Mathematics
Grade 6
15 min
Order fractions with like numerators or denominators
Order fractions with like numerators or denominators
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1
Introduction & Learning Objectives
Learning Objectives
Identify fractions with like numerators and like denominators.
Compare two fractions with like denominators using inequality symbols (<, >, =).
Compare two fractions with like numerators using inequality symbols (<, >, =).
Order a set of three or more fractions with like denominators from least to greatest or greatest to least.
Order a set of three or more fractions with like numerators from least to greatest or greatest to least.
Explain the reasoning behind ordering fractions with like numerators or denominators.
Ever wondered who got a bigger slice of pizza if one friend ate 3/8 and another ate 5/8? 🍕 Let's find out how to compare fractions easily!
In this lesson, you'll learn simple rules to compare and order fractions that sha...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole, written as a numerator over a denominator.In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator.
NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In $\frac{5}{8}$, the numerator is 5, meaning we are looking at 5 out of 8 equal parts.
DenominatorThe bottom number in a fraction, indicating the total number of equal parts the whole is divided into.In $\frac{5}{8}$, the denominator is 8, meaning the whole is divided into 8 equal parts.
Like DenominatorsFractions that have the same denominator.$\frac{1}{5}$, $\frac{3}{5}$, and $\frac{4}{5}$ all have like denominators (5).
Like NumeratorsFractions that have the same numerator.$\frac{2}{3}$, $\frac{2}{7...
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Core Formulas
Rule for Comparing Fractions with Like Denominators
For fractions $\frac{a}{c}$ and $\frac{b}{c}$ where $c \neq 0$, if $a > b$, then $\frac{a}{c} > \frac{b}{c}$. If $a < b$, then $\frac{a}{c} < \frac{b}{c}$.
When fractions share the same denominator, it means the whole is divided into the same number of equal parts. Therefore, the fraction with the larger numerator represents a greater quantity because it includes more of those equal parts.
Rule for Comparing Fractions with Like Numerators
For fractions $\frac{a}{b}$ and $\frac{a}{c}$ where $a \neq 0$, if $b < c$, then $\frac{a}{b} > \frac{a}{c}$. If $b > c$, then $\frac{a}{b} < \frac{a}{c}$.
When fractions share the same numerator, it means you are considering the same number of parts. The fraction w...
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Challenging
If 12/n < 12/15, which of the following MUST be true about the whole number n?
A.n is greater than 15.
B.n is less than 15.
C.n is equal to 15.
D.n can be any number.
Challenging
Four fractions are ordered from least to greatest: F1, F2, F3, F4. All four fractions have a numerator of 5. The denominators are 6, 9, 11, and 15. What is fraction F4?
A.5/6
B.5/9
C.5/11
D.5/15
Challenging
Given the statement: 'For fractions with like numerators, the fraction with the smaller denominator is the larger fraction.' Which of the following scenarios provides the best real-world explanation for this rule?
A.Sharing 3 identical pizzas among 5 people means each person gets a larger share (3/5) than if you share the same 3 pizzas among 8 people (3/8).
B.Eating 3 slices of a pizza cut into 8 slices means you ate less than someone who ate 5 slices of the same pizza.
C.If you have 5 dollars and your friend has 8 dollars, your friend has more money.
D.race that is 3/4 of a mile long is shorter than a race that is 7/8 of a mile long.
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