How is the common numerator strategy applied to compare $4/9$ and $8/17$?

Conditions

• Comparing two positive proper or improper fractions
• One numerator is a multiple of the other

Reasoning, step by step

1. Identify the least common multiple of the numerators (LCM of 4 and 8 is 8).
2. Scale up the fraction with the smaller numerator: multiply $4/9$ by $2/2$ to get $8/18$.
3. Keep the other fraction unchanged if its numerator already matches the LCM: $8/17$ stays as is.
4. Compare the denominators: since $17 < 18$, the unit size in $8/17$ is larger than in $8/18$.
5. Conclude that $8/17 > 8/18$, therefore $8/17 > 4/9$.

Example

The script states: 'We multiply four ninths by two halves, which gives us eighteen eighths... Hence $8/17>8/18=4/9$.'

Common misconceptions

• Assuming that a larger denominator always means a larger total value for the fraction.
• Forgetting to scale both the numerator and denominator simultaneously when creating equivalent fractions.

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Explore next

• When is the common numerator method more efficient than cross-multiplication?
• How does this logic apply if one numerator is negative?