What you’ll learn
Compare rational numbers.
Key idea
Equivalent fractions multiply numerator and denominator by the same factor.
Scale the numerator and denominator together; compare signed numerators only after a positive common denominator is established.
Worked example
Classify examples and non-examples for the concept 'Compare rational numbers'.
Is -9/9 < -8/10 a valid comparison on the number line? Classify using equivalent fractions with a common denominator.
- Convert both fractions to denominator 90, keeping their signs.
- Compare scaled numerators -90 and -72; the direction is <.
Answer: Valid — -9/9=-90/90 and -8/10=-72/90, giving -9/9 < -8/10.
Quick Check
Classify examples and non-examples for the concept 'Compare rational numbers'.
Is -9/2 < -4/3 a valid comparison on the number line? Classify using equivalent fractions with a common denominator.