One of my students, Bonnie, was having trouble knowing how to deal with a fraction that needs to be distributed, such as 1/2(x + 10) = 20. She wasn't sure what to do with the fraction or how to solve the problem in the simplest way possible.
I encouraged her to treat the fraction like any other number. She could either distribute the fraction, or she could use division to immediately remove the fraction.
She wasn't sure how to do this at first, so I asked her to consider what she would do to "get rid of" a whole number such as 2 in an equation like 2x = 12. She suggested that she would divide both sides by two.
I suggested she apply this principle to the fraction in the first equation. If she divides both sides by 1/2, she will easily be able to solve for x. She seemed unsure of how to do this at first, so I encouraged her to explore the idea: to try it and see what happened. She canceled the halves on the left side of the equation, and then tried plugging 20 divided by 1/2 into her calculator. This enabled her to solve the problem she was working on.
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