10. GED® Fraction Strategy: Diagnose, Solve, Check

A student fully understands fractions when they can explain why the method works, not only get the answer.

Use this diagnostic checklist:

• Is this a part of one whole, several wholes, or a comparison?
• Are the pieces equal size?
• Do I need a common denominator?
• Does the phrase "of" mean multiplication?
• Does division mean "how many groups fit?"
• Should the final answer be less than 1, equal to 1, or more than 1?

Before solving, estimate. Example:
\[ \frac{7}{8}+\frac{1}{5} \]
is a little more than 1 because \(\frac{7}{8}\) is close to 1 and \(\frac{1}{5}\) adds a small amount. Exact work:
\[ \frac{7}{8}+\frac{1}{5}=\frac{35}{40}+\frac{8}{40}=\frac{43}{40}=1\frac{3}{40}. \]
The exact answer matches the estimate.

Error analysis example: A student says
\[ \frac{1}{2}+\frac{1}{3}=\frac{2}{5}. \]
The mistake is adding denominators. Correct solution:
\[ \frac{1}{2}=\frac{3}{6},\quad \frac{1}{3}=\frac{2}{6},\quad \frac{3}{6}+\frac{2}{6}=\frac{5}{6}. \]

Final mastery habit: after every missed fraction problem, write one sentence: "The clue was ___, so the operation should have been ___." That builds transfer to GED® word problems.