Objective A Identify the numerator and the denominator of a fraction. When the numerator is less than the denominator, it is a(n) fraction.
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1 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4. Section 4. Introduction to Fractions and Mixed Numbers Complete the outline as you view Lecture Video 4.. Pause the video as needed to fill in all blanks. Circle your answer to each numbered exercise. Then press Play to continue listening to the video. Objective A Identify the numerator and the denominator of a fraction. We can use to represent part of a whole. The number on top is the. The number on bottom is the. The bar between the numbers is the bar. When the numerator is less than the denominator, it is a(n) fraction. When the numerator is greater than or equal to the denominator, it is a(n) fraction. Identify the numerator and denominator of the fraction and determine whether the fraction is proper or improper.. 2 Determine whether the fraction is proper or improper
2 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4. Section 4. Introduction to Fractions and Mixed Numbers Objective B Write a fraction to represent parts of figures or real-life data. Represent the shaded portion of each figure with a fraction or mixed number.. 4. Write, in your own words, the definition of a proper fraction. Write, in your own words, the definition of an improper fraction. A(n) has a whole number part and a fraction part. Answer the questions about the application problem. 5. A bag contains 50 red or blue marbles, If 2 marbles are blue, a) What fraction of the marbles are blue? b) How many marbles are red? c) What fraction of the marbles are red? 49
3 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4. Section 4. Introduction to Fractions and Mixed Numbers Objective C Graph fractions on a number line. Graph the following fractions on a number line Objective D Review division properties for 0 and. Simplify each fraction by dividing Let n be any integer except o, n = n n = n 0 0 n = n is undefined 0 50
4 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4. Section 4. Introduction to Fractions and Mixed Numbers Objective E Write mixed numbers as improper fractions. In your own words, write the definition of a mixed number. Write the steps used to write a mixed number as an improper fraction. Write a Mixed Number as an Improper Fraction Step : Step 2: Step : Write each mixed number as an improper fraction The fraction bar means. 5
5 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4. Section 4. Introduction to Fractions and Mixed Numbers Objective F Write improper fractions as mixed numbers or whole numbers. Write the steps used to write improper fractions as a mixed numbers or whole numbers. Writing an Improper Fraction as a Mixed Number or a Whole Number Step : Step 2: Writing each improper fraction as an equivalent mixed number
6 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.2 Section 4.2 Factors and Simplest Form Complete the outline as you view Lecture Video 4.2. Pause the video as needed as you fill in all blanks. Circle your answer to each numbered exercise. Then press Play to continue listening to the video. Objective A Write a number as a product of prime numbers. A(n) is a natural number greater than whose only factors are and itself. The first few prime numbers are 2,, 5, 7,,, 7, 9, 2, 29, A(n) is a natural number greater than that is not prime. When a composite number is written as a product of prime numbers, this product is called the of the number. There is only one prime factorization for each composite number. Find the prime factorization of the whole number using the branching method.. 48 Find the prime factorization of the whole number using another method
7 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.2 Section 4.2 Factors and Simplest Form Objective B Write a fraction in simplest form. A fraction is in when the numerator and denominator have no common factors other than or. Writing a Fraction in Simplest Form To write a fraction in simplest form, write the of the numerator and the denominator and then both by all common factors. Simplify each fraction. Write in simplest form x 2 6x 5. 40xy 64xyz Objective C Determine whether two fractions are equivalent. Use to determine if two fractions are equal. Determine whether or not each pair of fractions are equivalent fractions. 6. 7? 5 = 8 54
8 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.2 Section 4.2 Factors and Simplest Form Pause and work 7.? 6 = 9 8 Objective D Solve problems by writing fractions in simplest form. Write a fraction in simplest form to represent the fraction in the application problem. 8. The outer wall of the Pentagon is 24 inches wide. Ten inches is concrete, 8 inches is brick, and 6 inches is limestone. What fraction of the wall is concrete? 0 in. 8 in. 6 in. 24 in. 55
