Properties of fractions
Also known as: fraction rules
The properties of fractions are the basic rules governing how fractions behave: a zero numerator makes the fraction equal zero, a zero denominator is undefined, and multiplying or dividing both parts by the same number produces an equivalent fraction.
A fraction represents division: the numerator (top) divided by the denominator (bottom). The properties of fractions are the handful of rules that follow from that definition, and they underpin nearly every fraction computation on standardized tests.
The zero rules come first. Zero in the numerator is fine — 0/7 equals 0, because zero divided by any nonzero number is zero. Zero in the denominator is undefined — 7/0 has no value, because no number times 0 gives 7. Next, any nonzero number over itself equals 1 (5/5 = 1), and any number over 1 equals itself (5/1 = 5).
Equivalent fractions follow from multiplying or dividing the numerator and denominator by the same nonzero number: 2/3 = 4/6 = 10/15. Dividing out common factors — reducing to lowest terms — reverses the process. Sign rules matter too: a negative in the numerator, the denominator, or out front all mean the same thing, and two negatives cancel. Finally, for positive fractions with the same numerator, the one with the larger denominator is smaller (1/8 < 1/3), since the whole is cut into more pieces.
The ACT tests these properties directly in its pre-algebra questions and indirectly everywhere fractions appear — comparing values, simplifying rational expressions, and spotting undefined expressions. Knowing instantly that 0/n = 0 while n/0 is undefined, and being able to build or reduce equivalent fractions, saves time across the entire math section.
Key takeaways
- A fraction is division: numerator divided by denominator.
- 0 in the numerator gives 0; 0 in the denominator makes the fraction undefined.
- Multiplying or dividing top and bottom by the same nonzero number creates an equivalent fraction.
- With equal positive numerators, a larger denominator means a smaller fraction.
- The ACT tests fraction properties in pre-algebra and throughout the math section.