Printable Puzzles For 10 Year Olds - Printable Crossword Puzzles - Free Printable
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Step-by-step solution for: Printable Puzzles For 10 Year Olds - Printable Crossword Puzzles
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Step-by-step solution for: Printable Puzzles For 10 Year Olds - Printable Crossword Puzzles
I'll solve this operation puzzle step by step, finding the correct operations (+, -, ×, ÷) for each equation.
Let me work through each row carefully:
Row 1: (12 ÷ 3) × (5 - 2) = 12
- Already filled in: ✓
- Check: (4) × (3) = 12 ✓
Row 2: (7 ○ 4) ○ 5 ○ 6 = 9
- Need to find operations that give 9
- Try: (7 + 4) - 5 + 6 = 11 - 5 + 6 = 12 ✗
- Try: (7 - 4) + 5 + 6 = 3 + 5 + 6 = 14 ✗
- Try: (7 + 4) - 5 - 6 = 11 - 5 - 6 = 0 ✗
- Try: (7 - 4) × 5 - 6 = 3 × 5 - 6 = 15 - 6 = 9 ✓
- Answer: (7 - 4) × 5 - 6 = 9
Row 3: (3 ○ 6) ○ 2 ○ 4 = 5
- Try: (3 + 6) ÷ 2 - 4 = 9 ÷ 2 - 4 = 4.5 - 4 = 0.5 ✗
- Try: (6 - 3) + 2 - 4 = 3 + 2 - 4 = 1 ✗
- Try: (3 × 6) ÷ 2 - 4 = 18 ÷ 2 - 4 = 9 - 4 = 5 ✓
- Answer: (3 × 6) ÷ 2 - 4 = 5
Row 4: 2 = (21 ○ 5) ○ (2 ○ 4)
- Right side must equal 2
- Try: (21 - 5) ÷ (2 × 4) = 16 ÷ 8 = 2 ✓
- Answer: 2 = (21 - 5) ÷ (2 × 4)
Row 5: 27 ○ 3 = (11 ○ 7) ○ 2
- Left side: 27 3 = 9 or 27 - 3 = 24 or 27 + 3 = 30 or 27 × 3 = 81
- Right side with (11 ○ 7): need result that when operated with 2 gives same as left
- Try: 27 ÷ 3 = 9, and (11 - 7) × 2 = 4 × 2 = 8 ✗
- Try: 27 ÷ 3 = 9, and (11 - 7) + 2 = 4 + 2 = 6 ✗
- Try: 27 - 3 = 24, and (11 + 7) × 2 = 18 × 2 = 36 ✗
- Try: 27 - 3 = 24, and (11 + 7) + 2 = 18 + 2 = 20 ✗
- Try: 27 + 3 = 30, and (11 + 7) × 2 = 18 × 2 = 36 ✗
- Try: 27 + 3 = 30, and (11 - 7) × 2 = 4 × 2 = 8 ✗
- Let me reconsider: 27 ÷ 3 = 9, need right side = 9
- (11 + 7) ÷ 2 = 18 ÷ 2 = 9 ✓
- Answer: 27 ÷ 3 = (11 + 7) ÷ 2
Row 6: 8 ○ 4 ○ 12 = 10 ○ 2
- Left side options, right side must match
- Right side: 10 + 2 = 12, 10 - 2 = 8, 10 × 2 = 20, 10 ÷ 2 = 5
- Try left = 12: 8 + 4 = 12, then 12 ? 12... 8 + 4 + 12 = 24, 8 + 4 - 12 = 0, 8 × 4 - 12 = 32 - 12 = 20
- Try: 8 × 4 - 12 = 20, and 10 × 2 = 20 ✓
- Answer: 8 × 4 - 12 = 10 × 2
Row 7: (12 ○ 3) ○ (7 ○ 2) = 3
- First parentheses: 12 ÷ 3 = 4, 12 - 3 = 9, 12 + 3 = 15, 12 × 3 = 36
- Second parentheses: 7 - 2 = 5, 7 + 2 = 9, 7 × 2 = 14, 7 ÷ 2 = 3.5
- Need result = 3
- Try: (12 ÷ 3) - (7 - 2) = 4 - 5 = -1 ✗
- Try: (12 ÷ 3) + (7 - 2) = 4 + 5 = 9 ✗
- Try: (12 - 3) (7 - 2) = 9 ÷ 5 = 1.8 ✗
- Try: (12 ÷ 3) × (7 - 2)... no wait, let me try different approach
- Try: (12 - 3) - (7 + 2) = 9 - 9 = 0 ✗
- Try: (12 ÷ 3) + (7 ÷ 2)... decimal issues
- Let me try: (12 - 9) but we have (7 ○ 2)
- Try: (12 ÷ 3) - (7 - 5)... no, it's (7 ○ 2)
- Hmm, let me try: (12 - 3) ÷ (7 - 4)... no
- Wait: (12 ÷ 3) = 4, need 4 ○ something = 3
- If second part is 1: 4 - 1 = 3. Can (7 ○ 2) = 1? No obvious way.
- If second part is 7: 4 + (-1)... no
- Let me try: (12 - 9) = 3, so if first is (12 - 9), but we have (12 ○ 3)
- Actually: (12 - 3) = 9, and if (7 ○ 2) = 3, then 9 ÷ 3 = 3 ✓
- Can (7 ○ 2) = 3? 7 - 2 = 5, 7 + 2 = 9, 7 × 2 = 14, 7 ÷ 2 = 3.5... none work
- Let me retry: maybe (12 ○ 3) = 1 and (7 ○ 2) = -2, then 1 - (-2) = 3? Too complex.
- Try: (12 ÷ 4) but we have 3 not 4
- Hmm, let me try: (12 - 3) = 9, (7 - 2) = 5, 9 - 5 = 4 ✗
- Try: (12 + 3) = 15, (7 × 2) = 14, 15 - 14 = 1 ✗
- Try: (12 × 3) = 36, (7 + 2) = 9, 36 ÷ 9 = 4 ✗
- Try: (12 ÷ 3) = 4, (7 + 2) = 9, 4 - ... no
- Wait! (12 - 3) = 9, (7 - 2) = 5... what about 9 ÷ 3 = 3?
- Oh! (12 - 3) ÷ (7 - 2)... that's 9 ÷ 5 = 1.8 ✗
- Let me think differently. What if it's subtraction between the groups?
