Fractions
Fractions represent parts of a whole using a numerator over a denominator separated by a fraction bar. In Grade 6 Saxon Math Course 1, the denominator shows the total number of equal parts the whole is divided into, while the numerator shows how many of those parts are being described. If 17 out of 25 seats on a bus are filled, the fraction of filled seats is 17/25. A solid grasp of what numerator and denominator each mean is the foundation for every fraction operation in middle school mathematics.
Key Concepts
Property A common fraction is written with two numbers and a fraction bar. The “bottom” number is the denominator, showing the number of equal parts in the whole. The “top” number, the numerator, shows the number of parts being represented.
Examples A circle with one of six equal parts shaded is represented by the fraction $\frac{1}{6}$.
If four out of five friends in a group are wearing hats, that's $\frac{4}{5}$ of the group.
Common Questions
What does the denominator of a fraction represent?
The total number of equal parts the whole has been divided into.
What does the numerator of a fraction represent?
How many of those equal parts are being counted or described.
A pizza has 8 slices and 3 are eaten. What fraction is left?
5 slices remain out of 8 total: 5/8.
What is the difference between a proper and improper fraction?
In a proper fraction, numerator < denominator (e.g., 3/4). In an improper fraction, numerator ≥ denominator (e.g., 7/4).
How do you write '7 out of 12' as a fraction?
Numerator = 7, denominator = 12: the fraction is 7/12.