Term
| What does the reflexive property say? |
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Definition
| A thing is equal to itself: a = a. |
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Term
| What does the symmetric property say? |
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Definition
Equations are true forward and backward:
If a = b, then b = a. |
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Term
| What does the transitive property say? |
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Definition
If two things are equal to the same thing, then they are equal to each other:
If a = c, and b = c, then a = b.
a and b are both equal to c. So they are equal to each other. |
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Term
| What does the substitution property say? |
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Definition
If two things are equal to each other, then they can replace each other in true equations, and the equations will remain true.
Example:
If 2a + 7 = b and a = 3b +5 then 2(3b+5) + 7 = b.
We replaced a in the first equation with 3b + 5. We can do that because a = 3b + 5. |
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Term
| What does the addition property say? |
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Definition
If equals are added to equals, then the sums are equal:
If a = b, then a + c = b + c. |
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Term
| What does the subtraction property say? |
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Definition
If equals are subtracted from equals, then the differences are equal:
If a = b, then a - c = b - c. |
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Term
| What does the multiplication property say? |
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Definition
If equals are multiplied by equals, then the products are equal:
If a = b, then ac = bc. |
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Term
| What does the division property say? |
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Definition
If equals are divided by equals, then the quotients are equal:
If a = b, then a/c = b/c. |
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