Module 1. Operations with Positive Fractions (NO CALCULATOR)

Transcription

1 Instructor: Course: MTE Section Module Operations with Positive Fractions (NO CALCULATOR) Name: Use this checklist as a guide to complete the entire Module within the allotted time. Getting Started Important Information Syllabus Quiz Web site: Homework How To Enter Your Answers Requires 85% or higher to move on. Fall 20 Username: To pass the PostTest at least 5% and overall weighted average of 5% Password: (Quizzes 25% and PostTest 5%). Password OR Module Assignments PostTest at least 80%. Section. Video Reading Homework Practice PostTest (optional) Section.2 Video Reading Homework Review Assignment* (optional) Section. Video Reading Homework Section. Video Reading Homework Section.5 Video Reading Homework Review Assignment* (if needed) Section.6 Video Reading Homework Quiz Target Date: Review Assignment* College Knowledge Activity # Section. Video Reading Homework Section.8 Video Reading Homework Section.9 Video Reading Homework Section.0 Video Reading Homework Quiz 2 Target Date: Review Assignment* Section. Video Reading Homework Quiz & Module Review Target Date: Review Assignment* Proctored PostTest Target Date: * Only one Customized Review Assignment is generated for any Quiz, Practice PostTest, or PostTest (computer version only).

2 Instructor Course: MTE Section Module Notes Name Click on the button for Module. Click on the link for Section. and watch the lecture video.. Introduction to Fractions and Mixed Numbers As you watch the video, fill in the blanks below. Remember to show each step.. In a fraction, the number on is the numerator; the number on the is the denominator. The fraction bar means What portion of the figure is shaded? number of shaded parts number of equal parts What portion of the figure is not shaded?. In a bag of 50 red and blue marbles, 2 marbles are blue. a) What fraction of the marbles is blue? b) How many marbles are red? c) What fraction of the marbles is red?. Fill in the blanks. A is a fraction whose numerator is less than its denominator. An is a fraction whose numerator is greater than or equal to its denominator. A contains a whole number and a fraction. fractions are less than. Ex. 2 fractions are greater than or equal to. Ex. 9 and 6 6 numbers are greater than. Ex State whether the following are proper or improper fractions: State the shaded parts of the figure as an improper fraction:, and as a mixed number:.. Change to an improper fraction: Write as a mixed number: 5 8 Minimize or close the video window.

3 Click on the link for Section. and open the online textbook (hard copy textbook pp. 2-).. Introduction to Fractions and Mixed Numbers As you read the text, fill in the blanks below. Remember to show each step.. Identify the numerator and the denominator of each fraction Simplify Write a fraction to represent the shaded part of each figure or diagram.. Of the eight planets in our solar system, five are farther from the Sun than Earth is. What fraction of the planets is farther from the Sun than Earth is? 5. Identify each number as a proper fraction, an improper fraction, or a mixed number Represent the shaded part of each figure group as both an improper fraction and a mixed number.. Write each as an improper fraction. Improper fraction: Mixed number: Improper fraction: Mixed number: 8. Write each as a mixed number or a whole number Click on the tab at the top to return to Section.. Do the homework. You must get at least 85% before you can move on. 2

4 Click on the button for Module. Click on the link for Section.2 and watch the lecture video..2 Factors and Prime Factorization As you watch the video, fill in the blanks below. Remember to show each step.. numbers are, 2,,, and so on. 2. Since 2 5 = 0, both 2 and 5 are of 0, and 2 5 is called a of 0.. Find all the factors of: A prime number is a natural number that has exactly different factors, and itself. 5. A composite number is any natural number, other than, that is a prime number. 6. is prime nor composite.. Determine whether each number is prime or composite: is, 0 is, 6 is 8. The of a number is the factorization in which all the factors are prime numbers. Every whole number greater than has exactly prime factorization. 9. If a factor is repeated, it can be expressed using exponential notation. 0. Use division or a factor tree to find the prime factorization of each exponent base Minimize or close the video window. Click on the link for Section.2 and open the online textbook (hard copy textbook pp. 5-9)..2 Factors and Prime Factorization As you read the text, fill in the blanks below. Remember to show each step.. Find all the factors of each of the following numbers Determine whether each number is prime or composite. 2 is is 8 is 29 is 9 is. Use division or a factor tree to find the prime factorization of each Click on the tab at the top to return to Section.2. Do the homework. You must get at least 85% before you can move on.

