using a letter.

(cost) = (price each) × (number).

cost = 500 × a

Omit the multiplication sign.

= 500a (won)

▸ 500a won

In a product of a number and a letter, omit the multiplication sign.

Example 2

If a = 3 and b = −2, find the value of 2a − 3b.

Substitute the values for the letters.

2a − 3b = 2 × 3 − 3 × (−2)

Compute.

= 6 + 6 = 12

▸ 12

Wrap a negative substitution in parentheses to avoid sign errors.

Exam Key Points

Key Notation

Numbers → letters (alphabetical), ÷ → fraction

3 × a × b = 3ab, x ÷ 5 = x/5

Grade-7 school exam type

If x = −2, what is the value of x² − 3x?

①−2

②2

③6

④10

⑤−10

▸ ④ 10

Substitute x = −2.

x² − 3x = (−2)² − 3 × (−2)

Compute.

= 4 + 6 = 10

🎯 Exam Key Points

①Drop × : numbers first, alphabetical order

②Coefficient 1 omitted; -1 written as just "-"

③Division must be written as a fraction

④Use parentheses (especially for negatives)

⑤Same letter repeated → power: x·x·x = x³

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Operations on Integers & Rationals

Linear Expressions

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