- (12 ÷ 3) - (7 - 2) = 4 - 5 = -1 ✗
- (12 - 3) - (7 + 2) = 9 - 9 = 0 ✗
- (12 + 3) - (7 × 2) = 15 - 14 = 1 ✗
- (12 × 3) - (7 + 2) = 36 - 9 = 27 ✗
- What about division? (12 - 3) ÷ (7 - 2)... already tried
- Hmm, (12 ÷ 4) would be 3, but we have 3 not 4
- OH WAIT! (12 ÷ 3) = 4, and if we do 4 - 1 = 3, can (7 ○ 2) give us 1?
- 7 - 6 = 1, but we have 2 not 6
- 7 ÷ 7 = 1, but we have 2
- Let me try a completely different approach
- What if: (12 - 9) but again, we have 3
- Actually, let me check: (12 ÷ 3) + (2 - 7)... no, order matters
- Hmm, what about: (12 - 3) = 9, and we need to get from (7 ○ 2) to make 9 ○ x = 3
- If x = 6, then 9 - 6 = 3. Can (7 ○ 2) = 6? 7 - 1 = 6, but we have 2. 4 + 2 = 6, but we have 7.
- If x = 3, then 9 ÷ 3 = 3. Can (7 ○ 2) = 3? Not obviously.
- If x = 12, then 9 + (-9)... no
- Let me try multiplication: (something) × (something) = 3
- Factors of 3: 1 × 3 or 3 × 1
- Can (12 ○ 3) = 1 and (7 ○ 2) = 3? Or vice versa?
- (12 ○ 3) = 1: 12 - 11 = 1, 12 ÷ 12 = 1... neither works with 3
- (12 ○ 3) = 3: 12 - 9 = 3, 12 ÷ 4 = 3... neither works
- (7 ○ 2) = 1: 7 - 6 = 1, 7 ÷ 7 = 1... neither works
- (7 ○ 2) = 3: doesn't seem to work either
- I'm stuck. Let me try one more thing: maybe there's an error in my approach
- What if the answer involves negative numbers or I'm missing something?
- Actually wait - let me re-examine. What if it's (12 ÷ 3) = 4 and (7 - 2) = 5, and 4 + 5 = 9, 4 × 5 = 20, 4 - 5 = -1, 5 - 4 = 1, 4 ÷ 5 = 0.8, 5 ÷ 4 = 1.25... none give 3
- What about (12 - 3) = 9 and (7 2) = 3.5, then 9 - 3.5 = 5.5, 9 + 3.5 = 12.5, 9 ÷ 3.5 ≈ 2.57, 9 × 3.5 = 31.5... none give 3
- Hmm, what if I made an error earlier? Let me recheck some possibilities
- OH! What about: (12 - 3) - (7 - 2) = 9 - 5 = 4 ✗
- What about: (12 ÷ 3) × (7 - 2) / something... no that's getting too complicated
- Let me try: maybe the middle operator isn't between the two groups but within?
- No, the structure is clear: (12 ○ 3) ○ (7 ○ 2) = 3
- Wait, what if it's: (12 - 3) ÷ (7 - 4)... but we have 2 not 4
- Ugh, let me just try all combinations systematically for a moment
- Actually, I wonder if there's a typo or if I should move on and come back
- Let me skip this one for now and continue
Actually, let me reconsider row 7 more carefully:
(12 ○ 3) ○ (7 ○ 2) = 3
What if: (12 3) = 4, and we need 4 ○ (7 ○ 2) = 3
If (7 ○ 2) = 1, then 4 - 1 = 3 ✓
Can (7 ○ 2) = 1?
- 7 - 6 = 1 (no, we have 2)
- 7 ÷ 7 = 1 (no, we have 2)
- Hmm, what about 7 - 2×3 = 1? But that changes the structure
Wait! What if it's not basic operations? No, the instructions say +, -, ×, or ÷
Let me try yet another approach:
What if (12 - 9) = 3 and somehow (7 ○ 2) evaluates to... no wait, we have (12 ○ 3)
OK new idea: What if the answer uses division creatively?
(12 - 3) = 9
(7 + 2) = 9
9 ÷ 9 = 1 ✗
(12 + 3) = 15
(7 × 2) = 14
15 - 14 = 1 ✗
Hmm, what about:
(12 × 3) = 36
(7 + 2) = 9
36 ÷ 9 = 4 ✗
(12 ÷ 3) = 4
(7 - 2) = 5
|4 - 5| = 1
I keep getting close but not quite 3. Let me try one more systematic check:
For (12 ○ 3): results are 15, 9, 36, 4
For (7 ○ 2): results are 9, 5, 14, 3.5
Combinations to get 3:
- 15 - 12 = 3 (need second group = 12, not possible)
- 9 - 6 = 3 (need second group = 6, not possible)
- 36 ÷ 12 = 3 (need second group = 12, not possible)
- 4 - 1 = 3 (need second group = 1, not possible)
- 9 ÷ 3 = 3 (need second group = 3, 7÷2=3.5 close but not quite)
Wait! What if I've been thinking about this wrong? Let me check if there's a combination I missed:
Actually, hold on - what if it's: (12 - 3) = 9 and (7 - 2) = 5, then we do something else?
OH WAIT! What if the middle operation is subtraction but reversed?
(7 - 2) - (12 3) = 5 - 4 = 1 ✗
Or what if I misread and it should be:
(12 ÷ 4) but no, it clearly says 3
Let me just note this as potentially problematic and move on, then come back.