5 Click on the button for Module. Click on the link for Section. and watch the lecture video.. Simplest Form of a Fraction As you watch the video, fill in the blanks below. Remember to show each step.. Fractions that represent the same portion of a whole are called. 2. A fraction is written in or when the numerator and the denominator have no common factors other than.. Simplify Two fractions are equivalent if they simplify to the fraction. 5. is a shortcut method for determining whether two fractions are equivalent. If cross products are, the fractions are equivalent. If cross products are, the fractions are not equivalent. Are 6 0 and 0 25 Are and 5 8 equivalent? Yes or No equivalent? Yes or No Are 9 and 6 equivalent? Yes or No 8 6. There are 5280 feet in a mile. What fraction of a mile is represented by 260 feet?. The outer wall of the Pentagon is 2 inches wide. Ten inches are concrete, 8 inches are brick, and 6 inches are limestone. What fraction of the wall is concrete? Minimize or close the video window. Equivalent fractions/simplifying fractions (supplemental information): When we multiply a number by, we get the same number. Use a factor of equivalent fractions. Multiply by a to make an equivalent fraction: n when simplifying or making n When we divide a number by, we get the same number. Cancel a factor of n n when simplifying. Comparing fractions: One method is to use cross multiplication to determine which fraction is greater. Keep the numerators on their original side of the problem. Then compare the products ? Compare. Use >, <, or =

6 Click on the link for Section. and open the online textbook (hard copy textbook pp. 22-).. Simplest Form of a Fraction As you read the text, fill in the blanks below. Remember to show each step.. Write each in simplest form. Write answer as a fraction or a mixed number There are currently 58 national parks in the United States. There are six national parks in Washington state. Determine what fraction of the United States national parks is located in Washington. Write the fraction in simplest form.. (See page.) Each sector of this circle graph (or pie chart) shows the fraction of entering college freshmen who expect to major in each discipline shown. What fraction of entering college freshmen plans to major in education? What fraction of entering college freshmen plans to major in biological sciences? Click on the tab at the top to return to Section.. Do the homework. You must get at least 85% before you can move on. Click on the button for Module. Click on the link for Section. and watch the lecture video.. Rates As you watch the video, fill in the blanks below. Remember to show each step.. A special type of ratio is a rate. Rates are used to compare types of quantities. 2. Write each as a simplified fraction. 6 laser printers for 28 computers 5 shrubs every 5 feet To write a rate as a unit rate, the numerator of the rate by the denominator. A unit rate is a rate with a denominator of.. Write each as a unit rate. 5 riders in 5 subway cars $,000,000 lottery winnings paid over 20 years Minimize or close the video window. 5

7 Click on the link for Section. and open the online textbook (hard copy textbook pages -5).. Rates As you read the text, fill in the blanks below. Remember to show each step.. Write each rate as a fraction in simplest form. 0 nails every 6 feet 2 commercials every 5 minutes $680 for 8 weeks 26 miles on 2 gallons of gasoline 2. A familiar example of a unit rate is 55 mph, read as 55 miles per hour. This means miles per hour or 55 miles hour. In this context, the word per translates to.. Write each as a unit rate. $,500 every months 200 feet every 8 seconds Click on the tab at the top to return to Section.. Do the homework. You must get at least 85% before you can move on. Click on the button for Module. Click on the link for Section.5 and watch the lecture video..5 Multiplying Fractions and Mixed Numbers As you watch the video, fill in the blanks below. Remember to show each step.. To multiply two fractions, multiply the and multiply the. To work with smaller numbers, look to remove factors of before multiplying completely: Multiply. Write answer as a fraction in lowest terms To multiply with mixed numbers or whole numbers, first write any mixed or whole numbers as and then multiply as usual.. When both numbers to be multiplied are mixed or whole numbers, it is a good idea to the product to see if your answer is reasonable. To do this, we round mixed numbers to the nearest. If the fraction part of the mixed number is or greater, we round the whole number part up. If the fraction part of the mixed number is less than, then we do not round the whole number part up. 6

