Mathematics
Grade 5
15 min
Add and subtract fractions with unlike denominators using models
Add and subtract fractions with unlike denominators using models
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Introduction & Learning Objectives
Learning Objectives
Identify fractions with unlike denominators.
Use fraction models (like fraction strips or area models) to represent fractions.
Find a common denominator for two fractions using visual models.
Create equivalent fractions using models to prepare for addition or subtraction.
Add fractions with unlike denominators by first finding a common denominator and using models.
Subtract fractions with unlike denominators by first finding a common denominator and using models.
Explain the process of adding or subtracting fractions with unlike denominators using models.
Have you ever tried to share a pizza cut into 8 slices with a friend who wants a piece from a pizza cut into 4 slices? 🍕 It can get tricky when the pieces aren't the same size!
In this lesson, y...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole or a part of a collection. It is written as a numerator over a denominator.In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator. It means 3 out of 4 equal parts.
NumeratorThe top number in a fraction that tells you how many parts of the whole you have.In $\frac{2}{5}$, the numerator is 2, meaning you have 2 parts.
DenominatorThe bottom number in a fraction that tells you how many equal parts the whole is divided into.In $\frac{2}{5}$, the denominator is 5, meaning the whole is divided into 5 equal parts.
Unlike DenominatorsFractions that have different denominators, meaning their wholes are divided into a different number of equal parts.$\frac{1}{2}$ and $\frac{1}{3}$ have unlike denominators (2...
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Core Formulas
Rule for Finding a Common Denominator
To add or subtract fractions with unlike denominators, you must first find a common denominator. This is often the Least Common Multiple (LCM) of the original denominators.
To find the LCM, list multiples of each denominator until you find the smallest number they share. For example, for denominators 2 and 3, multiples of 2 are (2, 4, 6, 8...) and multiples of 3 are (3, 6, 9...). The LCM is 6.
Rule for Creating Equivalent Fractions
To change a fraction into an equivalent fraction with a new denominator, multiply both the numerator and the denominator by the same non-zero number: $\frac{a}{b} = \frac{a \times c}{b \times c}$
This rule ensures that the value of the fraction remains the same, even though its appearance changes. For example,...
4 more steps in this tutorial
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Challenging
An area model is divided into 12 equal squares. Nine squares are shaded blue, and then two of those blue squares are crossed out. This model represents the solution to which original subtraction problem?
A.9/12 - 2/12
B.3/4 - 1/6
C.1/2 - 1/6
D.5/6 - 1/4
Challenging
A student tries to model 1/4 + 2/3. They draw a rectangle, divide it into 7 parts, and shade 3 of them, claiming the answer is 3/7. Which statement best explains the fundamental error in their modeling process?
A.The student should have used a circle instead of a rectangle.
B.The student added the numerators and denominators before modeling, which is incorrect. The model's parts are also likely not of equal size.
C.The student should have shaded 4 parts, not 3.
D.The student correctly found the sum but modeled it incorrectly.
Challenging
After using models to solve 1/2 + 1/3 = 5/6 and 1/3 + 1/4 = 7/12, you notice a pattern. The common denominator used in the model (6 and 12) is the _____ of the original denominators.
A.Sum
B.Difference
C.Product or Least Common Multiple
D.Greatest Common Factor
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