Compare 1/2 and 1/3
Compare these two fractions to find which is greater, lesser, or if they are equal.
Answer:
\frac{1}{2} > \frac{1}{3}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to compare two fractions:
First fraction: 1/2
Second fraction: 1/3
We'll use the cross-multiplication method.
\frac{1}{2} \quad \text{vs} \quad \frac{1}{3}
Step 2
Cross Multiply
Multiply each numerator by the opposite denominator:
1 × 3 = 3 (left side)
1 × 2 = 2 (right side)
The larger product tells us which fraction is larger.
1 \times 3 = 3 \quad \text{and} \quad 1 \times 2 = 2
Step 3
Compare the Products
3 is greater than 2
Since the left product is larger, the left fraction is larger.
\frac{1}{2} > \frac{1}{3}
Step 4
Verify with Decimals
We can verify by converting to decimals:
1/2 = 0.5
1/3 = 0.333333
0.5 is greater than 0.333333 ✓
0.5 > 0.333333