Mathematical Operations • Topic 3 of 4

Interchange of Signs & Numbers

You are asked which interchange of two signs (or two numbers) makes a given equation correct, or to evaluate after a stated swap. Apply the swap throughout the equation and check both sides balance under BODMAS.

Swap everywhere, then evaluate

When told two signs (or two numbers) are interchanged, apply the swap to every occurrence in the expression, then compute with BODMAS.

"If + and − are interchanged: 6 + 2 − 4" → swap to "6 − 2 + 4" = 8.

With "which swap makes it true" items, it is usually fastest to test each option's swap against the equation rather than solving algebraically — plug, swap, check.

✅ Solved examples

1. If + and − are interchanged, find the value of 6 + 2 − 4.
Swap signs: 6 − 2 + 4 = 8.
2. If × and + are interchanged, find the value of 5 × 3 + 2.
Swap: 5 + 3 × 2 = 5 + 6 = 11 (BODMAS).
3. If the numbers 4 and 6 are interchanged, find the value of 4 + 2 × 6.
Swap numbers: 6 + 2 × 4 = 6 + 8 = 14.
4. If ÷ and × are interchanged, find the value of 8 ÷ 2 × 4.
Swap: 8 × 2 ÷ 4 = 16 ÷ 4 = 4.

✏️ Practice — try these, take hints as needed

1. Swap + and × in 2 + 3 × 4; new value?
2×3+4.
BODMAS: 6+4.
—
10
2. Swap − and ÷ in 12 − 4 ÷ 2; new value?
12÷4−2.
3−2.
—
1
3. Swap numbers 3 and 9 in 3 + 6 = 9 → ?
9 + 6.
—
—
15
4. Swap × and +: 5 × 2 + 1; new value?
5+2×1.
5+2.
—
7
5. Swap ÷ and −: 10 ÷ 5 − 1; new value?
10−5÷1.
10−5.
—
5

📝 Topic test — 8 questions

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