Simplify.

-2(3)^2 - 8 ÷ 2 + 6
A) -18
B) -16**
C) -7
D) 7

Lucy is trying to find a rational number between 3/8 and and 6/7
What would help her to find this number?
A)Divide 3/8 by 6/7***
B)Multiply 3/8 by 6/7
C)Convert 3/8 and 6/7 to Fractions with a common denominator.
D) Find a common numerator and multiply the denominators by this number.

When you multiply a number by 1
4
, the result is
A) 50% of the original number.
B) 400% of the original number.
C) four times the original number.
D) one-fourth the original number. ***

*When you multiply a number by 1/4

To simplify the expression -2(3)^2 - 8 ÷ 2 + 6, we need to follow a specific order of operations called PEMDAS.

1. First, we need to evaluate the exponent: (3)^2 = 9.
2. Then, we multiply -2 by 9: -2 * 9 = -18.
3. Next, we divide 8 by 2: 8 ÷ 2 = 4.
4. Finally, we add the results of previous steps: -18 - 4 + 6 = -16.

Therefore, the simplified expression is -16, which corresponds to option B.

To find a rational number between 3/8 and 6/7, Lucy can utilize the method of comparing fractions.

1. Option A, dividing 3/8 by 6/7, will not help Lucy find a rational number between the given fractions.
2. Option B, multiplying 3/8 by 6/7, will not help either because it will only give the product of the two fractions.
3. Option C, converting 3/8 and 6/7 to fractions with a common denominator, will help Lucy compare the fractions better, thus assisting in finding the rational number between them.
4. Option D, finding a common numerator and multiplying the denominators by this number, is not necessary for finding a rational number between the given fractions.

Therefore, the correct answer is option C.

When you multiply a number by 1/4, the result is one-fourth of the original number. Hence, the correct answer is option D.