How to Cross Multiply to Compare Fractions
Comparing fractions is an essential skill in mathematics, especially when dealing with real-world problems. One of the most common methods to compare fractions is by using cross multiplication. Cross multiplication is a straightforward process that allows you to determine whether one fraction is greater, smaller, or equal to another. In this article, we will discuss how to cross multiply to compare fractions and provide some practical examples to help you understand the concept better.
Understanding Cross Multiplication
Cross multiplication is based on the property that if two fractions are equal, then the product of their numerators is equal to the product of their denominators. In other words, if we have two fractions, a/b and c/d, they are equal if and only if a d = b c. By cross multiplying, we can find out if this property holds true for the fractions we are comparing.
Step-by-Step Guide to Cross Multiplication
Here is a step-by-step guide on how to cross multiply to compare fractions:
1. Write down the two fractions you want to compare, for example, 3/4 and 5/6.
2. Multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. In our example, this would be 3 6 and 4 5.
3. Compare the products you obtained in step 2. If the product of the numerators is greater than the product of the denominators, then the first fraction is greater. If the product of the numerators is smaller, then the first fraction is smaller. If both products are equal, then the fractions are equal.
Example 1: Comparing 3/4 and 5/6
Let’s apply the cross multiplication method to compare the fractions 3/4 and 5/6.
1. Write down the fractions: 3/4 and 5/6.
2. Multiply the numerators and denominators: 3 6 = 18 and 4 5 = 20.
3. Compare the products: 18 is smaller than 20.
From this comparison, we can conclude that 3/4 is smaller than 5/6.
Example 2: Comparing 7/8 and 9/12
Now, let’s compare the fractions 7/8 and 9/12 using cross multiplication.
1. Write down the fractions: 7/8 and 9/12.
2. Multiply the numerators and denominators: 7 12 = 84 and 8 9 = 72.
3. Compare the products: 84 is greater than 72.
Hence, we can say that 7/8 is greater than 9/12.
Conclusion
Cross multiplication is a valuable tool for comparing fractions. By following the simple steps outlined in this article, you can easily determine whether one fraction is greater, smaller, or equal to another. Practice with various examples will help you become more proficient in this skill and improve your overall understanding of fractions.
