1. The problem involves verifying and understanding the arithmetic operations and the relationships between numbers in the rectangles and circles. 2. First, check the simple arithmetic operations given: - $25 - 5 = 20$ (not 5 as stated, so the correct result is 20) - $5 + 10 = 15$ (correct) - $46 - 18 = 28$ (correct) - $39 \div 13 = 3$ (correct) - $28 + 3 = 31$ (correct) - $11 - 5 = 6$ (correct) - $44 \div 5 = 8.8$ (correct) - $44 \div 8.8 = 5$ (not 25 as stated, correct result is 5) - $6^2 = 36$ - $22 + 5 = 27$ - $25 \div 5 = 5$ (correct) - $5 + 10 = 15$ (correct) 3. Now, interpret the graph shapes and numbers: - Top-left rectangle: numbers 25 (top), 20 (left), 10 (right), 5 (bottom) with circle 15 inside. The circle number 15 could represent a value related to these edges, possibly the sum or difference. - Center rectangle: numbers 39 (left), 46 (bottom), 13 (top), 18 (right) with circle 31 inside. - Right rectangle: numbers 44 (left), 11 (bottom), 2 (top), 5 (right) with circle 28 inside. - Bottom-left rectangle: numbers 30 (top), 18 (left), 15 (right) with circle 8 inside. - Below 8: rectangle with numbers 48 (top), 6 (left), 3 (right) with circle 6 inside and nearby 16. - Rectangle labeled 13: numbers 54 (top), 27 (bottom), 2 (right) with circle 40 inside and adjacent 14. - Rectangle labeled 14: numbers 8 (top), 24 (left), 16 (right) with circle 16 inside. - Rectangle labeled 15: numbers 144 (top), 12 (right), 1 (bottom) with circle 13 inside and nearby 7. 4. The circles likely represent some function of the rectangle's side numbers, such as sums, differences, or other operations. 5. For example, in the center rectangle: - Sum of left and right: $39 + 18 = 57$ - Sum of top and bottom: $13 + 46 = 59$ - Circle number is 31, which is less than these sums, so possibly a different operation. 6. In the right rectangle: - $44 - 11 = 33$ - $5 - 2 = 3$ - Circle is 28, which is close to $33 - 5 = 28$, suggesting the circle might be the difference between left-bottom and right-top. 7. In the bottom-left rectangle: - $30 - 18 = 12$ - $15 - 8 = 7$ - Circle is 8, which might be related to these differences. 8. The handwritten notes and numbers likely correspond to these relationships. Final answers: - Corrected arithmetic results: $25 - 5 = 20$, $44 \div 8.8 = 5$, $6^2 = 36$, $22 + 5 = 27$ - Circle values represent specific operations on rectangle side numbers, possibly differences or sums as shown.