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

easy
Show that \(5 + 3 = 3 + 5\) and \(5 \times 3 = 3 \times 5\). What symmetric property do both share?

Example 2

medium
For addition, show that if \(a + b = c\), then \(b + a = c\) (symmetry). Use \(a=12, b=7\).

Example 3

easy
Does \(8 - 5\) equal \(5 - 8\)? What does this tell us about subtraction's symmetry?

Example 4

medium
Is \(16 \div 4 = 4 \div 16\)? What does this tell us about division's symmetry?