Final answer:
Cross multiplying involves multiplying opposite numerators and denominators in a pair of fractions. For the fractions 5/12 and 20/48, cross multiplication yields two equal products, 240, showing that the fractions are equivalent. This example relates to the concept of reciprocals and simplifies complex fraction operations.
Step-by-step explanation:
When students encounter cross multiplying fractions, it's an important concept to grasp, especially in middle school mathematics. To cross multiply two fractions like 5/12 and 20/48, you multiply the numerator (top number) of one fraction by the denominator (bottom number) of the other fraction and do the same with the other pair of numbers.
To illustrate:
- Multiply the numerator of the first fraction by the denominator of the second fraction: 5 × 48.
- Then, multiply the numerator of the second fraction by the denominator of the first fraction: 20 × 12.
- The results are two products: 240 and 240.
- Since both products are equal, it implies in a proportion that the two fractions are equivalent.
This example also relates to the concept of reciprocals as mentioned in the lesson excerpt. Understanding reciprocals can help simplify complex fraction multiplication and division problems, as it allows one to easily flip the numerator and denominator of a fraction. This is demonstrated in the provided example A.1.2 where the process of multiplying by a number is shown to be similar to dividing it by its reciprocal, except for adjustments in decimal placement.