Write equivalent expressions using properties
Key Notes :
You can use properties of operations to write equivalent expressions. Here are some common properties:
| Commutative property of addition | a+b=b+a |
| Commutative property of multiplication | ab=ba |
| Associative property of addition | (a+b)+c=a+(b+c) |
| Associative property of multiplication | (ab)c=a(bc) |
| Distributive property | a(b+c)=ab+ac |
Learn with an example
🎈 Complete the expressions.
🎈Write each answer as a number, a variable, or the product of a number and a variable.
| 4 + 6 w + 8 | |
| = ________ + 4 + 8 | Commutative property of addition |
| = 6w + ________ | Add |
- Look at the first two expressions.
| 4 + 6w + 8 | |
| = ? + 4 + 8 | Commutative property of addition |
- Changing the order of addends does not change the sum. These expressions are equivalent if the missing term is 6w.
| 4 + 6w + 8 | |
| = 6w + 4 + 8 | Commutative property of addition |
- Look at the last two expressions.
| 6w + 4 + 8 | |
| = 6w + ? | Add |
- These expressions are equivalent if the missing term is 12.
| 6w + 4 + 8 | |
| = 6w + 12 | Add |
✈️ Complete the expressions.
✈️ Write each answer as a number, a variable, or the product of a number and a variable.
| 9s . 2 | |
| = 2. _____ | Commutative property of multiplication |
| = _______ | Multiply |
Look at the first two expressions.
| 9s . 2 | |
| = 2. ? | Commutative property of multiplication |
Changing the order of factors does not change the product. These expressions are equivalent if the missing term is 9s.
| 9s . 2 | |
| = 2. 9s | Commutative property of multiplication |
Look at the last two expressions.
| 2 . 9s | |
| ? | Multiply |
These expressions are equivalent if the missing term is 18s.
| 2 . 9s | |
| = 18s | Multiply |
✈️Complete the expressions.
✈️Write each answer as a number, a variable, or the product of a number and a variable.
| 7q . 4 | |
| = 4 .________ | Commutative property of multiplication |
| =_________ | Multiply |
Look at the first two expressions.
| 7q . 4 | |
| = 4 . ? | Commutative property of multiplication |
Changing the order of factors does not change the product. These expressions are equivalent if the missing term is 7q.
| 7q . 4 | |
| = 4 .7q | Commutative property of multiplication |
Look at the last two expressions.
| 4 .7q | |
| = ? | Multiply |
These expressions are equivalent if the missing term is 28q.
| 4 .7q | |
| 28q | Multiply |
Let’s practice!🖊️
