key term - Cross-Multiplication

Definition

Cross-multiplication is a technique used to compare the relative size of fractions or to solve for an unknown value in a proportion. It involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa, to determine the relationship between the fractions.

5 Must Know Facts For Your Next Test

1. Cross-multiplication is used to compare the relative size of fractions by determining if they are equivalent.
2. The cross-multiplication algorithm states that if a/b = c/d, then ad = bc.
3. Cross-multiplication can be used to solve for an unknown value in a proportion by rearranging the equation.
4. In the context of adding and subtracting fractions, cross-multiplication is used to find a common denominator.
5. When simplifying complex rational expressions, cross-multiplication is used to identify common factors in the numerator and denominator.

Review Questions

• Explain how cross-multiplication can be used to compare the relative size of fractions.
  • Cross-multiplication is a technique used to compare the relative size of fractions by determining if they are equivalent. If two fractions, a/b and c/d, are equal, then the cross-products (ad and bc) will also be equal. By comparing the cross-products, you can determine if the fractions are equivalent, and therefore the same size, or if one fraction is larger or smaller than the other.
• Describe how cross-multiplication can be used to solve for an unknown value in a proportion.
  • Cross-multiplication can be used to solve for an unknown value in a proportion by rearranging the equation. If the proportion is written in the form a/b = c/d, then the cross-multiplication algorithm states that ad = bc. By isolating the unknown value, you can solve for it using this relationship. For example, if you have the proportion 3/x = 5/7, you can cross-multiply to get 3 * 7 = x * 5, and then solve for x.
• Analyze the role of cross-multiplication in the context of adding and subtracting fractions with unlike denominators.
  • When adding or subtracting fractions with unlike denominators, cross-multiplication is used to find a common denominator. By cross-multiplying the numerators and denominators of the fractions, you can determine the least common multiple of the denominators, which becomes the common denominator. This allows you to rewrite the fractions with the same denominator, making it possible to perform the addition or subtraction operation. Cross-multiplication is a crucial step in the process of finding a common denominator and simplifying fractions with unlike denominators.

Related terms

Proportion:

A proportion is an equation that states that two ratios are equal, often written in the form a/b = c/d.

Equivalent Fractions:

Equivalent fractions are fractions that represent the same value, such as 1/2 and 2/4.

Rational Expressions:

Rational expressions are algebraic expressions that can be written as a fraction, with a polynomial in the numerator and a non-zero polynomial in the denominator.