14. (32+48)+52=32+(48+52) associative
15. 256+0=256 identity property
16.3/10x10/3=1 inverse property
17.1x143=143 identity property
18. 81+(-81)=0 inverse property
18. Is -81 the inverse of 81?
The others look right.
14. To demonstrate the property of associativity, we need to evaluate both sides of the equation step by step.
First, let's solve the left side: (32 + 48) + 52.
To do this, we add the numbers inside the parentheses first: 32 + 48 = 80.
Then, we add the result to the remaining number: 80 + 52 = 132.
Now, let's solve the right side: 32 + (48 + 52).
Again, we add the numbers inside the parentheses first: 48 + 52 = 100.
Then, we add the initial number to the result: 32 + 100 = 132.
As you can see, both sides of the equation evaluate to the same value, 132. This confirms the property of associativity, where the grouping of numbers does not affect the final result.
15. The identity property is demonstrated when a number combined with the identity element (which is 0 in addition) doesn't change the value of that number. In this case, we have 256 + 0.
To solve it, we add 0 to 256: 256 + 0 = 256.
The result is the same as the original number, 256, proving the identity property.
16. The inverse property is related to the multiplication and division operations. In this equation, we have (3/10) × (10/3).
To solve it, we multiply the numerators together: 3 × 10 = 30.
And then, we multiply the denominators together: 10 × 3 = 30.
Finally, we divide the product of the numerators by the product of the denominators: 30/30 = 1.
The result is 1, demonstrating the inverse property, where multiplying a number by its reciprocal results in 1.
17. The identity property is shown when a number multiplied by the identity element (which is 1 in multiplication) doesn't change the value of that number. In this equation, we have 1 × 143.
To solve it, we multiply 1 by 143: 1 × 143 = 143.
The result is the same as the original number, 143, which confirms the identity property.
18. The inverse property is demonstrated in this equation, where we have 81 + (-81).
To solve it, we add the numbers together: 81 + (-81) = 0.
The sum is 0, indicating the inverse property, where adding a number to its additive inverse results in zero.