Compare 2/3 and 3/4
Compare these two fractions to find which is greater, lesser, or if they are equal.
Answer:
\frac{2}{3} < \frac{3}{4}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to compare two fractions:
First fraction: 2/3
Second fraction: 3/4
We'll use the cross-multiplication method.
\frac{2}{3} \quad \text{vs} \quad \frac{3}{4}
Step 2
Cross Multiply
Multiply each numerator by the opposite denominator:
2 × 4 = 8 (left side)
3 × 3 = 9 (right side)
The larger product tells us which fraction is larger.
2 \times 4 = 8 \quad \text{and} \quad 3 \times 3 = 9
Step 3
Compare the Products
8 is less than 9
Since the right product is larger, the right fraction is larger.
\frac{2}{3} < \frac{3}{4}
Step 4
Verify with Decimals
We can verify by converting to decimals:
2/3 = 0.666667
3/4 = 0.75
0.666667 is less than 0.75 ✓
0.666667 < 0.75