Mathematics
Grade 9
15 min
Compare fractions and mixed numbers
Compare fractions and mixed numbers
What you'll learn
- Apply geometric tools (compass and straightedge) to accurately construct a congruent angle to a given angle with 100% accuracy on a written assessment.
- Explain the geometric principles (e.g., properties of circles and radii) that justify the steps in constructing a congruent angle, using precise mathematical vocabulary, in a written explanation graded with a rubric assessing clarity and completeness.
- Identify and correct errors in incorrectly constructed congruent angles, providing a written justification for each correction with 90% accuracy.
- Compare and contrast different methods of constructing congruent angles, evaluating their efficiency and accuracy in a small group discussion, as assessed by a participation rubric.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Convert mixed numbers to improper fractions and vice versa to facilitate comparison.
Determine the least common denominator (LCD) for a set of fractions.
Compare fractions and mixed numbers by creating equivalent fractions with a common denominator.
Apply the cross-multiplication method as an efficient strategy to compare two fractions.
Order a set of rational numbers, including fractions and mixed numbers, from least to greatest or greatest to least.
Analyze and solve word problems that require the comparison of fractional quantities.
Which is a better deal: half of a pizza for $8, or 3/8 of the same pizza for $6? 🍕 Knowing how to compare fractions is key to making smart decisions!
This tutorial will strengthen your foundational skills in comparing fra...
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 category includes all fractions, mixed numbers, integers, and terminating or repeating decimals.The number 2 3/4 is a rational number because it can be written as the fraction 11/4.
Mixed NumberA number composed of a whole number and a proper fraction.4 1/2, which represents four whole units and one half of another unit.
Improper FractionA fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). Its value is always 1 or greater.9/4, which is the improper fraction equivalent of 2 1/4.
Equivalent FractionsFractions that represent the same numerical value, despite having different numerators and denom...
3
Core Formulas
Converting a Mixed Number to an Improper Fraction
a \frac{b}{c} = \frac{(a \times c) + b}{c}
To convert a mixed number into an improper fraction, multiply the whole number by the denominator, add the numerator, and place this new value over the original denominator. This form is necessary for most algebraic manipulations.
Comparison with a Common Denominator
Given \frac{a}{c} and \frac{b}{c}, if a > b, then \frac{a}{c} > \frac{b}{c}.
When two fractions share the same denominator, the fraction with the larger numerator represents a greater value. The core strategy for comparing fractions is to rewrite them as equivalent fractions with a common denominator.
The Cross-Multiplication Property
To compare \frac{a}{b} and \frac{c}{d} (where b, d > 0), compare the pro...
4 more steps in this tutorial
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Challenging
A student incorrectly reasons that 5/7 > 6/11 because '5 is closer to 7 than 6 is to 11'. This is an example of which common pitfall?
A.Incorrect mixed number conversion.
B.Mixing up cross-multiplication products.
C.Comparing numerators and denominators separately.
D.Forgetting to answer with the original numbers.
Challenging
Three cookie recipes require different amounts of sugar. Recipe A needs 2 1/2 cups, Recipe B needs 11/4 cups, and Recipe C needs 2 2/3 cups. If you want to make the recipe that uses the most sugar, which one should you choose?
A.Recipe A
B.Recipe B
C.Recipe C
D.Recipes A and C use the same amount.
Challenging
Compare the mixed numbers 4 5/8, 4 3/5, and 4 2/3. Which one is the largest?
A.4 5/8
B.4 3/5
C.4 2/3
D.They are all equal.
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Frequently asked questions
What grade level is "Compare fractions and mixed numbers"?
Compare fractions and mixed numbers is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Compare fractions and mixed numbers?
You'll be able to: Apply geometric tools (compass and straightedge) to accurately construct a congruent angle to a given angle with 100% accuracy on a written assessment; Explain the geometric principles (e.g., properties of circles and radii)….
Is "Compare fractions and mixed numbers" 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 Compare fractions and mixed numbers?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.