Understanding 3/4 × 2/3
To visualize the multiplication of two fractions, 3/4 and 2/3, we can break it down into a step-by-step process.
Step 1: Visual Representation of Fractions
- 3/4: Imagine a rectangle divided into 4 equal parts. Shade 3 of those parts to represent 3/4.
- 2/3: Now, take another rectangle divided into 3 equal parts. Shade 2 of those parts to represent 2/3.
Step 2: Multiplying the Fractions
- When multiplying fractions, you multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
- Numerators: 3 × 2 = 6
- Denominators: 4 × 3 = 12
Step 3: Resulting Fraction
- Combining these results gives you 6/12.
Step 4: Simplifying the Fraction
- To simplify 6/12, divide both the numerator and denominator by their greatest common divisor, which is 6.
- 6 ÷ 6 = 1
- 12 ÷ 6 = 2
- Thus, the simplified result is 1/2.
Conclusion
- The multiplication of 3/4 and 2/3 equals 1/2.
- This means if you take 3/4 of a quantity and then take 2/3 of that result, you will end up with 1/2 of the original quantity.
This visual and step-by-step explanation clarifies how to multiply fractions effectively!