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Lesson 1. Rational Numbers & Equations. Simplifying Fractions. Warm-Up. List the factors of 21. List the factors of 12. What fraction is represented by the model? Write two fractions that are equivalent to. Simplifying Fractions. Targets: Write fractions in simplest form. Vocabulary. - PowerPoint PPT Presentation
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1. List the factors of 21.
2. List the factors of 12.
3. What fraction is represented by the model?
4. Write two fractions that are equivalent to .2
1
Fraction: A number that represents a part of a whole number.
Equivalent Fractions: Fractions that represent the same number but have different numerators and denominators.
Greatest Common Factor: Greatest factor that is common to two or more numbers.
Simplest Form: When a numerator and denominator’s only common factor is 1.
Divide the numerator and denominator by the greatest common factor (GCF).
- OR -
Divide the numerator and denominator by common factors until the only common factor is 1.
Find two fractions that are equivalent to .
Multiply the top and bottom by the same number.
Divide the top and bottom by the same number.
14
10
Find the GCF of 10 and 15.
Prime factorizations:◦10 = 2 · 5◦15 = 3 · 5
The only common factor is 5. GCF = 5.
Find the GCF of 24 and 36.
Prime factorizations:◦24 = 2 · 2 · 2 · 3◦36 = 2 · 2 · 3 · 3
Common factors: 2 · 2 · 3 = 12. GCF = 12.
Write the fraction in simplest form:
Find GCF of 20 and 50.
Prime factorization:◦20 = 2 · 2 · 5◦50 = 2 · 5 · 5
Greatest Common Factor: 2 · 5 = 10
Divide the numerator and denominator by the GCF.
50
20
Write the fraction in simplest form:
One common factor is 5.
A remaining common factor of 9 and 12 is 3.
One is the only remaining common factor. is in simplest form.
60
45
4
3
Find two fractions that are equivalent to .
Find the GCF of 32 and 48.
Write each fraction in simplest form.
a. b.
12
3
18
15
80
30