Symmetry in Operations Math Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
mediumIs \(16 \div 4 = 4 \div 16\)? What does this tell us about division's symmetry?
Solution
- 1 \(16 \div 4 = 4\).
- 2 \(4 \div 16 = 0.25\).
- 3 \(4 \neq 0.25\), so division is NOT symmetric.
Answer
No — division lacks symmetry
Division is not commutative. Only addition and multiplication have operational symmetry (commutativity).
About Symmetry in Operations
When exchanging or swapping operands or roles in an operation produces the same result or a symmetrically related one.
Learn more about Symmetry in Operations →More Symmetry in Operations Examples
Example 1 easy
Show that (5 + 3 = 3 + 5) and (5 times 3 = 3 times 5). What symmetric property do both share?
Example 2 mediumFor addition, show that if (a + b = c), then (b + a = c) (symmetry). Use (a=12, b=7).
Example 3 easyDoes (8 - 5) equal (5 - 8)? What does this tell us about subtraction's symmetry?