To find the value of the expression, we simplify each operation one step at a time:
1/2 - 3/4(11 + 5) + 1/4
First, solve the addition within the parentheses:
1/2 - 3/4(16) + 1/4
Next, calculate the product:
1/2 - 3/64 + 1/4
Now, find a common denominator for the fractions:
32/64 - 3/64 + 16/64
Combine the fractions:
(32 - 3 + 16) / 64
Simplify the numerator:
45/64
So, the value of the expression is 45/64.
To find the expression with the same value, we need to simplify the options and compare:
A) 45/64
B) (1/4 + 2/3) - (2/5 - 3/8)
C) 35 * 4 - 15 + 1/4
D) 28 + 2/3 * 21 - 4/6
Let's simplify each option to see if any of them match 45/64:
A) Already simplified and matches 45/64.
B) (1/4 + 2/3) - (2/5 - 3/8)
= (3/12 + 8/12) - (16/40 - 15/40)
= 11/12 - 1/40
= (11*40 - 1)/480
= (440 - 1)/480
= 439/480
Does not match 45/64.
C) 35 * 4 - 15 + 1/4
= 140 - 15 + 1/4
= 125 + 1/4
= (125*4 + 1)/4
= (500 + 1)/4
= 501/4
Does not match 45/64.
D) 28 + 2/3 * 21 - 4/6
= 28 + (2/3 * 21) - (4/6)
= 28 + (2*7) - (4/6)
= 28 + 14 - (4/6)
= 42 - (4/6)
= (42*6 - 4)/6
= (252 - 4)/6
= 248/6
Does not match 45/64.
So, the only option that has the same value is A) 45/64.
Margaret needs to find the value of the expression below.
1/2 - 3/4(11 + 5) + 1/4
Which expression has the same value?
3 answers
The expressions are
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
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
Let's simplify each expression to find the one that has the same value as the original expression.
A) 1/2 - (3/4 + 1/4) - 16
= 1/2 - (4/4) - 16
= 1/2 - 1 - 16
= 1/2 - 17/2
= (1 - 17)/2
= -16/2
= -8
B) (1/2 + 1/4) - 33/4 + 5
= (2/4 + 1/4) - 33/4 + 5
= 3/4 - 33/4 + 5
= (3 - 33 + 20)/4
= -10/4
= -5/2
C) 1/2 - 3/4 - 16 - 1/4
= 1/2 - (3/4 + 1/4) - 16
= 1/2 - 4/4 - 16
= 1/2 - 1 - 16
= 1/2 - 17/2
= (1 - 17)/2
= -16/2
= -8
D) (1/2 + 1/4) - 12
= (2/4 + 1/4) - 12
= 3/4 - 12
= (3 - 48)/4
= -45/4
So, the expression that has the same value as the original expression is C) 1/2 - 3/4 - 16 - 1/4. Both of these expressions simplify to -8.
A) 1/2 - (3/4 + 1/4) - 16
= 1/2 - (4/4) - 16
= 1/2 - 1 - 16
= 1/2 - 17/2
= (1 - 17)/2
= -16/2
= -8
B) (1/2 + 1/4) - 33/4 + 5
= (2/4 + 1/4) - 33/4 + 5
= 3/4 - 33/4 + 5
= (3 - 33 + 20)/4
= -10/4
= -5/2
C) 1/2 - 3/4 - 16 - 1/4
= 1/2 - (3/4 + 1/4) - 16
= 1/2 - 4/4 - 16
= 1/2 - 1 - 16
= 1/2 - 17/2
= (1 - 17)/2
= -16/2
= -8
D) (1/2 + 1/4) - 12
= (2/4 + 1/4) - 12
= 3/4 - 12
= (3 - 48)/4
= -45/4
So, the expression that has the same value as the original expression is C) 1/2 - 3/4 - 16 - 1/4. Both of these expressions simplify to -8.