Multiply: 2/3 x 3/5 =
A.
1/3
B.
2/5
C.
3/4
D.
11/9
The Correct answer and Explanation is:
To solve the multiplication of fractions problem 23×35\frac{2}{3} \times \frac{3}{5}32×53, follow these steps:
- Multiply the Numerators: To find the product of two fractions, start by multiplying the numerators (the top numbers) together. In this case, the numerators are 2 and 3.2×3=62 \times 3 = 62×3=6
- Multiply the Denominators: Next, multiply the denominators (the bottom numbers) together. The denominators here are 3 and 5.3×5=153 \times 5 = 153×5=15
- Form the New Fraction: Place the result of the numerator multiplication over the result of the denominator multiplication. This gives:615\frac{6}{15}156
- Simplify the Fraction: To simplify the fraction 615\frac{6}{15}156, find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 6 and 15 is 3.
- Divide both the numerator and the denominator by their GCD:6÷315÷3=25\frac{6 \div 3}{15 \div 3} = \frac{2}{5}15÷36÷3=52
- Final Result: The simplified form of 615\frac{6}{15}156 is 25\frac{2}{5}52.
So, the correct answer to 23×35\frac{2}{3} \times \frac{3}{5}32×53 is 25\frac{2}{5}52.
Explanation: When multiplying fractions, the process involves two main steps: multiplying the numerators together and multiplying the denominators together. This process is straightforward but requires careful attention to detail to ensure the final fraction is in its simplest form. Simplification is crucial because it reduces the fraction to its lowest terms, making it easier to understand and use in further calculations. In this case, after multiplying and simplifying 615\frac{6}{15}156 to 25\frac{2}{5}52, we achieve the final result, which is option B.