Mathematics
Grade 3
15 min
Compare fractions
Compare fractions
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1
Introduction & Learning Objectives
Learning Objectives
Compare two fractions with the same denominator by reasoning about their size.
Compare two fractions with the same numerator by reasoning about their size.
Use the symbols >, <, and = to record the results of fraction comparisons.
Use visual fraction models, like number lines and area models, to justify their comparisons.
Explain why one fraction is greater than, less than, or equal to another in their own words.
Recognize that comparisons are valid only when the two fractions refer to the same whole.
Would you rather have 1/4 of a pizza or 1/8 of a pizza? 🍕 Let's figure out which slice is bigger!
In this lesson, we will learn how to compare fractions to see which one is bigger, which is smaller, or if they are the same size. This is a very i...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that shows a part of a whole. It has a top number and a bottom number.1/2 means you have 1 part out of 2 equal parts.
NumeratorThe top number in a fraction. It tells you how many equal parts you have.In the fraction 3/4, the numerator is 3.
DenominatorThe bottom number in a fraction. It tells you how many equal parts the whole is divided into.In the fraction 3/4, the denominator is 4.
Greater Than (>)A symbol used to show that the first number is bigger than the second number. The symbol opens towards the bigger number, like an alligator's mouth.5 > 3
Less Than (<)A symbol used to show that the first number is smaller than the second number.3 < 5
Equal To (=)A symbol used to show that two fractions or numbers have the same value.2/4...
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Core Formulas
Comparing Fractions with the Same Denominator
If \frac{a}{d} and \frac{b}{d}, and a > b, then \frac{a}{d} > \frac{b}{d}
When the bottom numbers (denominators) are the same, the pieces are the same size. So, you just need to compare the top numbers (numerators). The fraction with the bigger numerator is the bigger fraction because you have more pieces.
Comparing Fractions with the Same Numerator
If \frac{a}{c} and \frac{a}{d}, and c < d, then \frac{a}{c} > \frac{a}{d}
When the top numbers (numerators) are the same, you have the same number of pieces. Now look at the denominators. The fraction with the smaller denominator is the bigger fraction because the whole is cut into fewer, larger pieces.
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Challenging
Which fraction could be placed in the blank to make the statement true? 1/3 < ___ < 5/6
A.1/6
B.1/2
C.6/6
D.1/12
Challenging
Three friends shared three identical cakes. Sara ate 4/6 of a cake. Tom ate more than Sara. Jen ate less than Sara but more than 1/3 of a cake. Which fractions could Tom and Jen have eaten?
A.Tom: 3/6, Jen: 2/6
B.Tom: 5/6, Jen: 1/6
C.Tom: 5/6, Jen: 3/6
D.Tom: 1/2, Jen: 2/3
Challenging
A garden is split into 12 equal rows. 1/4 of the rows are planted with corn, and 2/3 of the rows are planted with beans. Which statement is true?
A.More rows are planted with corn than beans.
B.More rows are planted with beans than corn.
C.An equal number of rows are planted with corn and beans.
D.All 12 rows are planted.
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