CreatorMath.com Geometry Vocabulary 095. Cross multiply -- The first step in solving a proportion.

095. Cross multiply -- The first step in solving a proportion. A proportion is one fraction made equal to another fraction. Since each fraction has a numerator, fraction bar, and a denominator, we now have a numerator, a fraction bar, and a denominator on one side of an equals sign with another numerator, a fraction bar, and a denominator on the other side of the equals sign. Here is an example of a proportion: 3/5 = 6/10. The proportion equation becomes solvable if one of the values is unknown as in x/5=6/10 or x/5=3/5. It is a little difficult to see the cross-multiplying in this format, but the numerator of the first fraction is multiplied by the denominator of the second and put equal to the denominator of the first fraction multiplied by the numerator of the second. If the two fractions were written and that description circled on the fractions, teachers say it looks like a cross as in the name “cross-multiply.” In all fairness, it really looks like an “x.” I often tell my students that cross multiplying should be called “x-multiplying.” But “x” is the most famous variable and for some unknown reason, we use “x” to mean multiplication in elementary school (and then teach students not to use an “x” after reaching algebra in the 6th or 7th grade). Back to our example, x/5=3/5, cross-multiplied is 5x=(3)(5) or 5x=15. With both sides divided by 5, we have x=3. I often get fed up with the “cross multiply” method and just revert to good-old equation-solving. It’s a little slower, but consistent with all equation-solving teaching. Given x/5=3/5, we would multiply both sides by 5 to “isolate the x.” We’d get (5)x/5=3(5)/5. After simplifying, the 5’s cancel on the left leaving x and the 5’s cancel on the right leaving 3, so x=3. To cross multiply, when solving a proportion, is to multiply the numerator of the first fraction by the denominator of the second fraction and then place it equal to the denominator of the first fraction multiplied by the numerator of the second fraction. Related Words: similar, proportion, proportional.

Cross multiply
The first step in solving a proportion
More than one
A fraction equal to a fraction

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