Cross Multiplication

Definition

Cross multiplication is a technique used to compare and manipulate fractions by establishing a relationship between the numerators and denominators of the fractions. This method is widely applied in various algebraic contexts, such as adding and subtracting fractions, solving equations with fractions or decimals, simplifying rational expressions, and solving proportion and similar figure applications.

5 Must Know Facts For Your Next Test

1. Cross multiplication is used to compare the relative size of fractions by establishing an equality between the products of the numerator and denominator of each fraction.
2. When solving equations with fractions, cross multiplication can be used to eliminate the fractions and solve for the unknown variable.
3. Cross multiplication is a crucial step in simplifying rational expressions by finding a common denominator and then adding or subtracting the fractions.
4. In solving proportion and similar figure applications, cross multiplication is used to find the missing term in the proportion.
5. Cross multiplication is also applied in solving uniform motion and work applications, where the relationship between distance, time, and speed or work, time, and power can be expressed as a proportion.

Review Questions

• Explain how cross multiplication can be used to add and subtract fractions with unlike denominators.
  • To add or subtract fractions with unlike denominators, we can use cross multiplication to find a common denominator. First, we multiply the numerator and denominator of each fraction by the denominators of the other fractions. This creates fractions with a common denominator, which can then be added or subtracted by adding or subtracting the numerators and keeping the common denominator. Cross multiplication ensures that the relative size of the fractions is maintained throughout the process.
• Describe how cross multiplication is used to solve equations with fractions or decimals.
  • When solving equations with fractions or decimals, cross multiplication can be used to eliminate the fractions or decimals and solve for the unknown variable. By multiplying both sides of the equation by the least common multiple of the denominators, the fractions or decimals are removed, and the equation can be solved using standard algebraic techniques. This method ensures that the original relationship between the variables is preserved, allowing for the accurate solution of the equation.
• Analyze the role of cross multiplication in solving proportion and similar figure applications.
  • In proportion and similar figure applications, cross multiplication is used to find the missing term in a proportion. The proportion is set up as an equality between two ratios, and cross multiplication is applied to solve for the unknown value. By multiplying the numerators and denominators of the proportions, an equation is created that can be solved for the missing term. This method is crucial in determining unknown lengths, areas, or volumes in similar figures, as well as in solving various real-world applications involving proportional relationships.

Related terms

Fraction: A fraction is a numerical quantity that represents a part of a whole, expressed as a numerator divided by a denominator.

Proportion: A proportion is a statement of equality between two ratios, where the relationship between the numerators and denominators is maintained.

Rational Expression: A rational expression is a quotient of two polynomial expressions, where the denominator is not allowed to be zero.