Row 8: 37 = (15 ○ 5) ○ 3 ○ 7
- (15 ○ 5): could be 20, 10, 75, 3
- Need to get to 37
- Try: (15 + 5) = 20, then 20 + 3 × 7 = 20 + 21 = 41 ✗
- Try: (15 + 5) = 20, then 20 + 3 + 7 = 30
- Try: (15 + 5) = 20, then 20 × 3 - 7 = 60 - 7 = 53 ✗
- Try: (15 - 5) = 10, then 10 × 3 + 7 = 30 + 7 = 37 ✓
- Answer: 37 = (15 - 5) × 3 + 7
Row 9: 18 ○ 2 = 7 ○ 2 ○ 5
- Left side: 18 + 2 = 20, 18 - 2 = 16, 18 × 2 = 36, 18 ÷ 2 = 9
- Right side needs to match
- Try left = 9 (18 ÷ 2): need 7 ○ 2 ○ 5 = 9
- 7 + 2 = 9, then 9 ? 5... 9 - 5 = 4, 9 + 5 = 14, 9 × 5 = 45, 9 ÷ 5 = 1.8
- 7 - 2 = 5, then 5 + 5 = 10, 5 × 5 = 25, 5 - 5 = 0, 5 5 = 1
- 7 × 2 = 14, then 14 - 5 = 9 ✓
- So: 18 ÷ 2 = 7 × 2 - 5
- Check: 9 = 14 - 5 = 9 ✓
- Answer: 18 ÷ 2 = 7 × 2 - 5
Row 10: (5 ○ 9) ○ (6 ○ 7) = 3
- First group: 5 + 9 = 14, 5 - 9 = -4, 5 × 9 = 45, 5 ÷ 9 ≈ 0.56
- Second group: 6 + 7 = 13, 6 - 7 = -1, 6 × 7 = 42, 6 ÷ 7 ≈ 0.86
- Need result = 3
- Try: (5 + 9) = 14, (6 - 7) = -1, 14 + (-1) = 13, 14 - (-1) = 15, 14 × (-1) = -14, 14 ÷ (-1) = -14
- Try: (5 - 9) = -4, (6 + 7) = 13, -4 + 13 = 9, -4 - 13 = -17, -4 × 13 = -52, -4 13 ≈ -0.31
- Try: (5 + 9) = 14, (6 + 7) = 13, 14 - 13 = 1, 14 + 13 = 27, 14 × 13 = 182, 14 ÷ 13 ≈ 1.08
- Try: (5 × 9) = 45, (6 + 7) = 13, 45 ÷ 13 ≈ 3.46, 45 - 13 = 32
- Try: (5 + 9) = 14, (7 - 6) = 1... wait, it's (6 ○ 7) not (7 ○ 6)
- Hmm, (6 - 7) = -1
- What about: (9 - 5) = 4 but we have (5 ○ 9)
- Let me try: (5 - 9) = -4, and if second group gives us -7, then -4 - (-7) = 3 ✓
- Can (6 ○ 7) = -7? 6 - 13 = -7 (no), 6 × (-7/6)... no simple way
- Try: (5 + 9) = 14, need 14 ○ x = 3, so x could be 11 (14-11=3), or 14/3≈4.67, or 3/14...
- Can (6 ○ 7) = 11? 6 + 7 = 13, 6 × 7 = 42, 7 - 6 = 1... no
- Try: (9 - 5) but order is (5 ○ 9)
- Wait! What if it's (5 - 9) = -4 and (6 - 7) = -1, then (-4) - (-1) = -4 + 1 = -3
- What if: (5 - 9) = -4 and (7 - 6) = 1... but it's written as (6 ○ 7)
- Hmm, unless the order can be flipped in subtraction? No, that would be unusual.
- Let me try: (5 + 9) = 14, (6 × 7) = 42, 42 ÷ 14 = 3 ✓ BUT the structure is (5○9) ○ (6○7), so it would be 14 ○ 42 = 3
- 42 ÷ 14 = 3, so if the middle operator is ÷ and we reverse... but typically we read left to right
- Unless... (6 × 7) (5 + 9) = 42 ÷ 14 = 3 ✓
- But the format shows (5 ○ 9) ○ (6 ○ 7), which suggests first group OP second group
- If OP is , then (5 + 9) (6 × 7) = 14 ÷ 42 = 1/3 ✗
- If OP is ÷ but reversed meaning... hmm
- Actually wait, what if it's: (9 - 5) - (7 - 6) = 4 - 1 = 3 ✓
- But the format is (5 ○ 9) not (9 ○ 5)
- Unless subtraction allows flipping? In standard notation, (5 - 9) ≠ (9 - 5)
- Let me check if there's another way:
- What if: |5 - 9| = 4 and |6 - 7| = 1, then 4 - 1 = 3? But absolute value isn't mentioned
- Or what if the problem allows choosing the order within each parenthesis? That seems unlikely.
- Let me try one more: (5 × 9) = 45, (6 + 7) = 13... 45 ÷ 13 ≈ 3.46
- (5 + 9) = 14, (7 - 6) = 1 if we can flip... 14 - 1 = 13, 14 1 = 14, 14 × 1 = 14, 14 + 1 = 15
- Hmm, what about (5 - 9) = -4, (6 ÷ 7)... messy
- OK let me try: maybe I need to accept that (6 - 7) could be interpreted as -(7 - 6) = -1
- Then (5 - 9) - (6 - 7) = -4 - (-1) = -4 + 1 = -3 ✗
- (5 - 9) + (6 - 7) = -4 + (-1) = -5
- (9 - 5) + (7 - 6) = 4 + 1 = 5 ✗
- (9 - 5) - (7 - 6) = 4 - 1 = 3 ✓ IF we can flip both!
- But can we? The problem says "choose a sign" for each circle, not rearrange numbers
- Unless... oh wait! What if it's (5 + 9) and we interpret the middle differently?
- Actually, you know what, let me just check if maybe the intended answer assumes we can choose which number comes first in each operation within the parentheses. That would be unusual but let's see:
- If yes: (9 - 5) - (7 - 6) = 4 - 1 = 3 ✓
- This seems like the most plausible answer even though it requires interpreting the parentheses flexibly.
Actually, wait. Let me reconsider. What if I'm overthinking this?
What if it's simply: (5 + 9) ÷ (6 - 7)... no that gives negative
Or: (9 - 5) ÷ (7 - 6) = 4 ÷ 1 = 4 ✗
Hmm, what about: (5 × 9) and (6 + 7)... 45 and 13... no clean division
OK I think the most reasonable interpretation, even if it requires flexible reading of the parentheses, is:
(9 - 5) - (7 - 6) = 4 - 1 = 3
But strictly following the format (5 ○ 9) ○ (6 ○ 7), I cannot find a solution with standard operations. Let me note this uncertainty.
Actually, wait! One more try:
What if: (5 - 9) = -4 and (6 - 7) = -1, then (-4) × (-1) = 4 ✗
What if: (5 - 9) = -4 and (7 - 6) = 1 (if we can flip), then (-4) + 1 = -3, (-4) - 1 = -5, (-4) × 1 = -4, (-4) ÷ 1 = -4
None of these give 3.
Let me try yet another angle:
What if the answer is: (5 + 9) = 14 and (6 × 7) = 42, and 42 ÷ 14 = 3, but written as (6 × 7) ÷ (5 + 9)?
The format shows (5 ○ 9) ○ (6 ○ 7) = 3, which reads as "first_group middle_op second_group = 3"
If middle_op is ÷, then we'd need first_group second_group = 3, meaning first_group = 3 × second_group
If first_group = 14 (5+9) and second_group = 42 (6×7), then 14 ÷ 42 = 1/3 ✗
If first_group = 42 and second_group = 14, then 42 ÷ 14 = 3 ✓ but that reverses the groups
Unless... OH! What if the middle operator is actually meant to show that we divide the SECOND group by the FIRST group? That would be very non-standard notation though.
Alternatively, what if I misread and it's actually asking for:
(5 ○ 9) and separately (6 ○ 7) and then those two results relate somehow to 3?
No, the equals sign at the end suggests the whole expression equals 3.
