Question

Margaret needs to find the value of the expression below.
1/2-3/4(11+5)+1/4
Which expression has the same value?
1/2-(3/4+1/4)-16
(1/2+1/4)-33/4+5
1/2-3/4-16-1/4
(1/2+1/4)-12

Answer 1

To find the value of the expression, we can follow the order of operations (PEMDAS/BODMAS - Parentheses/Brackets, Order/Indices, Multiplication/Division, Addition/Subtraction):

1/2 - 3/4(11+5) + 1/4

First, solve the parentheses:

1/2 - 3/4 * 16 + 1/4

Next, perform the multiplication:

1/2 - (48/4) + 1/4

Simplify the fractions:

1/2 - 12 + 1/4

Now, add or subtract from left to right:

(1/2 - 12) + 1/4

Combine like terms:

(-23/2) + 1/4

To add or subtract fractions, we need a common denominator. In this case, the common denominator is 4:

(-23/2) + (1/4)

To make the fractions have a common denominator, we need to multiply the numerator and denominator of the first fraction by 2:

(-23/2)*(2/2) + 1/4

Simplifying:

(-46/4) + 1/4

Now that we have a common denominator, we can add the fractions:

(-46 + 1)/4

(-45/4)

So, the value of the original expression is -45/4.

Now, let's check which expression has the same value:

1/2 - (3/4 + 1/4) - 16 = 1/2 - (4/4) - 16 = 1/2 - 1 - 16 = (1/2 - 2 - 16) = -33/2 - 16 = -49/2

(1/2 + 1/4) - 33/4 + 5 = (2/4 + 1/4) - 33/4 + 20/4 = 3/4 - 33/4 + 20/4 = (-30/4) + 20/4 = -10/4

1/2 - 3/4 - 16 - 1/4 = -1/4 - 16 - 1/4 = -17/4 - 1/4 = -18/4

(1/2 + 1/4) - 12 = (2/4 + 1/4) - 12 = 3/4 - 12 = -45/4

Therefore, the expression (1/2 + 1/4) - 12 has the same value as the original expression.