Improper Fractions Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Identify whether each fraction is proper or improper, and explain: 37\frac{3}{7}, 99\frac{9}{9}, 115\frac{11}{5}.

Solution

  1. 1
    37\frac{3}{7}: numerator 3<3 < denominator 77 ⇒\Rightarrow proper fraction (value less than 1).
  2. 2
    99\frac{9}{9}: numerator == denominator ⇒\Rightarrow improper fraction (value equals 1).
  3. 3
    115\frac{11}{5}: numerator 11>11 > denominator 55 ⇒\Rightarrow improper fraction (value greater than 1, specifically 2152\frac{1}{5}).

Answer

37 proper; 99 improper (=1); 115 improper (=215)\frac{3}{7} \text{ proper};\ \frac{9}{9} \text{ improper (}=1\text{)};\ \frac{11}{5} \text{ improper (}=2\tfrac{1}{5}\text{)}
A fraction is improper when its numerator is greater than or equal to its denominator, meaning its value is at least 1. Proper fractions have value strictly between 0 and 1.

About Improper Fractions

A fraction where the numerator is greater than or equal to the denominator, representing a value of one or more.

Learn more about Improper Fractions →

More Improper Fractions Examples

Example 2 medium

You have [formula] quarter-slices of pizza ([formula] each). Write this as an improper fraction and

Example 3 easy

Write [formula] as a mixed number.

Example 4 medium

Multiply [formula] and give the answer as both an improper fraction and a mixed number.

Example 5 medium

Convert [formula] to a mixed number, then convert [formula] to an improper fraction.

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