Mathematical Operations • Topic 4 of 4

Balancing Equations

You must choose the correct set of signs (from options) to fill blanks so the equation balances. Use estimation: the size of the target tells you whether you need × (big jump) or +/− (small change). Then verify with BODMAS.

Estimate the size, then test signs

Look at the target value. A large target usually needs a × somewhere; a target close to the numbers needs + or −. Try the most likely signs, then verify with BODMAS.

"6 _ 2 _ 3 = 15" → the target 15 is bigger than the parts, so try ×: 6 × 2 + 3 = 15. Correct.

Verify, don't guess. Once you pick signs, always recompute the full left-hand side with BODMAS and confirm it equals the right-hand side before answering.

✅ Solved examples

1. Fill: 6 _ 2 _ 3 = 15 with (×, +).
6 × 2 + 3 = 15. Correct.
2. Fill: 8 _ 4 _ 2 = 6 with (−, ÷).
8 − 4 ÷ 2 = 8 − 2 = 6. Correct.
3. Fill: 5 _ 3 _ 2 = 17 with (×, +).
5 × 3 + 2 = 17. Correct.
4. Fill: 9 _ 3 _ 1 = 4 with (÷, +).
9 ÷ 3 + 1 = 4. Correct.

✏️ Practice — try these, take hints as needed

1. 7 _ 2 _ 1 = 15 with (×, +)?
7×2+1.
—
—
15 (×, +)
2. 10 _ 2 _ 3 = 8 with (÷, +)?
10÷2+3.
5+3.
—
8 (÷, +)
3. 6 _ 3 _ 2 = 20 with (×, +)?
6×3+2.
—
—
20 (×, +)
4. 12 _ 4 _ 1 = 2 with (÷, −)?
12÷4−1.
3−1.
—
2 (÷, −)
5. 4 _ 5 _ 2 = 22 with (×, +)?
4×5+2.
—
—
22 (×, +)

📝 Topic test — 8 questions

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