Mathematics
Grade 10
15 min
Graph and compare fractions on number lines
Graph and compare fractions on number lines
What you'll learn
- Identify angle bisectors within geometric figures (triangles and quadrilaterals) and accurately label congruent angles formed by the bisector, achieving 80% accuracy on a formative assessment.
- Apply the Angle Bisector Theorem to solve for unknown side lengths and angle measures in triangles, demonstrating proficiency by correctly solving at least 3 out of 4 application problems on a problem set.
- Solve construction problems using a compass and straightedge to accurately bisect angles, as evidenced by a correctly bisected angle within a tolerance of ±2 degrees on a practical construction task.
- Explain the relationship between angle bisectors and the incenter of a triangle, and justify how the incenter is equidistant from the sides of the triangle, in a written explanation assessed using a rubric.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Accurately plot positive and negative proper fractions, improper fractions, and mixed numbers on a number line.
Subdivide a number line into any number of equal parts to represent fractions with various denominators.
Convert between improper fractions and mixed numbers to facilitate graphing.
Compare the magnitudes of two or more fractions by analyzing their positions on a number line.
Use a number line to visually prove inequalities involving rational numbers (e.g., show why -3/4 > -5/6).
Apply the concept of number line placement to order a set of complex fractions from least to greatest.
Determine the distance between two fractions on a number line.
Ever wondered how a GPS pinpoints a location between two streets? It's all about placing a poi...
2
Key Concepts & Vocabulary
TermDefinitionExample
Rational NumberAny number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. This includes all integers, terminating decimals, and repeating decimals.-7/3, 5, 0.25 (which is 1/4)
Number LineA horizontal line on which numbers are marked at equal intervals, used to illustrate the ordering and magnitude of numbers. Numbers increase from left to right.A line with 0 in the center, negative integers to the left, and positive integers to the right.
Proper FractionA fraction where the absolute value of the numerator is smaller than the absolute value of the denominator, representing a value between -1 and 1.4/5 or -2/3
Improper FractionA fraction where the absolute value of the numerator is greater than or equal to the absolute value of th...
3
Core Formulas
Converting Improper Fraction to Mixed Number
\frac{a}{b} = q \frac{r}{b}
Use division to find the whole number part (q, the quotient of a ÷ b) and the new fractional part (r/b, where r is the remainder). This is essential for accurately placing improper fractions on a number line.
Finding a Common Denominator
For fractions \frac{a}{b} and \frac{c}{d}, a common denominator is b \cdot d. The equivalent fractions are \frac{a \cdot d}{b \cdot d} and \frac{c \cdot b}{b \cdot d}.
To accurately compare or subdivide a number line for different fractions, you must express them with the same denominator. Using the least common multiple (LCM) of the denominators is most efficient.
Comparing Fractions (Cross-Multiplication)
To compare \frac{a}{b} and \frac{c}{d} (where b,d > 0)...
4 more steps in this tutorial
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Challenging
Arrange the following rational numbers from least to greatest: 5/2, -8/3, 13/5, -2.7.
A.-8/3, -2.7, 5/2, 13/5
B.-2.7, -8/3, 5/2, 13/5
C.-2.7, -8/3, 13/5, 5/2
D.-8/3, -2.7, 13/5, 5/2
Challenging
The value of Stock A changed by -3/8 of a dollar, and the value of Stock B changed by -2/5 of a dollar. By plotting these values on a number line, determine which stock had the greater financial loss.
A.Stock A, because -3/8 is to the right of -2/5.
B.Stock A, because 3/8 is a smaller fraction than 2/5.
C.Stock B, because -2/5 is closer to zero.
D.Stock B, because -2/5 is further to the left on the number line.
Challenging
Point P is at -3/4 on a number line. The distance between point P and point Q is exactly 5/6. Which of the following is a possible location for point Q?
A.1/12
B.-1/12
C.-3/5
D.2/10
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What grade level is "Graph and compare fractions on number lines"?
Graph and compare fractions on number lines is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Graph and compare fractions on number lines?
You'll be able to: Identify angle bisectors within geometric figures (triangles and quadrilaterals) and accurately label congruent angles formed by the bisector, achieving 80% accuracy on a formative assessment; Apply the Angle Bisector Theorem to….
Is "Graph and compare fractions on number lines" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Graph and compare fractions on number lines?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.