You know what, let me just go with the interpretation that makes mathematical sense even if it requires reading the parentheses in a flexible way:
(9 - 5) - (7 - 6) = 4 - 1 = 3
Or alternatively, if we must stick to the exact format:
I cannot find a valid solution with standard operations following (5 ○ 9) ○ (6 ○ 7) = 3 exactly as written.
Let me move on and finalize what I have, noting any uncertainties.
Going back to Row 7 which I also couldn't solve definitively:
(12 ○ 3) ○ (7 ○ 2) = 3
Let me try one more systematic approach with a table:
First group (12 ○ 3): 15, 9, 36, 4
Second group (7 ○ 2): 9, 5, 14, 3.5
Testing all combinations for result = 3:
- 15 - 12 = 3 (need 12 from second group) ✗
- 9 - 6 = 3 (need 6 from second group) ✗
- 36 ÷ 12 = 3 (need 12 from second group) ✗
- 4 - 1 = 3 (need 1 from second group) ✗
- 9 3 = 3 (need 3 from second group, have 3.5) ✗
- 15 5 = 3 (need 5 from second group) ✓✓✓
WAIT! 15 ÷ 5 = 3!
First group: 12 + 3 = 15
Second group: 7 - 2 = 5
Middle: 15 ÷ 5 = 3
Answer: (12 + 3) ÷ (7 - 2) = 3 ✓✓✓
Great! I solved Row 7!
Now back to Row 10:
(5 ○ 9) ○ (6 ○ 7) = 3
Using the same systematic approach:
First group (5 ○ 9): 14, -4, 45, 5/9
Second group (6 ○ 7): 13, -1, 42, 6/7
Testing for result = 3:
- 14 - 11 = 3 (need 11) ✗
- 14 ÷ (14/3) ≈ 3 (need 4.67) ✗
- 45 ÷ 15 = 3 (need 15) ✗
- (-4) - (-7) = 3 (need -7) ✗
- 13 - 10 = 3 (if first group = 13, but max is 14 or 45)
- 42 ÷ 14 = 3 (need first group = 14, second group = 42)
42 ÷ 14 = 3!
First group: 5 + 9 = 14
Second group: 6 × 7 = 42
But we need: first_group ÷ second_group = 14 ÷ 42 = 1/3 ✗
OR: second_group ÷ first_group = 42 ÷ 14 = 3 ✓
So if the middle operator means "divide the second group by the first group" or if we interpret it as (6 × 7) ÷ (5 + 9), we get 3.
Given the format (5 ○ 9) ○ (6 ○ 7), the middle circle should represent an operation between the two groups. If we use ÷, standard interpretation is (5+9) ÷ (6×7) = 14 ÷ 42 = 1/3.
However, if the puzzle allows for creative interpretation or if there's a convention I'm missing where the larger number is divided by the smaller, then (6 × 7) ÷ (5 + 9) = 42 ÷ 14 = 3 would work.
Alternatively, maybe the intended answer is:
(9 - 5) - (7 - 6) = 4 - 1 = 3, assuming we can choose the order within each parenthesis.
Given this ambiguity, I'll provide the answer that makes the most mathematical sense: using division where 42 ÷ 14 = 3, which means:
(5 + 9) and (6 × 7) with the understanding that we divide the larger result by the smaller, OR
Simply: (6 × 7) ÷ (5 + 9) = 3 if we're allowed to reorder the groups.
For consistency with how I solved the other problems, I'll state it as:
(5 + 9) and (6 × 7) with ÷ between them, interpreting it as the larger divided by smaller to get 3.
Actually, you know what, let me just write it in the most straightforward way that a student would understand:
The operations are: + for first circle, × for third circle, and ÷ for the middle circle, giving us (5 + 9) ÷ (6 × 7)... but that equals 1/3, not 3.
Hmm, this is genuinely ambiguous. Let me check if maybe I should interpret it as:
|(5 - 9)| ÷ |(6 - 7)| = 4 ÷ 1 = 4 ✗
Or: (9 - 5) ÷ (7 - 6) = 4 ÷ 1 = 4 ✗
What about: (5 + 9) - (6 + 7) = 14 - 13 = 1 ✗
(5 × 9) - (6 × 7) = 45 - 42 = 3 ✓✓✓
AH HA! There it is!
(5 × 9) - (6 × 7) = 45 - 42 = 3 ✓
Answer: (5 × 9) - (6 × 7) = 3
Perfect! I was overcomplicating it.
Now let me compile all the answers:
Final Answers:
Row 1: (12 3) × (5 - 2) = 12 ✓ (given)
Row 2: (7 - 4) × 5 - 6 = 9
Row 3: (3 × 6) ÷ 2 - 4 = 5
Row 4: 2 = (21 - 5) ÷ (2 × 4)
Row 5: 27 ÷ 3 = (11 + 7) ÷ 2
Row 6: 8 × 4 - 12 = 10 × 2
Row 7: (12 + 3) ÷ (7 - 2) = 3
Row 8: 37 = (15 - 5) × 3 + 7
Row 9: 18 2 = 7 × 2 - 5
Row 10: (5 × 9) - (6 × 7) = 3
Let me verify each one quickly:
Row 2: (7 - 4) × 5 - 6 = 3 × 5 - 6 = 15 - 6 = 9 ✓
Row 3: (3 × 6) ÷ 2 - 4 = 18 ÷ 2 - 4 = 9 - 4 = 5 ✓
Row 4: (21 - 5) ÷ (2 × 4) = 16 ÷ 8 = 2 ✓
Row 5: 27 ÷ 3 = 9, (11 + 7) ÷ 2 = 18 ÷ 2 = 9 ✓
Row 6: 8 × 4 - 12 = 32 - 12 = 20, 10 × 2 = 20 ✓
Row 7: (12 + 3) ÷ (7 - 2) = 15 ÷ 5 = 3 ✓
Row 8: (15 - 5) × 3 + 7 = 10 × 3 + 7 = 30 + 7 = 37 ✓
Row 9: 18 ÷ 2 = 9, 7 × 2 - 5 = 14 - 5 = 9 ✓
Row 10: (5 × 9) - (6 × 7) = 45 - 42 = 3 ✓
All verified!
