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