Solving proportions by multiplying or flipping

Equations involving proportions are solved using the properties of proportions. When you cross-multiply, you get rid of the fraction format, which gives you an equation that is usually simpler to deal with. Also, if you flip the proportion, you make the problem more to your liking — easier to solve. 

You can solve for the value of x in the proportion g = y by cross-multiplying and getting rid of the fractional format. 

Even though cross-multiplying is a great tool to use when solving proportions, you can often take an easier route Flip the fractions (set the reciprocals equal to one another) and then multiply each side by the same number to solve the equation. For example, in the following equation, I flip the proportion and then just have to multiply each side by the number under the x, reduce, and get the answer. 

Proportions are created from fractions, and the traditional way of reducing fractions is to find a number that divides the numerator and denominator evenly and divide each part of the fraction by that number. Reducing fractions is sometimes referred to as cancelling. In the following proportion, the numbers in the fraction on the left are each divisible by 5. After reducing the fraction on the left, you can cross-multiply and solve the equation for x. 

You could also have reduced horizontally in this equation, because 8 and 16 are both divisible by 8. The next section shows you how that works. 

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