9 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4. Section 4. Multiplying and Dividing Fractions Complete the outline as you view Lecture Video 4.. Pause the video as needed as you fill in all blanks. Circle your answer to each numbered exercise. Then press Play to continue listening to the video. Objective A Multiply fractions. Multiplying Fractions To multiply two fractions, multiply the numerators and multiply the denominators. If a, b, c, and d represent numbers, and b and d are not 0, we have a c a i c i =. b d b i d Multiply the fractions. Simplify if possible i i 7 8 Write, in your own words, the process used to multiply fractions. Multiply and simplify.. x y 2 i y x 56
10 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4. Section 4. Multiplying and Dividing Fractions Objective B Evaluate exponential expressions with fractional bases. Evaluate the expression Objective C Divide fractions. Reciprocal of a Fraction Two numbers are of each other if their product is. The reciprocal of the fraction a b is b a because a b a i i = b = b a b i a Give the reciprocal of each number. 5. The reciprocal of 7 2 is because 6. The reciprocal of because 5 6 is 57
11 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4. Section 4. Multiplying and Dividing Fractions 7. The reciprocal of is Dividing Fractions To divide two fractions, multiply the first fraction by the reciprocal of the second fraction. If a, b, c, and d represent numbers and b, c, and d are not 0, then a c a d a i d = i = b d b c b i c reciprocal Divide the fractions In your own words, write the process you will use to divide fractions. Divide. Write the quotient in simplest form. 9. y 20 58
12 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4. Section 4. Multiplying and Dividing Fractions Simplify by multiplying and dividing i 2 6 Objective D Multiply and divide given fractional replacement values. Use the given replacement values to evaluate each expression If x = and y =, 5 Find a) xy and b) x y a) xy b) x y Objective E Solve applications that require multiplication of fractions. Solve the application. 2. The radius of a circle is one-half of its diameter. If the diameter of a circle is 8 of an inch, what is the radius? Remember... of means multiplication 59
13 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.4 Section 4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions Complete the outline as you view Lecture Video 4.4. Pause the video as needed as you fill in all blanks. Circle your answer to each numbered exercise. Then press Play to continue listening to the video. Objective A Add or subtract like fractions. Adding or Subtracting Like Fractions (Fractions with the Same Denominator) If a, b, and c are numbers and b is not 0, then a c a+ c + = and b b b also a c a c = b b b In other words, to add or subtract fractions with the same denominator, add or subtract their numerators and write the sum or difference over the common denominator. Add or Subtract In general the following is true: a a a = = as long as b is not 0 b b b Remember... numerator + numerator denominator 60
14 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.4 Section 4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions. 6 7x 5x Subtract. Give the answer in simplest form Objective B Add or subtract given fractional replacement values. 6. Evaluate x yif x = and 5 y = 5 x y = Objective C Solve problems by adding or subtracting like fractions. means distance around. 7. Find the perimeter 5 2 meters 7 2 meters 6
15 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.4 Section 4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions Objective D Find the least common denominator of a list of fractions. The (LCD) of a list of fractions is the smallest positive number divisible by all the denominators in the list. (The least common denominator is also the least common multiple (LCM) of the denominators. Write the steps used to find the least common denominator of a list of fractions when using Method. Method : Finding the LCD of a List of fractions Using Multiples of the Largest Number. Step : Step 2: Use Method to find the LCD of the fractions , 9 5 Write the steps used to find the least common denominator when using Method 2. Method 2: Finding the LCD of a list of denominators using prime factorization. Step : Step 2: Step : 62
16 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.4 Section 4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions Use Method 2 to find the least common denominator (LCD) of the fractions ,, 2 56 Objective E Write equivalent fractions. have the same value. Write an equivalent fraction to the first fraction that has the given denominator =. 2 2y = = 9 6a 6
17 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.5 Section 4.5 Adding and Subtracting Unlike Fractions Complete the outline as you view Lecture Video 4.5. Pause the video as needed as you fill in all blanks. Circle your answer to each numbered exercise. Then press Play to continue listening to the video. Objective A Add or subtract unlike fractions. Write the steps used to add or subtract unlike fractions. Adding or Subtracting Unlike Fractions Step : Step 2: Step : Step 4: Add or subtract the fractions y
