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Lesson 1 – Introduction to Rational Numbers

- Learning Goals:
- I can convert between mixed and improper fractions
- I can perform all four operations with fractions
- I can reduce fractions to lowest terms

Lesson 1 – Introduction to Rational Numbers

Numbers are grouped together based on their characteristics:

Natural Numbers (Counting numbers): {1, 2, 3, …}

Whole Numbers (including 0): {0, 1, 2, 3,…}

Integers ( Positive or negative whole numbers):

{…-2, -1, 0, 1, 2…}

Rational Numbers: All numbers in the form where a and b are integers and b

(Ex. 0, ,

Lesson 1 – Introduction to Rational Numbers

Whole

Rational

Natural

Integers

0.5, -5.89

1, 2, 3

0

-1, -2

Lesson 1 – Introduction to Rational Numbers

Types of Fractions:

1. Proper: When the numerator (top number) is less than the denominator (bottom number)

2. Improper: When the numerator (top number) is greater than the denominator (bottom number)

3. Mixed: When a whole number is combined with a fraction

Lesson 1 – Introduction to Rational Numbers

Lowest terms: A fraction is in lowest terms when there are no common factors between the numerator and the denominator.

Examples:

Lesson 1 – Introduction to Rational Numbers

Equivalent Fractions: two fractions that are the same.

- Success Criteria for making equivalent fractions:
- Multiply or divide
- What you do to the top you must do to the bottom

Lesson 1 – Introduction to Rational Numbers

Example: Find an equivalent fraction to

Lesson 1 – Introduction to Rational Numbers

- Success Criteria for converting Mixed Fractions to Improper Fractions:
- Multiply the whole number by the denominator and add the numerator. This gives you the numerator for your improper fraction
- Keep the denominator the same
- Negative signs out front of the fraction are not involved in the calculation

Lesson 1 – Introduction to Rational Numbers

- Success Criteria for converting Improper Fractions to Mixed Fractions:
- Count how many times the denominator will go into the numerator. This gives you your whole number to put in front of the fraction
- Take the remainder and use it as your numerator
- Your denominator stays the same
- Leave negative signs out front

Lesson 1 – Introduction to Rational Numbers

- Success Criteria for Adding and Subtracting Fractions:
- Convert mixed fractions into improper fractions first
- Find a common denominator
- Add the numerators
- Keep the denominator the same

Lesson 1 – Introduction to Rational Numbers

- Success Criteria for Multiplying Fractions
- Convert mixed fractions into improper fractions first
- You DO NOT need a common denominator
- Whole numbers have an imaginary denominator of 1
- Multiply the numerators
- Multiply the denominators

Lesson 1 – Introduction to Rational Numbers

- Success Criteria for Dividing Fractions
- Convert mixed fractions into improper fractions first
- You DO NOT need a common denominator
- Change the division sign to a multiplication sign
- Flip the second fraction
- Multiply the numerators
- Multiply the denominators

Lesson 1 – Introduction to Rational Numbers

- Practice
- Pg. 186 Q# 6
- Read top of pg. 14
- Pg. 14 Q# 1 bcefhi, 2-7 parts bcef for all, 8ab

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