Conversion Strategy 1: Use a Proportion

Recall from the previous Lesson that you determined two fractions that were equal - a proportion - and solved for an unknown when using this strategy.

 

Example 2

    How many pounds are there in 12 tons?

    The conversion ratio for pounds and tons is 2000 lbs = 1 ton, which can also be written as «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#B94A48¨»«mrow»«mn»2000«/mn»«mo»§#160;«/mo»«mi»lbs«/mi»«/mrow»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mi»ton«/mi»«/mrow»«/mfrac»«mo mathcolor=¨#B94A48¨»=«/mo»«mn mathcolor=¨#B94A48¨»1«/mn»«/math» or «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#B94A48¨»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mi»ton«/mi»«/mrow»«mrow»«mn»2000«/mn»«mo»§#160;«/mo»«mi»lbs«/mi»«/mrow»«/mfrac»«mo mathcolor=¨#B94A48¨»=«/mo»«mn mathcolor=¨#B94A48¨»1«/mn»«/math».

    Letting x represent the unknown number of pounds gives the equation x lbs = 12 ton, which can be rewritten as . You now have multiple expressions that are equal to 1, so they must be equal to each other. Choose the conversion ratio format that has the same unit location as the expression with the variable.

    Now solve the equation to determine the value of x.

    There are 24 000 pounds in 12 tons.