Mathematics
Grade 10
15 min
Put fractions in order
Put fractions in order
What you'll learn
- Identify and state the geometric postulates and theorems (e.g., Vertical Angle Theorem, Linear Pair Postulate, Angle Addition Postulate) that justify steps in angle proof problems with 80% accuracy on a formative assessment.
- Solve multi-step algebraic equations derived from angle relationships (e.g., complementary angles, supplementary angles, angles formed by parallel lines and a transversal) to determine unknown angle measures with 75% accuracy on a problem set.
- Explain the logical reasoning behind each step in a two-column proof involving angle relationships, demonstrating understanding by correctly completing at least 3 out of 4 assigned proofs.
- Apply the properties of parallel lines cut by a transversal (e.g., corresponding angles, alternate interior angles, same-side interior angles) to construct and justify angle relationships in geometric diagrams, achieving a score of at least 80% on a related quiz.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Order sets of positive and negative rational fractions using the Least Common Denominator (LCD) method.
Efficiently compare any two fractions using the cross-multiplication technique.
Convert various fractions to their decimal equivalents for comparison and ordering.
Order fractions that include irrational numbers, such as π or √2, by using appropriate approximations.
Substitute values into algebraic fractions to compare their magnitudes.
Analyze a given set of fractions and select the most efficient ordering strategy.
Which is a better deal: getting 3/4 of a pizza for $10 or 4/5 of a pizza for $11? 🍕 Let's figure out how to compare these values precisely!
This tutorial will equip you with advanced strategies for ordering any set of fractions, incl...
2
Key Concepts & Vocabulary
TermDefinitionExample
Least Common Denominator (LCD)The smallest positive integer that is a multiple of the denominators of a given set of fractions. It's also known as the Least Common Multiple (LCM) of the denominators.For the fractions 1/6 and 3/8, the denominators are 6 and 8. The multiples of 6 are 6, 12, 18, 24... and the multiples of 8 are 8, 16, 24... The LCD is 24.
Equivalent FractionsFractions that represent the same value, even though they may have different numerators and denominators. They are created by multiplying or dividing the numerator and denominator by the same non-zero number.3/5 is equivalent to 6/10 because both the numerator and denominator were multiplied by 2. Both equal 0.6.
Improper FractionA fraction where the absolute value of the numerator is greater t...
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Core Formulas
Least Common Denominator (LCD) Method
To compare \( \frac{a}{b} \) and \( \frac{c}{d} \), find the LCD. Convert each fraction to an equivalent fraction with the LCD. Then, compare the new numerators.
This is the most reliable method for ordering three or more fractions. Once all fractions share the same denominator, the one with the largest numerator is the largest fraction (for positive fractions).
Cross-Multiplication Rule
To compare \( \frac{a}{b} \) and \( \frac{c}{d} \) (for b, d > 0): If \( a \cdot d > b \cdot c \), then \( \frac{a}{b} > \frac{c}{d} \). If \( a \cdot d < b \cdot c \), then \( \frac{a}{b} < \frac{c}{d} \).
This is a quick and powerful shortcut for comparing exactly two fractions. Be cautious when negative numbers are involved, as the ineq...
4 more steps in this tutorial
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Challenging
For any positive integer x, what is the correct order from least to greatest for the fractions: A = (x+1)/x, B = x/(x+1), and C = (x+2)/(x+1)?
A.B, C, A
B.C, B, A
C.A, C, B
D.B, A, C
Challenging
Arrange the fractions 5/6, 7/9, 11/15, and 13/18 from least to greatest.
A.11/15, 13/18, 5/6, 7/9
B.13/18, 11/15, 7/9, 5/6
C.13/18, 7/9, 11/15, 5/6
D.5/6, 7/9, 11/15, 13/18
Challenging
For which of the following positive integer values of 'n' is the algebraic fraction (n+3)/(2n-1) greater than 1?
A.n = 5
B.n = 4
C.n = 3
D.n = 6
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Frequently asked questions
What grade level is "Put fractions in order"?
Put fractions in order is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Put fractions in order?
You'll be able to: Identify and state the geometric postulates and theorems (e.g., Vertical Angle Theorem, Linear Pair Postulate, Angle Addition Postulate) that justify steps in angle proof problems with 80% accuracy on a formative assessment….
Is "Put fractions in order" 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 Put fractions in order?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.