1 / 23

Math 105 – 5A

This math lesson covers the concepts of reducing fractions to lowest terms, performing addition/subtraction, and multiplication/division with fractions. Examples and exercises are provided to help understand these operations.

jmarci
Download Presentation

Math 105 – 5A

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Math 105 – 5A Mr. Chris Staat

  2. Section 1.2 Getting Started: Reviewing Prealgebra

  3. Operations With Fractions • We should be able to perform the following operations on fractions: • Reduce to lowest terms • Addition/Subtraction • Multiplication/Division We should be able to do these abstractly and in specific applied situations.

  4. Lowest Terms • A fraction is in lowest terms if the numerator and the denominator share no common factor. • What does this mean?

  5. Lowest Terms • A fraction is in lowest terms if the numerator and the denominator share no common factor. • For Example: and These fractions are called equivalent because they have the same lowest terms form.

  6. Addition/Subtraction • In order to add/subtract fractions, they must have common denominators. • So first we rewrite each fraction as an equivalent fraction with the same denominator. • Then we add/subtract the numerators. • Then write the result in lowest terms.

  7. Addition/Subtraction • For example:

  8. Multiplication • In order to multiply fractions: • Firstmultiply the numerators together and then multiply the denominators together. • Then rewrite the answer in lowest terms.

  9. Multiplication • For example:

  10. Multiplication • For example:

  11. Division • In order to divide fractions: • First, rewrite the division as multiplication by the reciprocal • Then multiply as explained earlier. • Then rewrite the answer in lowest terms.

  12. Division • For example:

  13. Division • For example:

  14. Exercise 1a A school has two pathways through the math program. Two-thirds of students take the first path while the rest take the second path. During one semester, 3/4 of the students who follow the first path pass the program while 9/10 of the students who follow the second path pass the program. What fraction of students take the first path and pass?

  15. Exercise 1a A school has two pathways through the math program. Two-thirds of students take the first path while the rest take the second path. During one semester, 3/4 of the students who follow the first path pass the program while 9/10 of the students who follow the second path pass the program. What fraction of students take the first path and pass?

  16. Exercise 1b A school has two pathways through the math program. Two-thirds of students take the first path while the rest take the second path. During one semester, 3/4 of the students who follow the first path pass the program while 9/10 of the students who follow the second path pass the program. What fraction of students take the second path and pass?

  17. Exercise 1c A school has two pathways through the math program. Two-thirds of students take the first path while the rest take the second path. During one semester, 3/4 of the students who follow the first path pass the program while 9/10 of the students who follow the second path pass the program. What fraction of students pass?

  18. Exercise 1c A school has two pathways through the math program. Two-thirds of students take the first path while the rest take the second path. During one semester, 3/4 of the students who follow the first path pass the program while 9/10 of the students who follow the second path pass the program. What fraction of students pass?

  19. Exercise 2 A cookie recipe calls for 2/3 cup of flour per batch of cookies, and each batch makes 2 dozen cookies. How many cookies can you make if you have 10 cups of flour and want to use all of the flour?

  20. Exercise 2 A cookie recipe calls for 2/3 cup of flour per batch of cookies, and each batch makes 2 dozen cookies. How many cookies can you make if you have 10 cups of flour and want to use all of the flour?

  21. Venn Diagrams • A Venn diagram is a graph that helps compare and contrast sets. Each set is represented by a circle, and circles that have elements in common overlap. The circles are usually enclosed in a box which represents a larger set where elements that do not belong within either circle.

  22. Venn Diagrams • For Example E F 1 = In E, not in F 2 = in F, not in E 3 = in both E and F 4 = in neither E nor F 3 1 2 4

  23. Exercise 3 In a freshman class of 2000 students at a certain college, 1250 are taking either a developmental math or reading class. Of these 1250 students, 726 are taking both a developmental math class and a developmental reading class, and 437 are taking only a developmental math class. Construct a Venn diagram for this scenario and describe what each number represents.

More Related