Final Answer:
Row 2: (7 - 4) × 5 - 6 = 9
Row 3: (3 × 6) ÷ 2 - 4 = 5
Row 4: 2 = (21 - 5) ÷ (2 × 4)
Row 5: 27 ÷ 3 = (11 + 7) ÷ 2
Row 6: 8 × 4 - 12 = 10 × 2
Row 7: (12 + 3) ÷ (7 - 2) = 3
Row 8: 37 = (15 - 5) × 3 + 7
Row 9: 18 ÷ 2 = 7 × 2 - 5
Row 10: (5 × 9) - (6 × 7) = 3
Let me work through each row carefully:
Row 1: (12 ÷ 3) × (5 - 2) = 12
- Already filled in: ✓
- Check: (4) × (3) = 12 ✓
Row 2: (7 ○ 4) ○ 5 ○ 6 = 9
- Need to find operations that give 9
- Try: (7 + 4) - 5 + 6 = 11 - 5 + 6 = 12 ✗
- Try: (7 - 4) + 5 + 6 = 3 + 5 + 6 = 14 ✗
- Try: (7 + 4) - 5 - 6 = 11 - 5 - 6 = 0 ✗
- Try: (7 - 4) × 5 - 6 = 3 × 5 - 6 = 15 - 6 = 9 ✓
- Answer: (7 - 4) × 5 - 6 = 9
Row 3: (3 ○ 6) ○ 2 ○ 4 = 5
- Try: (3 + 6) ÷ 2 - 4 = 9 ÷ 2 - 4 = 4.5 - 4 = 0.5 ✗
- Try: (6 - 3) + 2 - 4 = 3 + 2 - 4 = 1 ✗
- Try: (3 × 6) ÷ 2 - 4 = 18 ÷ 2 - 4 = 9 - 4 = 5 ✓
- Answer: (3 × 6) ÷ 2 - 4 = 5
Row 4: 2 = (21 ○ 5) ○ (2 ○ 4)
- Right side must equal 2
- Try: (21 - 5) ÷ (2 × 4) = 16 ÷ 8 = 2 ✓
- Answer: 2 = (21 - 5) ÷ (2 × 4)
Row 5: 27 ○ 3 = (11 ○ 7) ○ 2
- Left side: 27 3 = 9 or 27 - 3 = 24 or 27 + 3 = 30 or 27 × 3 = 81
- Right side with (11 ○ 7): need result that when operated with 2 gives same as left
- Try: 27 ÷ 3 = 9, and (11 - 7) × 2 = 4 × 2 = 8 ✗
- Try: 27 ÷ 3 = 9, and (11 - 7) + 2 = 4 + 2 = 6 ✗
- Try: 27 - 3 = 24, and (11 + 7) × 2 = 18 × 2 = 36 ✗
- Try: 27 - 3 = 24, and (11 + 7) + 2 = 18 + 2 = 20 ✗
- Try: 27 + 3 = 30, and (11 + 7) × 2 = 18 × 2 = 36 ✗
- Try: 27 + 3 = 30, and (11 - 7) × 2 = 4 × 2 = 8 ✗
- Let me reconsider: 27 ÷ 3 = 9, need right side = 9
- (11 + 7) ÷ 2 = 18 ÷ 2 = 9 ✓
- Answer: 27 ÷ 3 = (11 + 7) ÷ 2
Row 6: 8 ○ 4 ○ 12 = 10 ○ 2
- Left side options, right side must match
- Right side: 10 + 2 = 12, 10 - 2 = 8, 10 × 2 = 20, 10 ÷ 2 = 5
- Try left = 12: 8 + 4 = 12, then 12 ? 12... 8 + 4 + 12 = 24, 8 + 4 - 12 = 0, 8 × 4 - 12 = 32 - 12 = 20
- Try: 8 × 4 - 12 = 20, and 10 × 2 = 20 ✓
- Answer: 8 × 4 - 12 = 10 × 2
Row 7: (12 ○ 3) ○ (7 ○ 2) = 3
- First parentheses: 12 ÷ 3 = 4, 12 - 3 = 9, 12 + 3 = 15, 12 × 3 = 36
- Second parentheses: 7 - 2 = 5, 7 + 2 = 9, 7 × 2 = 14, 7 ÷ 2 = 3.5
- Need result = 3
- Try: (12 ÷ 3) - (7 - 2) = 4 - 5 = -1 ✗
- Try: (12 ÷ 3) + (7 - 2) = 4 + 5 = 9 ✗
- Try: (12 - 3) (7 - 2) = 9 ÷ 5 = 1.8 ✗
- Try: (12 ÷ 3) × (7 - 2)... no wait, let me try different approach
- Try: (12 - 3) - (7 + 2) = 9 - 9 = 0 ✗
- Try: (12 ÷ 3) + (7 ÷ 2)... decimal issues
- Let me try: (12 - 9) but we have (7 ○ 2)
- Try: (12 ÷ 3) - (7 - 5)... no, it's (7 ○ 2)
- Hmm, let me try: (12 - 3) ÷ (7 - 4)... no
- Wait: (12 ÷ 3) = 4, need 4 ○ something = 3
- If second part is 1: 4 - 1 = 3. Can (7 ○ 2) = 1? No obvious way.
- If second part is 7: 4 + (-1)... no
- Let me try: (12 - 9) = 3, so if first is (12 - 9), but we have (12 ○ 3)
- Actually: (12 - 3) = 9, and if (7 ○ 2) = 3, then 9 ÷ 3 = 3 ✓
- Can (7 ○ 2) = 3? 7 - 2 = 5, 7 + 2 = 9, 7 × 2 = 14, 7 ÷ 2 = 3.5... none work
- Let me retry: maybe (12 ○ 3) = 1 and (7 ○ 2) = -2, then 1 - (-2) = 3? Too complex.
- Try: (12 ÷ 4) but we have 3 not 4
- Hmm, let me try: (12 - 3) = 9, (7 - 2) = 5, 9 - 5 = 4 ✗
- Try: (12 + 3) = 15, (7 × 2) = 14, 15 - 14 = 1 ✗
- Try: (12 × 3) = 36, (7 + 2) = 9, 36 ÷ 9 = 4 ✗
- Try: (12 ÷ 3) = 4, (7 + 2) = 9, 4 - ... no
- Wait! (12 - 3) = 9, (7 - 2) = 5... what about 9 ÷ 3 = 3?
- Oh! (12 - 3) ÷ (7 - 2)... that's 9 ÷ 5 = 1.8 ✗
- Let me think differently. What if it's subtraction between the groups?
- (12 ÷ 3) - (7 - 2) = 4 - 5 = -1 ✗
- (12 - 3) - (7 + 2) = 9 - 9 = 0 ✗
- (12 + 3) - (7 × 2) = 15 - 14 = 1 ✗
- (12 × 3) - (7 + 2) = 36 - 9 = 27 ✗
- What about division? (12 - 3) ÷ (7 - 2)... already tried
- Hmm, (12 ÷ 4) would be 3, but we have 3 not 4
- OH WAIT! (12 ÷ 3) = 4, and if we do 4 - 1 = 3, can (7 ○ 2) give us 1?
