Question

Simplify using order of operations. Show all steps
3 x 1/2 - 1/4

Answer 1

To simplify the expression \(3 \times \frac{1}{2} - \frac{1}{4}\), we will follow the order of operations (also known as PEMDAS/BODMAS rules). We will perform the multiplication first, followed by the subtraction.

### Step 1: Perform the multiplication
\[
3 \times \frac{1}{2} = \frac{3 \times 1}{2} = \frac{3}{2}
\]

### Step 2: Rewrite the expression
Now substituting back into the expression, we have:
\[
\frac{3}{2} - \frac{1}{4}
\]

### Step 3: Find a common denominator
To subtract these fractions, we need a common denominator. The denominators are 2 and 4. The least common denominator (LCD) is 4.

### Step 4: Convert the fractions to have the same denominator
Convert \(\frac{3}{2}\) to a fraction with a denominator of 4:
\[
\frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4}
\]

### Step 5: Subtract the fractions
Now we can perform the subtraction:
\[
\frac{6}{4} - \frac{1}{4} = \frac{6 - 1}{4} = \frac{5}{4}
\]

### Final result
The simplified form of the expression \(3 \times \frac{1}{2} - \frac{1}{4}\) is:
\[
\frac{5}{4}
\]

Thus, the answer is \(\frac{5}{4}\) or \(1 \frac{1}{4}\) if expressed as a mixed number.