Write (1)/(4) + (1)/(4) in its simplest form.

(1)/(4) + (1)/(4) = (2)/(4) = (1)/(2).

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Algebraic Manipulation practice questions — Honors Math

16 free multiple-choice problems on algebraic manipulation, ordered to match Honors Math difficulty, each with a full worked solution. No account needed — and there's a fresh problem set every day.

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Problem #0813 UK GCSE

Beginnerfundamental-algebra

Expand and simplify .

Problems & worked solutions

Problem #0813 UK GCSE

Problem 1 — Algebraic Manipulation

Expand and simplify $2 (x + 3) + 4$ .

Show answer & worked solution

A. $2 x + 7$
B. $2 x + 10$ ✓ correct
C. $6 x + 10$
D. $2 x + 14$

$2 (x + 3) + 4 = 2 x + 6 + 4 = 2 x + 10$ .

Problem #0811 UK GCSE

Problem 2 — Algebraic Manipulation

Expand $2 (3 x - 5)$ .

Show answer & worked solution

A. $6 x - 5$
B. $5 x - 10$
C. $6 x - 10$ ✓ correct
D. $6 x + 10$

$2 (3 x - 5) = 6 x - 10$ .

Problem #0817 UK GCSE

Problem 3 — Algebraic Manipulation

Fully factorise $10 a b + 15 a$ .

Show answer & worked solution

A. $5 a (2 b + 3)$ ✓ correct
B. $5 (2 a b + 3 a)$
C. $a (10 b + 15)$
D. $5 a (2 b + 15)$

$10 a b + 15 a = 5 a (2 b + 3)$ .

Problem #0807 UK GCSE

Problem 4 — Algebraic Manipulation

Simplify $\frac{x^{2}}{x}$ (for $x \neq 0$ ).

Show answer & worked solution

A. $x$ ✓ correct
B. $x^{2}$
C. $1$
D. $\frac{1}{x}$

$\frac{x^{2}}{x} = x$ for $x \neq 0$ .

Problem #0819 UK GCSE

Problem 5 — Algebraic Manipulation

Make $x$ the subject of $y = 3 x$ .

Show answer & worked solution

A. $x = \frac{y}{3}$ ✓ correct
B. $x = 3 y$
C. $x = y - 3$
D. $x = \frac{3}{y}$

$y = 3 x \Rightarrow x = \frac{y}{3}$ .

Problem #0815 UK GCSE

Problem 6 — Algebraic Manipulation

Factorise $x^{2} + 5 x$ .

Show answer & worked solution

A. $x (x + 5)$ ✓ correct
B. $x (x + 5 x)$
C. $5 x (x + 1)$
D. $x^{2} (1 + 5)$

$x^{2} + 5 x = x (x + 5)$ .

Problem #0809 UK GCSE

Problem 7 — Algebraic Manipulation

Write $\frac{1}{4} + \frac{1}{4}$ in its simplest form.

Show answer & worked solution

A. $\frac{2}{8}$
B. $\frac{1}{2}$ ✓ correct
C. $\frac{1}{16}$
D. $\frac{1}{8}$

$\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$ .

Problem #0821 UK GCSE

Problem 8 — Algebraic Manipulation

The circumference of a circle is $C = 2 π r$ . Make $r$ the subject.

Show answer & worked solution

A. $r = \frac{C}{2 π}$ ✓ correct
B. $r = 2 π C$
C. $r = \frac{2 π}{C}$
D. $r = C - 2 π$

$C = 2 π r \Rightarrow r = \frac{C}{2 π}$ .

Problem #0820 UK GCSE

Problem 9 — Algebraic Manipulation

Make $x$ the subject of $y = 2 x - 1$ .

Show answer & worked solution

A. $x = \frac{y + 1}{2}$ ✓ correct
B. $x = \frac{y - 1}{2}$
C. $x = \frac{y}{2} + 1$
D. $x = 2 y + 1$

$y = 2 x - 1 \Rightarrow y + 1 = 2 x \Rightarrow x = \frac{y + 1}{2}$ .

Problem #0814 UK GCSE

Problem 10 — Algebraic Manipulation

Factorise $6 x + 9$ .

Show answer & worked solution

A. $3 (2 x + 3)$ ✓ correct
B. $3 (2 x + 9)$
C. $6 (x + 3)$
D. $3 (6 x + 9)$

$HCF (6, 9) = 3$ , so $6 x + 9 = 3 (2 x + 3)$ .

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