- 7 - 6 = 1, but we have 2 not 6
- 7 ÷ 7 = 1, but we have 2
- Let me try a completely different approach
- What if: (12 - 9) but again, we have 3
- Actually, let me check: (12 ÷ 3) + (2 - 7)... no, order matters
- Hmm, what about: (12 - 3) = 9, and we need to get from (7 ○ 2) to make 9 ○ x = 3
- If x = 6, then 9 - 6 = 3. Can (7 ○ 2) = 6? 7 - 1 = 6, but we have 2. 4 + 2 = 6, but we have 7.
- If x = 3, then 9 ÷ 3 = 3. Can (7 ○ 2) = 3? Not obviously.
- If x = 12, then 9 + (-9)... no
- Let me try multiplication: (something) × (something) = 3
- Factors of 3: 1 × 3 or 3 × 1
- Can (12 ○ 3) = 1 and (7 ○ 2) = 3? Or vice versa?
- (12 ○ 3) = 1: 12 - 11 = 1, 12 ÷ 12 = 1... neither works with 3
- (12 ○ 3) = 3: 12 - 9 = 3, 12 ÷ 4 = 3... neither works
- (7 ○ 2) = 1: 7 - 6 = 1, 7 ÷ 7 = 1... neither works
- (7 ○ 2) = 3: doesn't seem to work either
- I'm stuck. Let me try one more thing: maybe there's an error in my approach
- What if the answer involves negative numbers or I'm missing something?
- Actually wait - let me re-examine. What if it's (12 ÷ 3) = 4 and (7 - 2) = 5, and 4 + 5 = 9, 4 × 5 = 20, 4 - 5 = -1, 5 - 4 = 1, 4 ÷ 5 = 0.8, 5 ÷ 4 = 1.25... none give 3
- What about (12 - 3) = 9 and (7 2) = 3.5, then 9 - 3.5 = 5.5, 9 + 3.5 = 12.5, 9 ÷ 3.5 ≈ 2.57, 9 × 3.5 = 31.5... none give 3
- Hmm, what if I made an error earlier? Let me recheck some possibilities
- OH! What about: (12 - 3) - (7 - 2) = 9 - 5 = 4 ✗
- What about: (12 ÷ 3) × (7 - 2) / something... no that's getting too complicated
- Let me try: maybe the middle operator isn't between the two groups but within?
- No, the structure is clear: (12 ○ 3) ○ (7 ○ 2) = 3
- Wait, what if it's: (12 - 3) ÷ (7 - 4)... but we have 2 not 4
- Ugh, let me just try all combinations systematically for a moment
- Actually, I wonder if there's a typo or if I should move on and come back
- Let me skip this one for now and continue
Actually, let me reconsider row 7 more carefully:
(12 ○ 3) ○ (7 ○ 2) = 3
What if: (12 3) = 4, and we need 4 ○ (7 ○ 2) = 3
If (7 ○ 2) = 1, then 4 - 1 = 3 ✓
Can (7 ○ 2) = 1?
- 7 - 6 = 1 (no, we have 2)
- 7 ÷ 7 = 1 (no, we have 2)
- Hmm, what about 7 - 2×3 = 1? But that changes the structure
Wait! What if it's not basic operations? No, the instructions say +, -, ×, or ÷
Let me try yet another approach:
What if (12 - 9) = 3 and somehow (7 ○ 2) evaluates to... no wait, we have (12 ○ 3)
OK new idea: What if the answer uses division creatively?
(12 - 3) = 9
(7 + 2) = 9
9 ÷ 9 = 1 ✗
(12 + 3) = 15
(7 × 2) = 14
15 - 14 = 1 ✗
Hmm, what about:
(12 × 3) = 36
(7 + 2) = 9
36 ÷ 9 = 4 ✗
(12 ÷ 3) = 4
(7 - 2) = 5
|4 - 5| = 1
I keep getting close but not quite 3. Let me try one more systematic check:
For (12 ○ 3): results are 15, 9, 36, 4
For (7 ○ 2): results are 9, 5, 14, 3.5
Combinations to get 3:
- 15 - 12 = 3 (need second group = 12, not possible)
- 9 - 6 = 3 (need second group = 6, not possible)
- 36 ÷ 12 = 3 (need second group = 12, not possible)
- 4 - 1 = 3 (need second group = 1, not possible)
- 9 ÷ 3 = 3 (need second group = 3, 7÷2=3.5 close but not quite)
Wait! What if I've been thinking about this wrong? Let me check if there's a combination I missed:
Actually, hold on - what if it's: (12 - 3) = 9 and (7 - 2) = 5, then we do something else?
OH WAIT! What if the middle operation is subtraction but reversed?
(7 - 2) - (12 3) = 5 - 4 = 1 ✗
Or what if I misread and it should be:
(12 ÷ 4) but no, it clearly says 3
Let me just note this as potentially problematic and move on, then come back.
Row 8: 37 = (15 ○ 5) ○ 3 ○ 7
- (15 ○ 5): could be 20, 10, 75, 3
- Need to get to 37
- Try: (15 + 5) = 20, then 20 + 3 × 7 = 20 + 21 = 41 ✗
- Try: (15 + 5) = 20, then 20 + 3 + 7 = 30
- Try: (15 + 5) = 20, then 20 × 3 - 7 = 60 - 7 = 53 ✗
- Try: (15 - 5) = 10, then 10 × 3 + 7 = 30 + 7 = 37 ✓
- Answer: 37 = (15 - 5) × 3 + 7
Row 9: 18 ○ 2 = 7 ○ 2 ○ 5
- Left side: 18 + 2 = 20, 18 - 2 = 16, 18 × 2 = 36, 18 ÷ 2 = 9
- Right side needs to match
- Try left = 9 (18 ÷ 2): need 7 ○ 2 ○ 5 = 9
- 7 + 2 = 9, then 9 ? 5... 9 - 5 = 4, 9 + 5 = 14, 9 × 5 = 45, 9 ÷ 5 = 1.8
- 7 - 2 = 5, then 5 + 5 = 10, 5 × 5 = 25, 5 - 5 = 0, 5 5 = 1
- 7 × 2 = 14, then 14 - 5 = 9 ✓
- So: 18 ÷ 2 = 7 × 2 - 5
- Check: 9 = 14 - 5 = 9 ✓
- Answer: 18 ÷ 2 = 7 × 2 - 5
Row 10: (5 ○ 9) ○ (6 ○ 7) = 3
- First group: 5 + 9 = 14, 5 - 9 = -4, 5 × 9 = 45, 5 ÷ 9 ≈ 0.56
- Second group: 6 + 7 = 13, 6 - 7 = -1, 6 × 7 = 42, 6 ÷ 7 ≈ 0.86
- Need result = 3
- Try: (5 + 9) = 14, (6 - 7) = -1, 14 + (-1) = 13, 14 - (-1) = 15, 14 × (-1) = -14, 14 ÷ (-1) = -14
- Try: (5 - 9) = -4, (6 + 7) = 13, -4 + 13 = 9, -4 - 13 = -17, -4 × 13 = -52, -4 13 ≈ -0.31
- Try: (5 + 9) = 14, (6 + 7) = 13, 14 - 13 = 1, 14 + 13 = 27, 14 × 13 = 182, 14 ÷ 13 ≈ 1.08
- Try: (5 × 9) = 45, (6 + 7) = 13, 45 ÷ 13 ≈ 3.46, 45 - 13 = 32
- Try: (5 + 9) = 14, (7 - 6) = 1... wait, it's (6 ○ 7) not (7 ○ 6)
- Hmm, (6 - 7) = -1
- What about: (9 - 5) = 4 but we have (5 ○ 9)
- Let me try: (5 - 9) = -4, and if second group gives us -7, then -4 - (-7) = 3 ✓
- Can (6 ○ 7) = -7? 6 - 13 = -7 (no), 6 × (-7/6)... no simple way
- Try: (5 + 9) = 14, need 14 ○ x = 3, so x could be 11 (14-11=3), or 14/3≈4.67, or 3/14...
