Cross multiplication provides a quick way to compare two fractions by creating equivalent fractions with a common denominator. Here's how it works:
Steps for Comparing Fractions Using Cross Multiplication
- Identify the two fractions you want to compare (e.g., a/b and c/d).
- Cross multiply the fractions. This means multiplying the numerator of the first fraction by the denominator of the second fraction (a d), and multiplying the numerator of the second fraction by the denominator of the first fraction (c b).
- Compare the results. The fraction corresponding to the larger product is the larger fraction.
Example
Let's compare 3/2 and 5/4 using cross multiplication.
- Fractions: 3/2 and 5/4
- Cross multiply:
- 3 * 4 = 12
- 5 * 2 = 10
- Compare: Since 12 is greater than 10, 3/2 is greater than 5/4. This is equivalent to converting the fractions to have a common denominator. In this case the common denominator is 8, thus 3/2 becomes 12/8 and 5/4 becomes 10/8. Since 12 is a greater numerator, 12/8 > 10/8.
Summary Table
| Fraction 1 | Fraction 2 | Cross Multiplication | Comparison | Result |
|---|---|---|---|---|
| a/b | c/d | a*d, c*b | a*d > c*b | a/b > c/d |
| a/b | c/d | a*d, c*b | a*d < c*b | a/b < c/d |
| a/b | c/d | a*d, c*b | a*d = c*b | a/b = c/d |
