Question

find each n. name the property that you used.

1. $3 \times 6 = 6 \times n$
2. $n \times 5 = 0$
3. $365 \times n = 365$
4. $(3 \times 2) \times n = 3 \times (2 \times 10)$
5. $5 \times 6 \times 4 \times 0 = n$
6. $n + 45 = 45$
7. $17 + 62 = 62 + n$
8. $21 + (n + 14) = (21 + 50) + 14$
9. $3 \times (14 - 14) = n$
10. $6 + (9 - n) = 6$

Explanation:

3. Step1: Apply Commutative Property of Multiplication

$3 \times 6 = 6 \times n$ matches $a \times b = b \times a$, so $n=3$.

4. Step1: Apply Zero Property of Multiplication

$n \times 5 = 0$: any number times 0 is 0, so $n=0$.

5. Step1: Apply Identity Property of Multiplication

$365 \times n = 365$: any number times 1 is itself, so $n=1$.

6. Step1: Apply Associative Property of Multiplication

$(3 \times 2) \times n = 3 \times (2 \times 10)$ matches $(a \times b) \times c = a \times (b \times c)$, so $n=10$.

7. Step1: Apply Zero Property of Multiplication

$5 \times 6 \times 4 \times 0 = n$: product with 0 is 0, so $n=0$.

8. Step1: Apply Identity Property of Addition

$n + 45 = 45$: 0 plus any number is the number, so $n=0$.

9. Step1: Apply Commutative Property of Addition

$17 + 62 = 62 + n$ matches $a + b = b + a$, so $n=17$.

10. Step1: Apply Associative Property of Addition

$21 + (n + 14) = (21 + 50) + 14$ matches $a + (b + c) = (a + b) + c$, so $n=50$.

11. Step1: Simplify inside parentheses first

$14 - 14 = 0$, then $3 \times 0 = n$, so $n=0$.

12. Step1: Isolate the parenthetical term

Subtract 6 from both sides: $9 - n = 0$, so $n=9$.

Answer:

1. $n=3$, Commutative Property of Multiplication
2. $n=0$, Zero Property of Multiplication
3. $n=1$, Identity Property of Multiplication
4. $n=10$, Associative Property of Multiplication
5. $n=0$, Zero Property of Multiplication
6. $n=0$, Identity Property of Addition
7. $n=17$, Commutative Property of Addition
8. $n=50$, Associative Property of Addition
9. $n=0$, Zero Property of Multiplication
10. $n=9$, Inverse Property of Addition (simplified)