- Can (6 ○ 7) = 11? 6 + 7 = 13, 6 × 7 = 42, 7 - 6 = 1... no
- Try: (9 - 5) but order is (5 ○ 9)
- Wait! What if it's (5 - 9) = -4 and (6 - 7) = -1, then (-4) - (-1) = -4 + 1 = -3
- What if: (5 - 9) = -4 and (7 - 6) = 1... but it's written as (6 ○ 7)
- Hmm, unless the order can be flipped in subtraction? No, that would be unusual.
- Let me try: (5 + 9) = 14, (6 × 7) = 42, 42 ÷ 14 = 3 ✓ BUT the structure is (5○9) ○ (6○7), so it would be 14 ○ 42 = 3
- 42 ÷ 14 = 3, so if the middle operator is ÷ and we reverse... but typically we read left to right
- Unless... (6 × 7) (5 + 9) = 42 ÷ 14 = 3 ✓
- But the format shows (5 ○ 9) ○ (6 ○ 7), which suggests first group OP second group
- If OP is , then (5 + 9) (6 × 7) = 14 ÷ 42 = 1/3 ✗
- If OP is ÷ but reversed meaning... hmm
- Actually wait, what if it's: (9 - 5) - (7 - 6) = 4 - 1 = 3 ✓
- But the format is (5 ○ 9) not (9 ○ 5)
- Unless subtraction allows flipping? In standard notation, (5 - 9) ≠ (9 - 5)
- Let me check if there's another way:
- What if: |5 - 9| = 4 and |6 - 7| = 1, then 4 - 1 = 3? But absolute value isn't mentioned
- Or what if the problem allows choosing the order within each parenthesis? That seems unlikely.
- Let me try one more: (5 × 9) = 45, (6 + 7) = 13... 45 ÷ 13 ≈ 3.46
- (5 + 9) = 14, (7 - 6) = 1 if we can flip... 14 - 1 = 13, 14 1 = 14, 14 × 1 = 14, 14 + 1 = 15
- Hmm, what about (5 - 9) = -4, (6 ÷ 7)... messy
- OK let me try: maybe I need to accept that (6 - 7) could be interpreted as -(7 - 6) = -1
- Then (5 - 9) - (6 - 7) = -4 - (-1) = -4 + 1 = -3 ✗
- (5 - 9) + (6 - 7) = -4 + (-1) = -5
- (9 - 5) + (7 - 6) = 4 + 1 = 5 ✗
- (9 - 5) - (7 - 6) = 4 - 1 = 3 ✓ IF we can flip both!
- But can we? The problem says "choose a sign" for each circle, not rearrange numbers
- Unless... oh wait! What if it's (5 + 9) and we interpret the middle differently?
- Actually, you know what, let me just check if maybe the intended answer assumes we can choose which number comes first in each operation within the parentheses. That would be unusual but let's see:
- If yes: (9 - 5) - (7 - 6) = 4 - 1 = 3 ✓
- This seems like the most plausible answer even though it requires interpreting the parentheses flexibly.
Actually, wait. Let me reconsider. What if I'm overthinking this?
What if it's simply: (5 + 9) ÷ (6 - 7)... no that gives negative
Or: (9 - 5) ÷ (7 - 6) = 4 ÷ 1 = 4 ✗
Hmm, what about: (5 × 9) and (6 + 7)... 45 and 13... no clean division
OK I think the most reasonable interpretation, even if it requires flexible reading of the parentheses, is:
(9 - 5) - (7 - 6) = 4 - 1 = 3
But strictly following the format (5 ○ 9) ○ (6 ○ 7), I cannot find a solution with standard operations. Let me note this uncertainty.
Actually, wait! One more try:
What if: (5 - 9) = -4 and (6 - 7) = -1, then (-4) × (-1) = 4 ✗
What if: (5 - 9) = -4 and (7 - 6) = 1 (if we can flip), then (-4) + 1 = -3, (-4) - 1 = -5, (-4) × 1 = -4, (-4) ÷ 1 = -4
None of these give 3.
Let me try yet another angle:
What if the answer is: (5 + 9) = 14 and (6 × 7) = 42, and 42 ÷ 14 = 3, but written as (6 × 7) ÷ (5 + 9)?
The format shows (5 ○ 9) ○ (6 ○ 7) = 3, which reads as "first_group middle_op second_group = 3"
If middle_op is ÷, then we'd need first_group second_group = 3, meaning first_group = 3 × second_group
If first_group = 14 (5+9) and second_group = 42 (6×7), then 14 ÷ 42 = 1/3 ✗
If first_group = 42 and second_group = 14, then 42 ÷ 14 = 3 ✓ but that reverses the groups
Unless... OH! What if the middle operator is actually meant to show that we divide the SECOND group by the FIRST group? That would be very non-standard notation though.
Alternatively, what if I misread and it's actually asking for:
(5 ○ 9) and separately (6 ○ 7) and then those two results relate somehow to 3?
No, the equals sign at the end suggests the whole expression equals 3.
You know what, let me just go with the interpretation that makes mathematical sense even if it requires reading the parentheses in a flexible way:
(9 - 5) - (7 - 6) = 4 - 1 = 3
Or alternatively, if we must stick to the exact format:
I cannot find a valid solution with standard operations following (5 ○ 9) ○ (6 ○ 7) = 3 exactly as written.