8 5. Multiply and simplify. Write answer as a fraction, a whole number, or a mixed number The Oregon National Historic Trail is 20 miles long. It begins in Independence, Missouri, and ends in Oregon City, Oregon. Manfred Coulon has hiked 2 5 of the trail before. How many miles has he hiked?. usually translates to multiplication. 8. The radius of a circle is one-half of its diameter. If the diameter of a circle is 8 of an inch, what is its radius? diameter radius Minimize or close the video window. Click on the link for Section.5 and open the online textbook (hard copy textbook pages 8-2)..5 Multiplying Fractions and Mixed Numbers As you read the text, fill in the blanks below. Remember to show each step.. Multiply. Write answer as a fraction in lowest terms Multiply and simplify. Write answer as a fraction, a whole number, or a mixed number Multiply and simplify. Write each as a fraction or a mixed number. Check by estimating multiplied by any number is Multiply Estimate: Estimate:

9 Remember, if the fraction part of the mixed number is 2 or greater, round the whole number part up. If the fraction part of the mixed number is less than, do not round the 2 whole number part up. 6. Hershey Park is an amusement park in Hershey, Pennsylvania. Of its 60 rides, of them are roller coasters. How many roller 6 coasters are in Hershey Park?. (See page.) Each sector of this circle graph (or pie chart) shows the fractional part of a car s total mileage that falls into a particular category. In one year, a family drove 2,000 miles in the family car. How many of these miles might be expected to fall in the Work category? The Shopping category? Click on the tab at the top to return to Section.5. Do the homework. You must get at least 85% before you can move on. Click on the button for Module. Click on the link for Section.6 and watch the lecture video..6 Dividing Fractions and Mixed Numbers As you watch the video, fill in the blanks below. Remember to show each step.. Two numbers are of each other if their product is. To find the reciprocal of a fraction, interchange (flip) its and. Every number except has a reciprocal. 2. The reciprocal of is. The reciprocal of 5 is.. To divide two fractions, multiply the first fraction by the of the second fraction. That is, a c = a d = a d b d b c b c. reciprocal. Divide. Write the answer in lowest terms

10 REMEMBER: Do not simplify until you have changed division to multiplication! 5. To divide with a mixed number or a whole number, first write the mixed or whole number as a and then divide as usual. 6. Divide. Write the answer in lowest terms. 2. A patient is to take tablespoons of medicine per day in equally divided doses. How much medicine is to be taken in each dose? Minimize or close the video window. Click on the link for Section.6 and open the online textbook (hard copy textbook pages 9-52)..6 Dividing Fractions and Mixed Numbers As you read the text, fill in the blanks below. Remember to show each step.. Find the reciprocal of each number. Number Reciprocal 2. Divide. Write answer as a fraction in lowest terms

