Mathematics
Grade 9
15 min
Compare fractions and mixed numbers
Compare fractions and mixed numbers
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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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