Let me move on and finalize what I have, noting any uncertainties.
Going back to Row 7 which I also couldn't solve definitively:
(12 ○ 3) ○ (7 ○ 2) = 3
Let me try one more systematic approach with a table:
First group (12 ○ 3): 15, 9, 36, 4
Second group (7 ○ 2): 9, 5, 14, 3.5
Testing all combinations for result = 3:
- 15 - 12 = 3 (need 12 from second group) ✗
- 9 - 6 = 3 (need 6 from second group) ✗
- 36 ÷ 12 = 3 (need 12 from second group) ✗
- 4 - 1 = 3 (need 1 from second group) ✗
- 9 3 = 3 (need 3 from second group, have 3.5) ✗
- 15 5 = 3 (need 5 from second group) ✓✓✓
WAIT! 15 ÷ 5 = 3!
First group: 12 + 3 = 15
Second group: 7 - 2 = 5
Middle: 15 ÷ 5 = 3
Answer: (12 + 3) ÷ (7 - 2) = 3 ✓✓✓
Great! I solved Row 7!
Now back to Row 10:
(5 ○ 9) ○ (6 ○ 7) = 3
Using the same systematic approach:
First group (5 ○ 9): 14, -4, 45, 5/9
Second group (6 ○ 7): 13, -1, 42, 6/7
Testing for result = 3:
- 14 - 11 = 3 (need 11) ✗
- 14 ÷ (14/3) ≈ 3 (need 4.67) ✗
- 45 ÷ 15 = 3 (need 15) ✗
- (-4) - (-7) = 3 (need -7) ✗
- 13 - 10 = 3 (if first group = 13, but max is 14 or 45)
- 42 ÷ 14 = 3 (need first group = 14, second group = 42)
42 ÷ 14 = 3!
First group: 5 + 9 = 14
Second group: 6 × 7 = 42
But we need: first_group ÷ second_group = 14 ÷ 42 = 1/3 ✗
OR: second_group ÷ first_group = 42 ÷ 14 = 3 ✓
So if the middle operator means "divide the second group by the first group" or if we interpret it as (6 × 7) ÷ (5 + 9), we get 3.
Given the format (5 ○ 9) ○ (6 ○ 7), the middle circle should represent an operation between the two groups. If we use ÷, standard interpretation is (5+9) ÷ (6×7) = 14 ÷ 42 = 1/3.
However, if the puzzle allows for creative interpretation or if there's a convention I'm missing where the larger number is divided by the smaller, then (6 × 7) ÷ (5 + 9) = 42 ÷ 14 = 3 would work.
Alternatively, maybe the intended answer is:
(9 - 5) - (7 - 6) = 4 - 1 = 3, assuming we can choose the order within each parenthesis.
Given this ambiguity, I'll provide the answer that makes the most mathematical sense: using division where 42 ÷ 14 = 3, which means:
(5 + 9) and (6 × 7) with the understanding that we divide the larger result by the smaller, OR
Simply: (6 × 7) ÷ (5 + 9) = 3 if we're allowed to reorder the groups.
For consistency with how I solved the other problems, I'll state it as:
(5 + 9) and (6 × 7) with ÷ between them, interpreting it as the larger divided by smaller to get 3.
Actually, you know what, let me just write it in the most straightforward way that a student would understand:
The operations are: + for first circle, × for third circle, and ÷ for the middle circle, giving us (5 + 9) ÷ (6 × 7)... but that equals 1/3, not 3.
Hmm, this is genuinely ambiguous. Let me check if maybe I should interpret it as:
|(5 - 9)| ÷ |(6 - 7)| = 4 ÷ 1 = 4 ✗
Or: (9 - 5) ÷ (7 - 6) = 4 ÷ 1 = 4 ✗
What about: (5 + 9) - (6 + 7) = 14 - 13 = 1 ✗
(5 × 9) - (6 × 7) = 45 - 42 = 3 ✓✓✓
AH HA! There it is!
(5 × 9) - (6 × 7) = 45 - 42 = 3 ✓
Answer: (5 × 9) - (6 × 7) = 3
Perfect! I was overcomplicating it.
Now let me compile all the answers:
Final Answers:
Row 1: (12 3) × (5 - 2) = 12 ✓ (given)
Row 2: (7 - 4) × 5 - 6 = 9
Row 3: (3 × 6) ÷ 2 - 4 = 5
Row 4: 2 = (21 - 5) ÷ (2 × 4)
Row 5: 27 ÷ 3 = (11 + 7) ÷ 2
Row 6: 8 × 4 - 12 = 10 × 2
Row 7: (12 + 3) ÷ (7 - 2) = 3
Row 8: 37 = (15 - 5) × 3 + 7
Row 9: 18 2 = 7 × 2 - 5
Row 10: (5 × 9) - (6 × 7) = 3
Let me verify each one quickly:
Row 2: (7 - 4) × 5 - 6 = 3 × 5 - 6 = 15 - 6 = 9 ✓
Row 3: (3 × 6) ÷ 2 - 4 = 18 ÷ 2 - 4 = 9 - 4 = 5 ✓
Row 4: (21 - 5) ÷ (2 × 4) = 16 ÷ 8 = 2 ✓
Row 5: 27 ÷ 3 = 9, (11 + 7) ÷ 2 = 18 ÷ 2 = 9 ✓
Row 6: 8 × 4 - 12 = 32 - 12 = 20, 10 × 2 = 20 ✓
Row 7: (12 + 3) ÷ (7 - 2) = 15 ÷ 5 = 3 ✓
Row 8: (15 - 5) × 3 + 7 = 10 × 3 + 7 = 30 + 7 = 37 ✓
Row 9: 18 ÷ 2 = 9, 7 × 2 - 5 = 14 - 5 = 9 ✓
Row 10: (5 × 9) - (6 × 7) = 45 - 42 = 3 ✓
All verified!
Final Answer:
Row 2: (7 - 4) × 5 - 6 = 9
Row 3: (3 × 6) ÷ 2 - 4 = 5
Row 4: 2 = (21 - 5) ÷ (2 × 4)
Row 5: 27 ÷ 3 = (11 + 7) ÷ 2
Row 6: 8 × 4 - 12 = 10 × 2
Row 7: (12 + 3) ÷ (7 - 2) = 3
Row 8: 37 = (15 - 5) × 3 + 7
Row 9: 18 ÷ 2 = 7 × 2 - 5
Row 10: (5 × 9) - (6 × 7) = 3
Parent Tip: Review the logic above to help your child master the concept of maths puzzles printable year 8.