Between
Elementary SchoolMiddle School
Definition
When you have a line with endpoints X and Z, a point Y is between points X and Z if it is on the XZ line segment. The idea of a number being between two other numbers is used in Euclid's proofs.
Worked examples
\(X\)———\(Y\)———\(Z\)
Point \(Y\) is between \(X\) and \(Z\) because it lies on segment \(XZ\).
\(5\) is between \(2\) and \(9\) because \(2 < 5 < 9\)
On the number line, a number is between two others when it falls strictly inside their interval.
Common mistakes
- Point \(Y\) is between \(X\) and \(Z\) if it is anywhere near the line → Point \(Y\) must lie exactly on segment \(XZ\) Being 'between' requires the point to be on the line segment itself, not just close to it.
- \(3\) is between \(3\) and \(7\) → \(3\) is an endpoint, not between \(3\) and \(7\) 'Between' means strictly inside the interval; endpoints are not between themselves and another point.
- If \(Y\) is between \(X\) and \(Z\), then \(XY + YZ \ne XZ\) → If \(Y\) is between \(X\) and \(Z\), then \(XY + YZ = XZ\) A point between two others divides the segment so the sum of the parts equals the whole (segment addition postulate).
Where you'll use it next
The between concept is foundational for segment addition, midpoint formulas, and inequality proofs in geometry. You'll also use it in algebra when solving compound inequalities and analyzing intervals on the number line.
Found in 1 StudyPug lesson
Comparing and ordering rational numbers
9th Grade9thGrade 9 Math
A rational number is a number that can be written as a fraction. In order to be called a rational number, the numerator and denominators of the fraction must be whole numbers. In this lesson, we will compare different rational numbers and sort out their order.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026