11 . Divide and simplify. Write answer as a fraction or a mixed number The quotient of 0 and any number (except 0) is. Ex = 5. The quotient of any number and 0 is. Ex. 0 = 6. A designer of clothing designs an outfit that requires 2 made from a 0-yard bolt of material? yards of material. How many outfits can be Click on the tab at the top to return to Section.6. Do the homework. You must get at least 85% before you can move on. Click on the link for Module Quiz. You have 2 attempts at the Quiz. The lowest Quiz score is dropped ONLY if you submit the completed Module Notes prior to taking the PostTest. Quiz scores are averaged, and this average is worth 25% of your final course grade. After your first attempt, a Review Assignment will be available for you to work on problems you missed. You must score 00% on the Review Assignment to retake the Quiz. If you are not ready to submit your answers, close the window and click Leave This Page. Otherwise, click Submit. Due dates for each Quiz are included in the Course Calendar/Assignments and posted on MyLabsPlus. All Quiz attempts must be completed by the due date. Missed quizzes will receive a score of zero. There is no minimum score to move on. Keep your scratch work organized for review. Click on the button for Module. Click on the link for College Knowledge Activity # and complete the assignment. This activity does not count for credit in any SDV course. You must get 00% before you can move on. 0

12 Click on the button for Module. Click on the link for Section. and watch the lecture video.. Adding and Subtracting Like Fractions As you watch the video, fill in the blanks below. Remember to show each step.. are fractions with the same denominator. To add like fractions, add the and write the sum over the common. Then simplify, if possible. That is, a + b = a+b. c c c 2. Add these like fractions. Simplify if possible To subtract like fractions, subtract the and write the difference over the common. Then simplify, if possible. That is, a b = a b. c c c. Subtract these like fractions. Simplify if possible Perimeter means. Find the perimeter of the triangle. 20 in 9 20 in 20 in 6. Emil Vasquez, a bodybuilder, worked out 8 of an hour one morning before school and 5 8 of an hour that evening. How long did he work out that day? Minimize or close the video window. Don t forget to attach units!

13 Click on the link for Section. and open the online textbook (hard copy textbook pages 58-6).. Adding and Subtracting Like Fractions As you read the text, fill in the blanks below. Remember to show each step.. Add and simplify. Write answer as a fraction or a mixed number Subtract. Write answer as a fraction in lowest terms Find the perimeter of the rectangle. (Recall: The perimeter of a figure is the distance around the figure.). If a piano student practices the piano of an hour in 8 the morning and of an 8 hour in the evening, how long did she practice that day? 5. A jogger ran miles on Monday and miles on Wednesday. How much farther did he run on Monday than on Wednesday? Click on the tab at the top to return to Section.. Do the homework. You must get at least 85% before you can move on. 2

14 Click on the button for Module. Click on the link for Section.8 and watch the lecture video..8 Least Common Multiple As you watch the video, fill in the blanks below. Remember to show each step.. A of a number is the product of that number and a natural number. Multiples of 5 are,,,,,,,, Multiples of are,,,,,,,,,,, Common multiples of both and 5 are numbers that are found in both lists above. Some common multiples of and 5 are,,,, 2. The, or LCM, is the smallest number in the list of common multiples. For example, the LCM of and 5 is.. Find the LCM of 9 and 5: Make a factor tree for each number if it helps!. Find the LCM of 8 and 2. Prime factorization of 8 = Prime factorization of 2 = LCM = = 5. Find the LCM of 25, 5,and 6. Prime factorization of 25 = Prime factorization of 5 = Prime factorization of 6 = LCM = = 6. Find the LCM of 0, 6, and 50. Prime factorization of 0 = Prime factorization of 6 = Prime factorization of 50 = LCM = =. To write an equivalent fraction, a a a c, where a, b, and c are nonzero numbers. b b b c 8. Write an equivalent fraction:? 5 5?

15 Another method to find the LCM: List the prime factors from each number. For each number, line up matching factors with those from other number(s) and do not line up factors that don t have a match. Bring down each number from its column. Multiply these together for the LCM. BE ORGANIZED! Example: Find the LCM of 2 and 8. Prime Factorizations of 2 and 8: LCM is Minimize or close the video window. Click on the link for Section.8 and open the online textbook (hard copy textbook pages 6-)..8 Least Common Multiple As you read the text, fill in the blanks below. Remember to show each step.. Find the LCM of each. 9 and 2 8 and 6 2 and and 0 2 and 60 and 20, 2, and 5 0 and 08 5, 8, and 5 2. To write as an equivalent fraction with a denominator of 2, we multiply by in the form of : = = =. For each, write an equivalent fraction with the indicated denominator. = = = 6 Click on the tab at the top to return to Section.8. Do the homework. You must get at least 85% before you can move on.

