To find the value of the expression, we can simply simplify each step.
First, we can simplify the expression inside the parentheses: $11 + 5 = 16$.
Next, we multiply $\frac{3}{4}$ by 16: $\frac{3}{4} \cdot 16 = 12$.
Then, we can simplify further: $\frac{1}{2} - 12 + \frac{1}{4} = -12 + \frac{1}{2} + \frac{1}{4}$.
Finally, we can add the fractions: $(-12) + \frac{1}{2} + \frac{1}{4} = \frac{-24}{2} + \frac{1}{2} + \frac{1}{4} = \frac{-24 + 1 + 2}{4} = \frac{-21}{4}$.
To find which expression has the same value, we can simplify each option and compare them to $\frac{-21}{4}$.
A. $1/2 - (3/4 + 1/4) - 16 = \frac{1}{2} - \frac{4}{4} - 16 = \frac{1}{2} - 1 - 16 = \frac{1}{2} - \frac{17}{2} = \frac{-16}{2} = -8$.
B. $(1/2 + 1/4) - 33/4 + 5 = \frac{1}{2} + \frac{1}{4} - \frac{33}{4} + 5 = \frac{2}{4} + \frac{1}{4} - \frac{33}{4} + 5 = \frac{3}{4} - \frac{33}{4} + 5 = -\frac{30}{4} + 5 = \frac{-30 + 20}{4} = -\frac{10}{4} = -\frac{5}{2}$.
C. $1/2 - 3/4 - 16 - 1/4 = \frac{1}{2} - \frac{3}{4} - \frac{1}{4} - 16 = \frac{2}{4} - \frac{3}{4} - \frac{1}{4} - 16 = \frac{-2}{4} - 16 = \frac{-2 - 64}{4} = \frac{-66}{4} = \frac{-33}{2}$.
D. $(1/2 +1/4) - 12 = \frac{1}{2} + \frac{1}{4} - 12 = \frac{2}{4} + \frac{1}{4} - 12 = \frac{3}{4} - 12 = \frac{3 - 48}{4} = \frac{-45}{4}$.
Therefore, the expression that has the same value as the original expression is expression C, $\boxed{\frac{-33}{2}}$.
Margaret needs to find the value of the expression below.
\frac{1}{2}\ -\ \frac{3}{4}\ \left(11+5\right)\ +\ \frac{1}{4}
Which expression has the same value?
A. 1/2 - (3/4 + 1/4) - 16
B. (1/2 + 1/4) - 33/4 + 5
C. 1/2 - 3/4 - 16 - 1/4
D. (1/2 +1/4) - 12
1 answer
1 answer