$\frac{3}{5} \cdot \frac{2}{3}$
Answer (1)
Multiply the numerators: 3 × 2 = 6 .
Multiply the denominators: 5 × 3 = 15 .
Form the fraction: 15 6 .
Simplify the fraction: 15 6 = 5 2 .
5 2
Explanation
Understanding the Problem We are asked to calculate the product of two fractions: 5 3 and 3 2 .
Multiplying Numerators To multiply fractions, we multiply the numerators together and the denominators together. The numerator of the first fraction is 3, and the numerator of the second fraction is 2. So, the numerator of the product is 3 × 2 = 6 .
Multiplying Denominators The denominator of the first fraction is 5, and the denominator of the second fraction is 3. So, the denominator of the product is 5 × 3 = 15 .
Forming the Fraction Therefore, the product of the two fractions is 15 6 .
Simplifying the Fraction Now we simplify the fraction 15 6 . Both the numerator and the denominator are divisible by 3. Dividing the numerator by 3, we get 6 ÷ 3 = 2 . Dividing the denominator by 3, we get 15 ÷ 3 = 5 .
Final Result So, the simplified fraction is 5 2 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you have 5 3 of a pizza left and you eat 3 2 of that remaining portion, you have eaten 5 2 of the whole pizza. Understanding how to multiply fractions helps in these situations.
