Mathematics
Grade 3
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 the numerator and denominator in a fraction.
Compare two fractions that have the same denominator.
By the end of of this lesson, students will be able to compare two fractions that have the same numerator.
Order a set of three or more fractions with like denominators from least to greatest.
Order a set of three or more fractions with like numerators from least to greatest.
Use the comparison symbols < (less than), > (greater than), and = (equal to) correctly with fractions.
If two friends each get 1 piece of cake, but one cake is cut into 4 slices and the other is cut into 8, who gets the bigger piece? 🎂 Let's find out!
In this lesson, we will learn how to compare and order fractions. Knowing how to tell which fraction is bigger is a...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that shows a part of a whole. The whole must be split into equal parts.The fraction 1/4 means we have one part out of four equal parts.
NumeratorThe top number in a fraction. It tells you how many equal parts you have.In the fraction 3/5, the numerator is 3. This means we have 3 parts.
DenominatorThe bottom number in a fraction. It tells you how many equal parts the whole is divided into.In the fraction 3/5, the denominator is 5. This means the whole was cut into 5 equal pieces.
Like DenominatorsWhen two or more fractions have the same bottom number. This means the pieces are all the same size.1/8, 3/8, and 7/8 all have like denominators.
Like NumeratorsWhen two or more fractions have the same top number. This means you have the same number of pieces...
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Core Formulas
Rule for Like Denominators
When denominators are the same, the fraction with the bigger numerator is the greater fraction. Example: $\frac{5}{8} > \frac{3}{8}$ because $5 > 3$.
Use this rule when the bottom numbers of the fractions you are comparing are the same. If the pieces are the same size, having more pieces means you have a bigger amount.
Rule for Like Numerators
When numerators are the same, the fraction with the smaller denominator is the greater fraction. Example: $\frac{1}{4} > \frac{1}{8}$ because $4 < 8$.
Use this rule when the top numbers of the fractions are the same. If you have the same number of pieces, the fraction made of bigger pieces (from a whole cut into fewer parts) is the greater fraction.
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Challenging
Four friends each have a different fraction of a pizza left. All the fractions have a numerator of 3. Leo's fraction is the largest. Mia's fraction is smaller than Pat's. Pat's fraction is 3/8. Sam's fraction is smaller than Mia's. Which could be Sam's fraction?
A.3/6
B.3/8
C.3/4
D.3/10
Challenging
A student says, "To order 2/5, 2/8, and 2/3 from least to greatest, I just look at the denominators. Since 3 < 5 < 8, the order must be 2/3, 2/5, 2/8." What is wrong with the student's reasoning?
A.The student's rule for ordering denominators is backwards for fractions with like numerators.
B.The student should have ordered the numerators instead.
C.The student ordered from greatest to least by mistake.
D.The student's reasoning is correct.
Challenging
Five runners are practicing. Their distances are 4/10, 4/5, 4/12, 4/8, and 4/4 of a mile. If you list their distances in order from shortest to longest, which distance is in the middle of the list?
A.4/10
B.4/5
C.4/12
D.4/8
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