📚 Practice With Worksheets
Strengthen number-line reasoning, integer placement, and fraction comparison with these related practice pages.
▶️ Learn With Videos
Connect fraction and integer locations to comparison, inequality, temperature, and movement on a number line.
🛠️ How to Use This Tool
Choose the fractional unit that will determine the spacing between tick marks and the size of each movement step.
Choose the visible number-line range, select Apply Settings, and then use the red and green buttons to move left or right by one or more fractional units.
Watch the point, jump arrow, current-position display, and equation to connect each movement with its fraction, mixed-number, or whole-number result.
🧠 Things to Notice
A larger denominator divides each whole into more equal parts, so the distance between consecutive fractional tick marks becomes smaller.
Moving right increases the value, while moving left decreases it. Values to the left of zero are negative, and values to the right are positive.
Improper fractions and mixed numbers name locations beyond one whole, and equivalent fractions occupy the same location even when their numerators and denominators differ.
📘 Vocabulary
Number line: A line on which numbers are placed in order according to their value.
Unit fraction: A fraction with a numerator of 1 that represents one equal part of a whole.
Denominator: The number below the fraction bar that tells how many equal parts make one whole.
Improper fraction: A fraction whose numerator is greater than or equal to its denominator.
Mixed number: A number written with a whole-number part and a proper-fraction part.
Equivalent fractions: Fractions that use different numerators and denominators but represent the same value and location.
📐 Fraction Movement on a Number Line
When each whole is divided into \(d\) equal parts, one tick-mark step has a value of \(\frac{1}{d}\). Moving \(k\) steps changes the position by \(\frac{k}{d}\).
\(x_{\text{new}}=x_{\text{start}}+\frac{k}{d}\)
Use a positive change to move right and a negative change to move left. The distance depends on the absolute value of the change, while the sign determines the direction.
\(x+\frac{k}{d}\text{ moves right, while }x-\frac{k}{d}\text{ moves left.}\)
Equivalent fractions represent the same point because multiplying the numerator and denominator by the same nonzero number does not change the fraction's value: \(\frac{a}{b}=\frac{ka}{kb}\).
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