Practice Symmetry in Operations in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
When exchanging or swapping operands or roles in an operation produces the same result or a symmetrically related one.
3 + 5 = 5 + 3 shows addition is symmetric. 3 - 5 \neq 5 - 3 shows subtraction isn't.
Example 1
easyShow 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?
Example 4
mediumIs \(16 \div 4 = 4 \div 16\)? What does this tell us about division's symmetry?