Simplify as indicated. State at least one property of multiplication or division that would prove your simplification process correct.
a. –(n + 4), to eliminate the parentheses
b. 6(-s), to eliminate the parentheses
c. 8(24 – n), to eliminate the parentheses
Calculate the answer.
[-12 + (-18)](-16 + -4)
Write the integer that is represented by
a. a collection of 9 red counters and 5 black counters.
repeat question, already answered
a. To simplify the expression - (n + 4) and eliminate the parentheses, you can distribute the negative sign to both terms inside the parentheses. This is possible because of the distributive property of multiplication over addition.
Applying the distributive property, we have:
-(n + 4) = -n - 4
One property that proves this simplification process correct is the distributive property of multiplication over addition, which states that for any real numbers a, b, and c:
a * (b + c) = a * b + a * c
In this case, we are using the negative sign as the multiplier (a) and the expression (n + 4) as the sum (b + c).
b. To simplify the expression 6(-s) and eliminate the parentheses, you can once again apply the distributive property of multiplication over addition.
Applying the distributive property, we have:
6(-s) = -6s
The distributive property proves the simplification process correct.
c. To simplify the expression 8(24 - n) and eliminate the parentheses, you can use the distributive property just like in the previous examples.
Applying the distributive property, we have:
8(24 - n) = 8 * 24 - 8 * n = 192 - 8n
The distributive property is once again the property that proves the simplification correct.
The answer to the expression [-12 + (-18)](-16 + -4) can be calculated step by step:
[-12 + (-18)](-16 + -4)
First, simplify the addition inside each set of parentheses:
[-12 + (-18)](-16 + -4)
= [-30](-20)
Next, calculate the product of the integers:
[-30](-20) = -30 * -20 = 600
The integer that is represented by a collection of 9 red counters and 5 black counters can be found by simply adding the number of red counters and the number of black counters together. In this case, the integer representation would be 9 + 5 = 14.