Mathematics
Grade 10
15 min
Least common denominator
Least common denominator
What you'll learn
- Identify the least common multiple (LCM) of two given numbers between 2 and 12 with 80% accuracy on a worksheet.
- Explain, in their own words, why finding the least common denominator (LCD) is important when adding or subtracting fractions with different denominators, as demonstrated through a short written response.
- Solve addition and subtraction problems involving fractions with unlike denominators by correctly determining and using the least common denominator, achieving at least 70% accuracy on a quiz.
- Apply the concept of least common denominator to compare and order fractions with unlike denominators, correctly ordering at least 4 out of 5 sets of fractions.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Identify the least common denominator (LCD) for two or more angle measures expressed in radians.
Add and subtract angles in radians by first converting them to equivalent fractions with a common denominator.
Apply the LCD to find positive and negative coterminal angles for a given angle in radians.
Calculate the measure of a complementary or supplementary angle when the given angle is in radians.
Solve geometric problems involving the sum or difference of sectors in a circle using the LCD.
Ever tried to add one-third of a pizza to one-fourth of another? 🍕 You need a common way to slice them! The same idea is crucial when we combine angles on a circle.
This tutorial connects a fundamental arithmetic skill, finding the least common denominator, to advanced...
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Key Concepts & Vocabulary
TermDefinitionExample
RadianA unit of measure for angles, based on the radius of a circle. One radian is the angle created when the arc length is equal to the radius. A full circle is 2π radians.A 90° angle is equivalent to π/2 radians. A 180° angle is equivalent to π radians.
Least Common Multiple (LCM)The smallest positive integer that is a multiple of two or more given integers.The LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly.
Least Common Denominator (LCD)The Least Common Multiple (LCM) of the denominators of two or more fractions. It's the smallest number you can use as a common denominator to add or subtract those fractions.For the fractions 1/4 and 5/6, the denominators are 4 and 6. The LCD is the LCM of 4 and 6, which is 12.
Cot...
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Core Formulas
Adding/Subtracting Angles in Radians
\frac{a\pi}{b} \pm \frac{c\pi}{d} = \frac{(ad \pm bc)\pi}{bd}
To add or subtract angles expressed as fractions of π, you must first find a least common denominator (LCD) for the fractions. Convert each fraction to an equivalent fraction with the LCD, then add or subtract the numerators.
Finding Coterminal Angles in Radians
\theta_{coterminal} = \theta + 2\pi k, \text{ where k is any integer } (..., -2, -1, 0, 1, 2, ...)
To find an angle coterminal with θ (in radians), add or subtract any integer multiple of 2π. When θ is a fraction, you must express 2π using the same denominator as θ. For example, to add 2π to π/3, you rewrite 2π as 6π/3.
Finding a Supplementary Angle in Radians
\theta_{supplement} = \pi - \theta
To find the suppl...
4 more steps in this tutorial
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Challenging
An angle θ is supplementary to π/5. A second angle, φ, is coterminal with θ and lies in the interval [2π, 4π). What is the value of φ?
A.9π/5
B.4π/5
C.19π/5
D.14π/5
Challenging
Three adjacent sectors of a circle have central angles measuring π/4, 2π/3, and π/6. What is the total angle of the three sectors combined?
A.4π/13
B.13π/12
C.11π/12
D.4π/3
Challenging
The sum of two angles, α and β, is 11π/8 and their positive difference is 3π/8. What is the measure of the larger angle?
A.π/2
B.14π/8
C.7π/8
D.π
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Frequently asked questions
What grade level is "Least common denominator"?
Least common denominator is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Least common denominator?
You'll be able to: Identify the least common multiple (LCM) of two given numbers between 2 and 12 with 80% accuracy on a worksheet; Explain, in their own words, why finding the least common denominator (LCD) is important when adding or subtracting….
Is "Least common denominator" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Least common denominator?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.