Mathematics
Grade 10
15 min
Add 3 or more fractions: word problems
Add 3 or more fractions: word problems
What you'll learn
- Identify the fractions needed to solve an addition word problem involving three or more fractions with unlike denominators in at least 4 out of 5 tries.
- Solve word problems involving the addition of three or more fractions with unlike denominators, showing all steps, and arriving at the correct answer with simplified fractions in 3 out of 4 problems.
- Explain the steps used to add three or more fractions with unlike denominators in a word problem, using mathematical vocabulary, to a partner with 80% accuracy.
- Apply knowledge of equivalent fractions to find a common denominator when adding three or more fractions in word problems and correctly solve at least 70% of the problems.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate word problems involving congruent figures into mathematical expressions requiring the addition of three or more fractions.
Calculate the least common multiple (LCM) of three or more denominators to establish a common denominator.
Accurately convert multiple fractions to equivalent fractions with a common denominator.
Sum three or more proper, improper, or mixed fractions and express the result in simplest form.
Apply fraction addition to solve for the perimeter of composite shapes formed from congruent figures.
Analyze geometric models by summing the fractional areas of distinct regions composed of congruent parts.
Ever designed a logo or floor plan by combining identical shapes? How would you calculate the total length of the border if each sid...
2
Key Concepts & Vocabulary
TermDefinitionExample
Congruent FiguresGeometric figures that have the exact same size and shape. All corresponding sides and corresponding angles are equal.Two triangles, ΔABC and ΔDEF, are congruent if AB=DE, BC=EF, AC=DF, and ∠A=∠D, ∠B=∠E, ∠C=∠F.
Composite FigureA geometric figure formed by joining two or more basic geometric figures.An L-shaped polygon can be viewed as a composite figure made of two rectangles.
PerimeterThe total distance around the exterior boundary of a two-dimensional shape. For composite figures, it is the sum of the lengths of the outer edges only.The perimeter of a shape made by placing two 3x3 squares side-by-side is 3+3+3+3+3+3 = 18, not the sum of their individual perimeters (12+12=24).
Least Common Multiple (LCM)The smallest positive integer that is a multip...
3
Core Formulas
Finding a Common Denominator
\frac{a}{b} + \frac{c}{d} + \frac{e}{f} = \frac{a \cdot (\frac{LCM}{b})}{LCM} + \frac{c \cdot (\frac{LCM}{d})}{LCM} + \frac{e \cdot (\frac{LCM}{f})}{LCM}
To add fractions with different denominators, first find the Least Common Multiple (LCM) of all denominators (b, d, f). Then, convert each fraction into an equivalent fraction with the LCM as the new denominator.
Adding Fractions with a Common Denominator
\frac{p}{n} + \frac{q}{n} + \frac{r}{n} = \frac{p+q+r}{n}
Once all fractions share the same denominator (n), add their numerators (p, q, r) and place the sum over the common denominator.
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Challenging
A banner is being designed from a large piece of cloth made of congruent triangles. The designer allocates 1/4 of the area for red fabric. Of the remaining area, 2/5 is allocated for blue. Of the new remaining area, 1/3 is allocated for green. What total fraction of the original banner is colored red, blue, or green?
A.1/2
B.3/5
C.2/3
D.7/10
Challenging
A composite shape is formed by joining 'n' congruent regular pentagons in a straight line, sharing one side between each adjacent pair. If the side length of each pentagon is 's', which expression represents the perimeter of the composite figure?
A.5ns
B.5s + 3s(n-1)
C.4s + 3s(n-1)
D.3n + 2
Easy
A graphic designer is creating a logo using a grid of 30 congruent squares. They color 1/3 of the squares blue, 1/5 of the squares green, and 1/6 of the squares purple. What total fraction of the logo is colored?
A.3/14
B.7/10
C.1/2
D.21/30
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Frequently asked questions
What grade level is "Add 3 or more fractions: word problems"?
Add 3 or more fractions: word problems is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Add 3 or more fractions: word problems?
You'll be able to: Identify the fractions needed to solve an addition word problem involving three or more fractions with unlike denominators in at least 4 out of 5 tries; Solve word problems involving the addition of three or more fractions with….
Is "Add 3 or more fractions: word problems" free to practice?
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How many practice questions are included with Add 3 or more fractions: word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.