Question

Match each statement with the property it illustrates. 1. -9 + 0 = -9 associative property of multiplication 2. (-9)(0) = (0)(-9) identity property of addition 3. (-9)(1) = -9 associative property of addition 4. -1(4 · 9) = (-1 · 4)9 identity property of multiplication 5. -9 + 1 = 1 + (-9) commutative property of multiplication 6. -1 + (4 + 9) = (-1 + 4) + 9 commutative property of addition

Answer 1

1. -9 + 0 = -9 identity property of addition

Adding zero does not change a number.

2. (-9)(0) = (0)(-9) commutative property of multiplication

The order of multiplication can be changed.

3. (-9)(1) = -9 identity property of multiplication

Multiplying by 1 does not change a number.

4. -1(4 · 9) = (-1 · 4)9 associative property of multiplication

Changing grouping does not change the product.

5. -9 + 1 = 1 + (-9) commutative property of addition

Changing the order does not change the sum.

6. -1 + (4 + 9) = (-1 + 4) + 9 associative property of addition

Changing the grouping does not change the product.

Answer 2

Statement Property

1. -9 + 0 = -9 Identity property of addition

2. (-9)(0) = (0)(-9) Commutative property of multiplication

3. (-9)(1) = -9 Identity property of multiplication

4. -1(4 · 9) = (-1 · 4)9 Associative property of multiplication

5. -9 + 1 = 1 + (-9) Commutative property of addition

6. -1 + (4 + 9) = (-1 + 4) + 9 Associative property of addition

Explanation:

Identity property of addition: If a is a number, then the addition of the number and identity element gives the same number. Identity element of addition is 0.

`a+0=a`

Commutative property of addition: If a and b are two numbers, then

`a+b=b+a`

Associative property of addition: If a, b and c are three numbers, then

`a+(b+c)=(a+b)+c`

Identity property of multiplication: If a is a number, then the product of the number and identity element gives the same number. Identity element of multiplication is 1.

`(a)(1)=a`

Commutative property of multiplication: If a and b are two numbers, then

`ab=ba`

Associative property of multiplication: If a, b and c are three numbers, then

`a(bc)=(ab)c`

Statement Property

1. -9 + 0 = -9 Identity property of addition

2. (-9)(0) = (0)(-9) Commutative property of multiplication

3. (-9)(1) = -9 Identity property of multiplication

4. -1(4 · 9) = (-1 · 4)9 Associative property of multiplication

5. -9 + 1 = 1 + (-9) Commutative property of addition

6. -1 + (4 + 9) = (-1 + 4) + 9 Associative property of addition