Mathematics
Grade 10
15 min
Graph and compare fractions on number lines
Graph and compare fractions on number lines
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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 รท 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)...
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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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