Compare 1/2 and 2/3
Compare these two fractions to find which is greater, lesser, or if they are equal.
Answer:
\frac{1}{2} < \frac{2}{3}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to compare two fractions:
First fraction: 1/2
Second fraction: 2/3
We'll use the cross-multiplication method.
\frac{1}{2} \quad \text{vs} \quad \frac{2}{3}
Step 2
Cross Multiply
Multiply each numerator by the opposite denominator:
1 × 3 = 3 (left side)
2 × 2 = 4 (right side)
The larger product tells us which fraction is larger.
1 \times 3 = 3 \quad \text{and} \quad 2 \times 2 = 4
Step 3
Compare the Products
3 is less than 4
Since the right product is larger, the right fraction is larger.
\frac{1}{2} < \frac{2}{3}
Step 4
Verify with Decimals
We can verify by converting to decimals:
1/2 = 0.5
2/3 = 0.666667
0.5 is less than 0.666667 ✓
0.5 < 0.666667