Fraction multiplication follows a simple rule: multiply the numerators together and multiply the denominators together. The general formula is a over b times c over d equals a times c over b times d. For example, one half times one third equals one times one over two times three, which equals one sixth. We can visualize this using rectangular area models where the result represents the overlapping area.
让我们通过复杂的例子学习化简技巧。第一个例子中，三分之二乘以四分之三等于十二分之六，通过分子分母同时除以六化简为二分之一。我们也可以使用交叉约分法在相乘前化简。对于九分之四乘以八分之三，我们将四与八约分得到一和二，将九与三约分得到三和一，最终得到六分之一。这种方法通常让计算更简单。
When multiplying mixed numbers, we must first convert them to improper fractions. For example, to multiply two and one third times one and one half, we first convert two and one third to seven thirds by multiplying two times three plus one over three. Similarly, one and one half becomes three halves. Then we multiply seven thirds times three halves to get twenty-one sixths. Finally, we convert back to a mixed number: twenty-one sixths equals three and one half.
Fraction division uses the reciprocal method. To divide by a fraction, we multiply by its reciprocal instead. The rule is: a over b divided by c over d equals a over b times d over c. For example, one half divided by one fourth equals one half times four over one, which equals four halves or two. We can visualize this by asking: how many one-fourth pieces fit into one half? The answer is two pieces, confirming our calculation.
Let's practice division with more examples. For three fourths divided by two thirds, we find the reciprocal of two thirds, which is three halves, then multiply three fourths times three halves to get nine eighths. For five sixths divided by one half, we multiply five sixths times two over one to get ten sixths, which simplifies to five thirds. In real-world applications, like a recipe problem where you need three fourths cup of flour but want to make half the recipe, you multiply three fourths times one half to get three eighths cup of flour.