In the realm of fractions, it’s often necessary to perform cross-multiplication, an indispensable technique that unlocks the secrets of equating fractions and solving mathematical problems involving these elusive numbers. Whether you’re a student navigating the intricacies of algebra or an engineer tackling complex calculations, mastering cross-multiplication is a cornerstone of mathematical prowess.
Imagine two fractions, each a dance of numbers separated by a horizontal line: a/b and c/d. The goal of cross-multiplication is to establish an equation that unveils their equality. We multiply the numerator of the first fraction (a) by the denominator of the second (d), and vice versa, resulting in a/d. This enigmatic dance continues, as we multiply the denominator of the first fraction (b) by the numerator of the second (c), giving us b/c. These two newly formed fractions, a/d and b/c, hold the key to determining whether the original fractions, a/b and c/d, are equal.
In this mathematical tango, the fractions a/b and c/d are like two partners, each taking turns leading and following. By cross-multiplying, we create two new fractions that mirror their movements. If the resulting fractions, a/d and b/c, are equal, then the original fractions, a/b and c/d, share an unbreakable bond of equality. Conversely, if the fractions dance to different tunes, then their equality remains elusive.
How To Cross Multiply Fractions
Cross multiplication is a method used to simplify fractions by multiplying the numerator of one fraction with the denominator of the other fraction, and vice versa. This technique is useful when adding or subtracting fractions with unlike denominators.
To cross multiply fractions, follow these steps:
1. Write the two fractions side by side.
2. Multiply the numerator of the first fraction by the denominator of the second fraction.
3. Multiply the numerator of the second fraction by the denominator of the first fraction.
4. Write the products obtained in step 2 and step 3 as the numerator and denominator of a new fraction.
For example, to cross multiply the fractions 2/3 and 4/5, we have:
2/3 x 4/5 = (2 x 4) / (3 x 5) = 8 / 15
People Also Ask
What is cross multiplication used for?
Cross multiplication is used to simplify fractions when adding or subtracting fractions with unlike denominators.
How do you cross multiply fractions with variables?
To cross multiply fractions with variables, follow the same steps as described in the main article, but use variables instead of numbers.
Is there a calculator that can cross multiply fractions?
Yes, there are many online calculators that can cross multiply fractions. You can search for “fraction calculator” and find several options.