18 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.5 Section 4.5 Adding and Subtracting Unlike Fractions Objective B Write fractions in order. Insert < or > to form a true statement Objective C Evaluate expressions given fractional replacement values. 6. Evaluate 2 y + x if x = and y = 4. Remember how to Multiply Fractions: numerator i numerator denominator i denominator Objective D Solve problems by adding or subtracting unlike fractions. Remember... Perimeter means distance around. Find the perimeter of the parallelogram cm cm cm 4 5 cm 65
19 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.6 Section 4.6 Complex Fractions and Review of Order of Operations Complete the outline as you view Lecture Video 4.6. Pause the video as needed as you fill in all blanks. Circle your answer to each numbered exercise. Then press Play to continue listening to the video. Objective A Simplify complex fractions. A fraction whose numerator or denominator or both of these contain fractions is called a. Method for Simplifying Complex Fractions The first method makes use of the fact that a fraction bar means division. Simplify the complex fraction using Method To divide fractions: The first fraction times the of the second fraction. To multiply fractions: numerator times over denominator times. Method 2 for Simplifying Complex Fractions The second method for simplifying complex fractions is to multiply the numerator and the denominator of the complex fraction by the of all the fractions in its numerator and its denominator. Use Method 2 to simplify the complex fraction. 2. x
20 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.6 Section 4.6 Complex Fractions and Review of Order of Operations Objective B Review the order of operations. Write the steps in order of the order of operations Step : Order of Operations Step 2: Step : Step 4: Using the order of operations, simplify the expression Objective C Evaluate expressions given replacement values. 2 x 4. Evaluate if x =, yz y = 2 5, and z =
21 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.7 Section 4.7 Operations on Mixed Numbers Complete the outline as you view Lecture Video 4.7. Pause the video as needed as you fill in all blanks. Circle your answer to each numbered exercise. Then press Play to continue listening to the video. Objective A Graph positive and negative fractions and mixed numbers.. Graph the following numbers on the number line: 4,,, 4, Objective B Multiply or divide mixed or whole numbers. Multiplying or Dividing Fractions and Mixed Numbers or Whole Numbers To multiply or divide with mixed numbers or whole numbers, first write any mixed or whole numbers as improper fractions and then multiply or divide as usual. Multiply. Write the final answer as a mixed number i 2 Divide. Write the final answer as a mixed number
22 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.7 Section 4.7 Operations on Mixed Numbers Objective C Add or subtract mixed numbers. Adding or Subtracting Mixed Numbers To add or subtract mixed numbers, add or subtract the fraction parts and then add or subtract the whole number parts. Add Objective D Solve problems containing mixed numbers. Solve the application problem. 5. If Tucson s average rainfall is the average does Tucson get than Yuma? 4 inches and Yuma s is 5 inches, how much more rain, on Objective E Perform operations on negative mixed numbers. Add the mixed numbers Remember... To add numbers with unlike signs, subtract absolute values. The answer has the same sign as the number with the larger absolute value. 69
23 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.8 Section 4.8 Solving Equations Containing Fractions Complete the outline as you view Lecture Video 4.8. Pause the video as needed as you fill in all blanks. Circle your answer to each numbered exercise. Then press Play to continue listening to the video. Objective A Solve equations containing fractions. Equation: expression = expression Solve the equations using the properties of equality.. x 5 = 2 6 To check, replace the variable (in the original equation) with the proposed solution and see that a true statement results z =
24 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.8 Section 4.8 Solving Equations Containing Fractions Objective B Solve equations by multiplying by the LCD. Write the steps used to solve an equation in x. Solving an Equation in x Step : Step 2: Step : Step 4: Step 5: Step 6: Solve the equations x = 6 4 x x =
25 Prealgebra Seventh Edition, Elayn Martin-Gay Sec. 4.8 Section 4.8 Solving Equations Containing Fractions Objective C Review adding and subtracting fractions. Add the fractions. 5. x x
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