What expression has the same value
1/2 - 3/4 (11+5) + 1/4
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
The expression 1/2 - 3/4 (11+5) + 1/4 can be simplified by performing the operations inside the parentheses first, then working with the fraction subtraction and addition.
11 + 5 = 16
Now the expression becomes 1/2 - 3/4 (16) + 1/4.
Next, we multiply 3/4 by 16:
3/4 (16) = 48/4 = 12
Now the expression becomes 1/2 - 12 + 1/4.
To add or subtract fractions, they need a common denominator. In this case, the common denominator is 4, so we convert 1/2 to have the same denominator:
1/2 = 2/4
Now the expression becomes 2/4 - 12 + 1/4.
Combining the fractions:
2/4 - 12 + 1/4 = (2 + 1)/4 - 12 = 3/4 - 12.
The expression is now 3/4 - 12.
To subtract a whole number from a fraction, we need to convert the whole number to a fraction with the same denominator:
12 = 12/1
Now the expression becomes 3/4 - 12/1.
To subtract fractions, they need a common denominator. In this case, the common denominator is 4, so we convert 12/1 to have the same denominator:
12/1 = 48/4
Now the expression becomes 3/4 - 48/4.
To subtract the fractions:
3/4 - 48/4 = (3 - 48)/4 = -45/4.
Therefore, the expression 1/2 - 3/4 (11+5) + 1/4 is equivalent to -45/4.
Out of the given options, the expression that has the same value as -45/4 is:
C. 1/2 - 3/4 - 16 - 1/4