91Ó°ÊÓ

Cross multiplication is a method used to solve proportions. In a proportion, you have two fractions set equal to each other, like this: \(\frac{a}{b} = \frac{c}{d} \). The idea behind cross multiplication is to remove the fractions by multiplying the numerators and denominators across the equal sign.Let's look at an example: \(\frac{7}{a} = \frac{-6}{84} \)To perform cross multiplication, follow these steps:

• Multiply the numerator of the first fraction by the denominator of the second fraction.
• Multiply the numerator of the second fraction by the denominator of the first fraction.

In our example, we multiply 7 (numerator of the first fraction) by 84 (denominator of the second fraction), and \(-6 \) (numerator of the second fraction) by \(a\) (denominator of the first fraction):\[7 \times 84 = -6 \times a \] This gives us the equation:\[588 = -6a\] Now, we've successfully removed the fractions and can move on to the next step.

Isolating the variable means making the variable the subject of the equation. In order to find the value of a variable, we need to get it alone on one side of the equation.In the equation from the previous step:\[588 = -6a\] We want to isolate \(a\). To do this, we need to get rid of the \(-6 \) that is multiplying \(a\). We achieve this by dividing both sides of the equation by \(-6\):\[a = \frac{588}{-6}\] This step isolates \(a\) on one side of the equation and tells us that \(a \) is equal to \(\frac{588}{-6} \).

Simplifying fractions involves reducing a fraction to its simplest form, where the numerator and denominator are as small as possible.In our example, we have:\[a = \frac{588}{-6}\] To simplify this fraction, we perform the division. Dividing 588 by \(-6\) gives us:\[a = -98\] Therefore, the value of \(a \) is \(-98\). Simplifying fractions as part of solving proportions helps you find the most straightforward answer.