Algebraic Expressions

Q1 How do you write a × 5 as an algebraic expression?

When a letter is multiplied by a number, the number goes first and the × sign is dropped: a × 5 = 5a.

Q2 When x = 3, what is the value of 2x − 4?

2×3 − 4 = 6 − 4 = 2.

Q3 What is 3x + 2x combined into a single term?

Like terms are combined by adding their coefficients: 3x + 2x = (3+2)x = 5x.

Q4 You buy 4 apples at ¥x each and 3 bananas at ¥200 each. What is the total?

The apples cost 4x yen and the bananas cost 200×3 = 600 yen, so the total is 4x + 600.

Q5 4a − a = ?

A lone a means 1a, so 4a − 1a = (4−1)a = 3a.

Q6 What is 2(x + 3) when you expand it?

Use the distributive property — the 2 multiplies both terms inside: 2×x + 2×3 = 2x + 6.

Q7 How do you write "3 times a, minus 7" as an expression?

"3 times a" is 3a, and "minus 7" subtracts 7 from that result, giving 3a − 7.

Q8 When x = −2, what is the value of x²?

(−2)² = (−2)×(−2) = 4. A negative times a negative is positive, so x² is never below 0.

Q9 What is 5x + 3 − 2x − 1 in its simplest form?

Combine the x terms: 5x − 2x = 3x. Then the plain numbers: 3 − 1 = 2. The answer is 3x + 2.

Q10 How do you write "the remainder when n is divided by 3" as an expression? (÷ here means plain division)

None of the first three expressions gives a remainder. A remainder is normally written by describing the whole division: n = 3q + r, where q is the quotient and r is the remainder. In later math and in programming this is handled by the mod operation.