Mathematics
Grade 10
15 min
Reduce fractions to lowest terms
Reduce fractions to lowest terms
What you'll learn
- Identify the greatest common factor (GCF) of the numerator and denominator of a given fraction with at least 80% accuracy.
- Solve for the simplified form of a fraction by dividing both the numerator and denominator by their greatest common factor, achieving at least 7 out of 10 correct solutions.
- Explain, in their own words, why dividing the numerator and denominator of a fraction by the same number does not change the value of the fraction.
- Apply the process of reducing fractions to lowest terms to solve real-world problems, such as simplifying measurements, with 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the Greatest Common Divisor (GCD) of the numerator and denominator in a fraction representing an angle ratio.
Reduce trigonometric ratios (sin, cos, tan) to their simplest form.
Express the measure of an angle as a simplified fraction of a full circle (360°) or a straight line (180°).
Simplify the fractional part of a radian measure when converting from degrees.
Apply fraction reduction to solve problems involving similar triangles and angle properties.
Verify that a fraction is in its lowest terms by confirming the GCD of the numerator and denominator is 1.
If a pizza is cut into 12 slices and you eat 8, what's the simplest way to describe the fraction of the pizza you ate? 🍕 This same skill is crucial for understanding angles!
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Key Concepts & Vocabulary
TermDefinitionExample
Lowest TermsA fraction is in lowest terms (or simplest form) when its numerator and denominator have no common factors other than 1. Their Greatest Common Divisor (GCD) is 1.The fraction 8/12 is not in lowest terms. By dividing both the numerator and denominator by their GCD of 4, we get 2/3, which is in lowest terms.
Greatest Common Divisor (GCD)The largest positive integer that divides two or more integers without leaving a remainder. It's also known as the Greatest Common Factor (GCF).For the numbers 24 and 36, the common divisors are 1, 2, 3, 4, 6, and 12. The Greatest Common Divisor is 12.
RatioA comparison of two quantities, often expressed as a fraction. In geometry, we often compare lengths of sides or measures of angles.In a right triangle, the ratio of...
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Core Formulas
The Fundamental Rule of Fraction Reduction
\frac{a}{b} = \frac{a \div \text{GCD}(a, b)}{b \div \text{GCD}(a, b)}
To reduce any fraction to its lowest terms, find the Greatest Common Divisor (GCD) of the numerator (a) and the denominator (b). Then, divide both the numerator and the denominator by their GCD.
Tangent Ratio Definition
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
In a right triangle, the tangent of an angle (θ) is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. This ratio must be simplified.
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Sign Up Free to ContinueSample Practice Questions
Easy
According to the tutorial, a fraction is in 'lowest terms' when its numerator and denominator have what property?
A.Their Greatest Common Divisor (GCD) is 1.
B.They are both even numbers.
C.The numerator is smaller than the denominator.
D.They are both prime numbers.
Easy
What is the Greatest Common Divisor (GCD) needed to reduce the fraction 28/42, as shown in the tutorial's trigonometric ratio example?
A.7
B.14
C.2
D.28
Easy
An angle of 90° is what fraction of a full circle (360°)? Express your answer in lowest terms.
A.9/36
B.1/2
C.1/4
D.90/360
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Frequently asked questions
What grade level is "Reduce fractions to lowest terms"?
Reduce fractions to lowest terms is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Reduce fractions to lowest terms?
You'll be able to: Identify the greatest common factor (GCF) of the numerator and denominator of a given fraction with at least 80% accuracy; Solve for the simplified form of a fraction by dividing both the numerator and denominator by their….
Is "Reduce fractions to lowest terms" 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 Reduce fractions to lowest terms?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.