What are examples of equivalent number sentences?

Equivalent number sentences are number sentences (equations) that, while looking different, have the same value on both sides of the equal sign. They ultimately express the same relationship or result.

Here are some examples to illustrate this concept:

• Example 1: Simple Addition

  • 5 + 3 = 8
  • 4 + 4 = 8
  • 2 + 6 = 8

  All three of these sentences are equivalent because they all equal 8.

• Example 2: Multiplication and Addition

  • 3 x 4 = 12
  • 6 + 6 = 12
  • 2 x 6 = 12
  • 10 + 2 = 12

  These examples show that equivalent number sentences can use different operations (multiplication and addition) but still result in the same value (12).

• Example 3: Subtraction and Addition

  • 15 - 5 = 10
  • 2 + 8 = 10
  • 20 - 10 = 10

  This showcases equivalence through subtraction and addition, all equalling 10.

• Example 4: More Complex Combinations

  • (2 x 5) + 3 = 13
  • 20 - 7 = 13
  • (1 x 10) + 3 = 13

  Here, we see that more complex expressions can also be equivalent if they simplify to the same value.

• Example 5: Using Variables

  • If x = 5, then x + 3 = 8
  • 4 + 4 = 8

  Even with variables, if the values result in the same answer, the equations can be considered equivalent given that the value of the variable is defined.

In summary, equivalent number sentences are different ways of expressing the same mathematical relationship or arriving at the same numerical result. The key is that both sides of each equation ultimately have the same value.