Mathematics
Grade 10
15 min
Add and subtract fractions with unlike denominators using models
Add and subtract fractions with unlike denominators using models
What you'll learn
- Identify the least common denominator (LCD) of two given fractions with unlike denominators with 80% accuracy.
- Solve addition and subtraction problems involving two fractions with unlike denominators using visual models (e.g., fraction bars, area models) and verify the solution with a written equation in at least 3 out of 4 attempts.
- Explain the process of finding a common denominator using models in their own words to a partner, demonstrating understanding of equivalent fractions and their role in adding/subtracting fractions.
- Apply their understanding of adding and subtracting fractions with unlike denominators to solve 2 out of 3 word problems using models and equations.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Construct a geometric model using congruent polygons to represent the sum or difference of two fractions with unlike denominators.
Justify the need for a common denominator by demonstrating the non-congruence of fractional parts from different denominators.
Determine the least common multiple (LCM) of two denominators by finding the smallest number of congruent sub-regions that can partition two initial congruent figures.
Translate a geometric model of fraction addition or subtraction into a standard numerical algorithm.
Prove that the value of a fraction remains unchanged when re-partitioning its model, by applying the concept of area preservation within congruent figures.
Articulate the relationship between the algebraic process of finding a common denomi...
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Key Concepts & Vocabulary
TermDefinitionExample
Congruent FiguresFigures that have the exact same size and shape. In this context, our 'whole' or '1' will always be represented by two or more congruent figures (e.g., two identical squares).Two 5cm x 5cm squares are congruent. One can be partitioned into 3 equal vertical strips (thirds), and the other can be partitioned into 4 equal horizontal strips (fourths).
Unit WholeThe single, complete object or figure that represents the number 1. All fractions are parts of this whole.A single, undivided rectangle represents the Unit Whole. The fraction 3/5 represents 3 congruent parts of that rectangle when it is divided into 5 congruent parts.
PartitionThe action of dividing a geometric figure into smaller, non-overlapping parts. To represent a fraction...
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Core Formulas
Addition of Fractions with Unlike Denominators
\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}
To add fractions, we must express them with a common denominator. Geometrically, 'bd' represents the total number of new, smaller congruent parts after re-partitioning the model. 'ad' and 'bc' represent the number of these new parts that correspond to the original fractions.
Subtraction of Fractions with Unlike Denominators
\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}
To subtract fractions, we also need a common denominator. The model shows the first fraction re-partitioned into 'ad' smaller congruent units, from which we remove 'bc' units, leaving the result over the new total number of units, 'bd'.
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Challenging
A proof begins by showing two congruent squares, one partitioned into 3 vertical strips (thirds) and one into 5 horizontal strips (fifths). The argument states that the 'fractional units' (a 1/3 strip and a 1/5 strip) are not congruent. How does this non-congruence logically lead to the necessity of a common partition?
A.Non-congruent shapes cannot be meaningfully combined by simply counting them; a new, smaller congruent unit must be established for both figures before a sum can be determined.
B.Non-congruent shapes have different perimeters, which complicates the calculation of the total area.
C.The total number of partitions (3+5=8) is not a valid denominator for the sum.
D.Vertical and horizontal strips can never be added together, regardless of their size.
Challenging
In modeling a/b + c/d, the geometric action of taking the first figure (already partitioned into 'b' vertical strips) and superimposing 'd' horizontal partition lines corresponds to which specific part of the algebraic formula \frac{ad + bc}{bd}?
A.The 'bc' term
B.The '+' operation
C.The 'bd' term
D.The 'ad' term
Challenging
A student is modeling 7/8 - 1/6. They correctly identify the LCM as 24 and re-partition the congruent figure for 7/8 into 24 sub-regions. How many sub-regions must be shaded, and what geometric principle guarantees the value of the represented fraction is preserved during this re-partitioning?
A.21 sub-regions must be shaded; guaranteed by the principle of rotational symmetry.
B.7 sub-regions must be shaded; guaranteed by the principle of congruence.
C.21 sub-regions must be shaded; guaranteed by the principle of area preservation.
D.14 sub-regions must be shaded; guaranteed by the principle of proportionality.
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Add and subtract fractions with unlike denominators using models is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Add and subtract fractions with unlike denominators using models?
You'll be able to: Identify the least common denominator (LCD) of two given fractions with unlike denominators with 80% accuracy; Solve addition and subtraction problems involving two fractions with unlike denominators using visual models (e.g….
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How many practice questions are included with Add and subtract fractions with unlike denominators using models?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.