Symmetry in Operations Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

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

1
\(5 + 3 = 8\) and \(3 + 5 = 8\). Equal! ✓
2
\(5 \times 3 = 15\) and \(3 \times 5 = 15\). Equal! ✓
3
Both operations are symmetric (commutative): swapping inputs gives the same output.
4
This is the commutative property for both addition and multiplication.

Answer

Both equal the same value; both are commutative

Operations with symmetry (commutativity) satisfy \(a \circ b = b \circ a\). Addition and multiplication both have this symmetry.

About Symmetry in Operations

When exchanging or swapping operands or roles in an operation produces the same result or a symmetrically related one.

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

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

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