1. Fractions, Mixed Numbers, and Rational Expressions
5.1
Fractions, Mixed Numbers, and Rational Expressions

2. Fraction: A number that describes a part of a whole.
 Numerator
 Denominator
Numerator: The number written in the top position of a fraction
Denominator: The number written in the bottom position of a fraction.

3. Rational Number: A number that can be expressed as a ratio of integers.

4. Name the Fraction Represented by a Shaded Region
Answer:
Explanation: There are 10 equal-sized divisions in the whole region and 3 are shaded.

5. Word Question
In a group of 35 people at a conference, 17 are wearing glasses. What fraction of the people at the conference are wearing glasses? What fraction are not wearing glasses?

6. You Try

7. Graph fractions on a Number Line
Divide the distance between 0 and 1 into X equal spaces, where X is the number in the denominator position.
Ex.

8. More Examples

9. Simplify Fractions
Simplify: The process of writing an equivalent expression with fewer symbols or smaller numbers
Simplest form: An equivalent expression written with the fewest symbols and the smallest numbers possible

10. Rules to Keep in Mind

11. Write Equivalent Fractions
An equivalent fractions are fractions that name the same number
Ex.
Rule of thumb, You can multiply or divide a fraction by any non- zero number as long as you do it to both the numerator and the denominator.

12. Examples

14. Use <, >, or = to Write a True Statement
We can easily compare fractions that have the same denominator by looking at their numerator.
What if they do not have the same denominator?

15. To Compare Two Fractions:
Write equivalent fractions that have a common denominator
Compare the numerators of the equivalent fractions

16. Example a.
Write equivalent fractions that have a common denominator, then compare numerators. A common multiple for 8 and 7 is 56, so our common denominator is 56.
Answer:

17. You Try

18. Write Improper Fractions as Mixed Numbers
Improper Fraction: A fraction in which the absolute value of the numerator is greater than or equal to the absolute value of the denominator.
ie. If the number on top is bigger than or equal to the number on the bottom.
Mixed Number: An Integer combined with a fraction.

19. To write an improper fraction as a mixed number:
Divide the denominator into the numerator.
Write the result in the following form.

20. Write the improper fraction as a mixed number.
Solution: Divide 20 by 3.
quotient
original denominator
remainder

21. Example

22. Write Mixed Numbers as Improper Fractions
The same but opposite
Multiply the integer by the denominator.
Add the resulting product to the numerator to find the numerator of the improper fraction.
Keep the same denominator.

23. Write the mixed number as an improper fraction.
Solution:
We multiplied 8 by 5 to get 40 , then added 7 to get 47 for the numerator of the improper fraction. We kept the denominator the same.

24. You Try