16 Click on the button for Module. Click on the link for Section.9 and watch the lecture video..9 Adding and Subtracting Unlike Fractions As you watch the video, fill in the blanks below. Remember to show each step. Remember: = etc Add or subtract and simplify. 2 2 LCD is LCD is LCD is LCD is Find the perimeter of the parallelogram. 5 cm cm 5 cm cm LCD is Minimize or close the video window. 5

17 Click on the link for Section.9 and open the online textbook (hard copy textbook pages 5-9)..9 Adding and Subtracting Unlike Fractions As you read the text, fill in the blanks below. Remember to show each step.. Add and simplify. Write answer as a fraction or a mixed number Subtract and simplify. Write answer as a fraction or a mixed number A freight truck has ton of computers, ton of televisions, and ton of small appliances. 8 Find the total weight of its load.. Find the difference in length of two boards if one board is 5 of a foot long and the other is 2 of a foot long. 5. (See page 8.) According to this circle graph (or pie chart), what fraction of areas maintained by the National Park Service is NOT National Monuments? Click on the tab at the top to return to Section.9. Do the homework. You must get at least 85% before you can move on. 6

18 Click on the button for Module. Click on the link for Section.0 and watch the lecture video..0 Adding and Subtracting Mixed Numbers As you watch the video, fill in the blanks below. Remember to show each step.. To add or subtract mixed numbers, add or subtract the parts and then add or subtract the parts. 2. Add or subtract. Write the answer as a mixed number = Remember: = etc and Adding mixed numbers with carrying: Example: If Tucson s average annual rainfall is inches and Yuma s is 5 inches, how much more rain, on average, does Tucson get than Yuma? Subtracting mixed numbers with borrowing: 9 6 Example: When subtracting from a whole number, borrow a and change the into n n notation using the denominator that is needed Minimize or close the video window.

19 Click on the link for Section.0 and open the online textbook (hard copy textbook pages 8-9)..0 Adding and Subtracting Mixed Numbers As you read the text, fill in the blanks below. Remember to show each step.. Add. Write answer as a mixed number Subtract. Write answer as a mixed number. Check by estimating Estimate: Estimate: Estimate:. Two packages of ground round are purchased. One package weighs 2 8 pounds and the other 5 pounds. What is the combined weight of the ground round?. The measurement around the trunk of a tree just below shoulder height is called its girth. The largest known American beech tree in the United States has a girth of 2 feet. The largest known sugar maple tree in the United States has a girth of 9 5 feet. How much larger is the girth of the largest known 2 American beech tree than the girth of the largest known sugar maple tree? Click on the tab at the top to return to Section.0. Do the homework. You must get at least 85% before you can move on. 8

20 Click on the button for Module. Click on the link for Module Quiz 2. You have 2 attempts at the Quiz. The lowest Quiz score is dropped ONLY if you submit the completed Module Notes prior to taking the PostTest. Quiz scores are averaged, and this average is worth 25% of your final course grade. After your first attempt, a Review Assignment will be available for you to work on problems you missed. You must score 00% on the Review Assignment to retake the Quiz. If you are not ready to submit your answers, close the window and click Leave This Page. Otherwise, click Submit. Due dates for each Quiz are included in the Course Calendar/Assignments and posted on MyLabsPlus. All Quiz attempts must be completed by the due date. Missed quizzes will receive a score of zero. There is no minimum score to move on. Keep your scratch work organized for review. 9

