Step 1: Simplify the expressions on both sides of the equation.
Left-hand side (LHS):
1/2 × (3/2 + 1/4)
To add the fractions inside the parentheses, we need a common denominator, which is 4. So, we convert 3/2 to have a denominator of 4:
3/2 = (3/2) × (2/2) = 6/4
Now, we can add the fractions:
LHS = 1/2 × (6/4 + 1/4)
LHS = 1/2 × (7/4)
To multiply, simply multiply the numerators and denominators separately:
LHS = (1 × 7)/(2 × 4)
LHS = 7/8
Step 2: Simplify the right-hand side (RHS).
RHS: -1/2 × 3/2 - 1/2 × 1/4
We'll start by multiplying the fractions separately:
RHS = (-1 × 3)/(2 × 2) - (1 × 1)/(2 × 4)
RHS = -3/4 - 1/8
Step 3: Combine the terms on the right-hand side (RHS).
To subtract fractions, we need a common denominator, which is 8. So, we convert -3/4 to have a denominator of 8:
-3/4 = (-3/4) × (2/2) = -6/8
Now, we can subtract the fractions:
RHS = -6/8 - 1/8
RHS = -7/8
Step 4: Compare the results on both sides of the equation.
LHS = 7/8
RHS = -7/8
The equation becomes:
7/8 = -7/8
The equation is not true; the LHS and RHS are not equal. Therefore, the initial statement is incorrect, and the equation 1/2 × (3/2 + 1/4) = - 1/2 × 3/2 - 1/2 × 1/4 is false.
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Answer:
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Answer:
Step-by-step explanation:
Step 1: Simplify the expressions on both sides of the equation.
Left-hand side (LHS):
1/2 × (3/2 + 1/4)
To add the fractions inside the parentheses, we need a common denominator, which is 4. So, we convert 3/2 to have a denominator of 4:
3/2 = (3/2) × (2/2) = 6/4
Now, we can add the fractions:
LHS = 1/2 × (6/4 + 1/4)
LHS = 1/2 × (7/4)
To multiply, simply multiply the numerators and denominators separately:
LHS = (1 × 7)/(2 × 4)
LHS = 7/8
Step 2: Simplify the right-hand side (RHS).
RHS: -1/2 × 3/2 - 1/2 × 1/4
We'll start by multiplying the fractions separately:
RHS = (-1 × 3)/(2 × 2) - (1 × 1)/(2 × 4)
RHS = -3/4 - 1/8
Step 3: Combine the terms on the right-hand side (RHS).
To subtract fractions, we need a common denominator, which is 8. So, we convert -3/4 to have a denominator of 8:
-3/4 = (-3/4) × (2/2) = -6/8
Now, we can subtract the fractions:
RHS = -6/8 - 1/8
RHS = -7/8
Step 4: Compare the results on both sides of the equation.
LHS = 7/8
RHS = -7/8
The equation becomes:
7/8 = -7/8
The equation is not true; the LHS and RHS are not equal. Therefore, the initial statement is incorrect, and the equation 1/2 × (3/2 + 1/4) = - 1/2 × 3/2 - 1/2 × 1/4 is false.