Mathematics
Grade 5
15 min
Add fractions with unlike denominators using models
Add fractions with unlike denominators using models
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1
Introduction & Learning Objectives
Learning Objectives
Identify fractions with unlike denominators.
Explain the concept of equivalent fractions using visual models.
Use fraction strips or area models to find a common denominator for two fractions.
Represent the sum of two fractions with unlike denominators using models.
Write the numerical sum of fractions after using models to find a common denominator.
Simplify the sum of fractions, if possible, by observing the models.
Have you ever tried to share a pizza cut into 4 slices with a friend who wants a piece from a pizza cut into 8 slices? 🍕 It can be tricky to add them up!
In this lesson, you will learn how to add fractions that have different-sized pieces, called 'unlike denominators'. We'll use fun visual tools like fraction strips and are...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole or a part of a collection.In the fraction 1/2, one part out of two equal parts is represented.
NumeratorThe top number in a fraction that tells you how many parts you have.In 3/4, the numerator is 3, meaning you have 3 parts.
DenominatorThe bottom number in a fraction that tells you how many equal parts the whole is divided into.In 3/4, the denominator is 4, meaning the whole is divided into 4 equal parts.
Unlike DenominatorsFractions that have different denominators, meaning their wholes are divided into a different number of equal parts.1/2 and 1/3 have unlike denominators (2 and 3).
Equivalent FractionsFractions that look different but represent the same amount or value.1/2 is equivalent to 2/4, 3/6, or 4/8. They...
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Core Formulas
Finding Equivalent Fractions
To find an equivalent fraction, 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 helps us change fractions so they have a common denominator, allowing us to add them. When using models, this means dividing each existing part into more smaller, equal parts.
Adding Fractions with Common Denominators
Once fractions have the same denominator, add only the numerators and keep the denominator the same: $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$
This is the final step after using models to convert fractions to a common denominator. You are simply counting how many parts of the same size you have in total.
5 more steps in this tutorial
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Challenging
A classmate says, 'To add 1/4 + 1/5, I can use a model with 9 parts because 4+5=9.' Which statement best explains the flaw in this reasoning using the concept of models?
A.model with 9 parts cannot be divided evenly into fourths or fifths, so you cannot accurately represent the original fractions.
B.The model should have 4 x 5 = 20 parts, not 4 + 5 = 9 parts.
C.Adding denominators is a procedural error; it has nothing to do with how models work.
D.Fraction strips would be a better model than an area model for this problem.
Challenging
Imagine using fraction strips to model the sum 1/2 + 1/4 + 1/8. To find the sum, you would first need to replace all the strips with strips of the smallest unit. What is the final sum?
A.3/14
B.7/8
C.3/8
D.5/8
Challenging
When using an area model to add 1/4 + 1/3, you create a grid by making 4 columns and 3 rows. In this model, what equivalent fractions have you created to represent 1/4 and 1/3?
A.1/12 and 1/12
B.4/12 and 3/12
C.3/12 and 4/12
D.4/7 and 3/7
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