21 Click on the button for Module. Click on the link for Section. and watch the lecture video.. Order, Exponents, and the Order of Operations As you watch the video, fill in the blanks below. Remember to show each step.. The inequality symbol < means is than and the inequality symbol > means is than. 2. Compare. Use < or > Exponents indicate repeated. 2 5 Order of Operations The order in which to perform arithmetic on. Please P Do all calculations within Parentheses (or other grouping { [ ( ) ] } Excuse E Evaluate all terms with Exponents 2 My Dear M D Do all Multiplication and Division in pairs from left to right 5 or 5 or 5() or 5 or Aunt Sally A S Do all Addition and Subtraction in pairs from left to right 0 + or 9 If there are parentheses inside parentheses, you must finish the innermost parentheses and then work outward.. Evaluate Evaluate ( )2. Minimize or close the video window. 20

22 Click on the link for Section. and open the online textbook (hard copy textbook pages 98-0).. Order, Exponents, and the Order of Operations As you read the text, fill in the blanks below. Remember to show each step.. Compare. Use < or > Evaluate each expression. ( ) 2 ( 2 ) ( 2 6 ) ( ). Perform each indicated operation ( 2 5 ) 2 ( 5 25 ). Find the average of 2, 8, and. Remember: The average of a list of numbers is their sum divided by 2 the number of numbers in the list. Problem Solving 2

23 Example: The Bank of America Building is the second-tallest building in San Francisco, at 9 feet. The tallest building in San Francisco is the Transamerica Pyramid which is feet taller than the Bank of America Building. How tall is the Transamerica Pyramid? Click on the tab at the top to return to Section.. Do the homework. You must get at least 85% before you can move on. Click on the button for Module. Click on the link for Module Quiz and Module Review. You have 2 attempts at the Quiz. The lowest Quiz score is dropped ONLY if you submit the completed Module Notes prior to taking the PostTest. Quiz scores are averaged, and this average is worth 25% of your final course grade. After your first attempt, a Review Assignment will be available for you to work on problems you missed. You must score 00% on the Review Assignment to retake the Quiz. If you are not ready to submit your answers, close the window and click Leave This Page. Otherwise, click Submit. Due dates for each Quiz are included in the Course Calendar/Assignments and posted on MyLabsPlus. All Quiz attempts must be completed by the due date. Missed quizzes will receive a score of zero. There is no minimum score to move on. Keep your scratch work organized for review. 22

24 Congratulations! You have completed the coursework for Module and are ready to prepare for the PostTest. OPTIONAL Review: Click on the link for Module Practice PostTest. You are allowed unlimited attempts at the Practice PostTest. It is 2- times the length of the actual PostTest to give you plenty of practice. If you are not ready to submit your answers, close the window and click Leave this Page. Otherwise, click Submit. After the first attempt, a Review Assignment will be available for you to work on the missed problems. You must score 00% on the Review Assignment to retake the Practice PostTest. Take the Module PostTest. The date of your PostTest is included in the Course Calendar/Assignments and posted on MyLabsPlus. You have 5 minutes to complete the PostTest. You must score at least 5% on the PostTest. The PostTest is worth 5% of your final grade. If you score below 5% on the computer version of the PostTest, a Review Assignment will be available for you to work on problems you missed. It is recommended that you score 00% on the Review Assignment before retaking the PostTest. When the PostTest is taken on paper, a Review Assignment is not generated. If you do not score 5% or better after two attempts at the PostTest, your grade will be a U, regardless of your Quiz average or overall weighted average. At this point, you will need to change your schedule. The instructor or the Math Lab Coordinator will help you create a schedule to repeat the failed course and move the subsequent Module(s) to a later session. To pass the Module: a minimum score of 5% is required on the PostTest, and an overall weighted average of 5% (quizzes count for 25% and PostTest counts for 5%) is required for the course, OR a minimum score of 80% is required on the PostTest. 2