Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown.
Level 1 · Warm-up
1 Simplify 3a × 5b. (as a simplified expression)
Show worked solution
3 × 5 = 15; a × b = ab → 15ab.
2 Simplify 2x × 6x. (like 12x2; type 12x^2)
Show worked solution
2 × 6 = 12; x × x = x2 → 12x2.
3 Simplify 10m ÷ 2. (as a simplified expression)
Show worked solution
10 ÷ 2 = 5 → 5m.
Level 2 · Core
4 Simplify (−4p) × 3q. (as a simplified expression)
Show worked solution
Different signs → negative; 4 × 3 = 12 → −12pq.
5 Simplify 18xy ÷ 6y. (as a simplified expression)
Show worked solution
18/6 = 3; y cancels → 3x.
6 Simplify (−2a) × (−3a). (like 6a2; type 6a^2)
Show worked solution
Neg × neg = pos; 2 × 3 = 6; a × a = a2 → 6a2.
Level 3 · Challenge
7 Simplify 20a2b ÷ 4ab. (as a simplified expression)
Show worked solution
20/4 = 5; one a cancels, b cancels → 5a.
8 A rectangle has area 24x2 and length 8x. Width? (as a simplified expression)
Show worked solution
Width = 24x2 ÷ 8x = 3x.
9 Simplify (−3m) × 2n × (−4m). (like 24m2n; type 24m^2n)
Show worked solution
Two negatives → positive; 3 × 2 × 4 = 24; m × m = m2 → 24m2n.