if ax + b /CX + d = p/q then q (ax + b) = p (CX + d). this process is called ??
The Correct Answer and Explanation is:
The correct answer is: Cross multiplication
Explanation:
Cross multiplication is a mathematical technique used to solve equations involving two fractions set equal to each other. It is especially useful when solving rational equations or proportions.
In the given expression:ax+bCx+d=pq\frac{ax + b}{Cx + d} = \frac{p}{q}Cx+dax+b=qp
we are equating two rational expressions. To eliminate the denominators and simplify the equation, we use cross multiplication, which involves multiplying the numerator of one side by the denominator of the other side and setting the products equal to each other. This gives:q(ax+b)=p(Cx+d)q(ax + b) = p(Cx + d)q(ax+b)=p(Cx+d)
This equation no longer contains fractions and can be solved using standard algebraic steps. The reason cross multiplication works is based on the property of proportions. If two fractions are equal, then the cross products are also equal. This is derived from multiplying both sides of the original equation by the product of the two denominators:(Cx+d)(q)⋅ax+bCx+d=(Cx+d)(q)⋅pq(Cx + d)(q) \cdot \frac{ax + b}{Cx + d} = (Cx + d)(q) \cdot \frac{p}{q}(Cx+d)(q)⋅Cx+dax+b=(Cx+d)(q)⋅qp
On the left-hand side, the denominator Cx+dCx + dCx+d cancels out, leaving q(ax+b)q(ax + b)q(ax+b). On the right-hand side, the qqq cancels out, leaving p(Cx+d)p(Cx + d)p(Cx+d). So we get:q(ax+b)=p(Cx+d)q(ax + b) = p(Cx + d)q(ax+b)=p(Cx+d)
This step makes it easier to work with the equation since the fractions are eliminated. Cross multiplication is commonly taught in algebra as a reliable way to handle equations involving proportions or rational expressions. It simplifies the problem and leads to a linear or quadratic equation that can be solved using normal algebraic rules.
