Equality as Relationship Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
mediumIf \(a = b\) and \(b = c\), what can we conclude about \(a\) and \(c\)? Give a numeric example.
Solution
- 1 By transitivity of equality: if \(a = b\) and \(b = c\), then \(a = c\).
- 2 Example: Let \(a = 2+3\), \(b = 5\), \(c = 10/2\).
- 3 \(2+3=5\) and \(5=10/2\), so \(2+3=10/2\).
- 4 Transitivity: equality chains through shared values.
Answer
\(a = c\) (by transitivity)
Equality is transitive: \(a=b\) and \(b=c\) implies \(a=c\). This lets us chain equalities together.
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 1 easy
Explain why (=) means 'the same value as', not just 'the answer is'. Use (3 + 5 = 4 times 2) as an e
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