Equality as Relationship Math Example 1
Follow the full solution, then compare it with the other examples linked below.
Example 1
easyExplain why \(=\) means 'the same value as', not just 'the answer is'. Use \(3 + 5 = 4 \times 2\) as an example.
Solution
- 1 Left side: \(3 + 5 = 8\).
- 2 Right side: \(4 \times 2 = 8\).
- 3 Both sides equal 8, so the equation expresses a relationship between two equivalent expressions.
- 4 The \(=\) sign means both sides name the same quantity.
Answer
Both sides equal 8; \(=\) expresses equivalence
Equality is a relationship between two expressions that have the same value. It is symmetric: if \(a = b\) then \(b = a\).
About Equality as Relationship
Understanding not as 'the answer is' but as expressing that two expressions represent the same value.
Learn more about Equality as Relationship →More Equality as Relationship Examples
Example 2 medium
If (a = b) and (b = c), what can we conclude about (a) and (c)? Give a numeric example.
Example 3 easyIs (5 times 6 = 30) the same kind of statement as (5 times 6 = 3 times 10)? Explain.
Example 4 mediumGiven (2x + 1 = 9), verify that (x = 4) is the solution. Then explain what equality means in this co