* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 2ch2l9
Survey
Document related concepts
Infinitesimal wikipedia , lookup
Vincent's theorem wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Location arithmetic wikipedia , lookup
Large numbers wikipedia , lookup
John Wallis wikipedia , lookup
Real number wikipedia , lookup
Surreal number wikipedia , lookup
Collatz conjecture wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Positional notation wikipedia , lookup
Transcript
Equivalent Fractions 2-9 and Mixed Numbers Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Objective: Students identify, write, and convert between equivalent fractions and mixed numbers Equivalent Fractions 2-9 and Mixed Numbers Warm Up Name a common factor for each pair. Possible answers: 1. 5 and 10 2. 9 and 12 5 3 3. 20 and 24 4 4. 10 and 14 2 5. 6 and 8 2 6. 8 and 15 1 Equivalent Fractions 2-9 and Mixed Numbers Problem of the Day Find a number less than 100 for which all three statements are true: • Divide by 3. Remainder of 2. • Divide by 4. Remainder of 3. • Divide by 5. Remainder of 4. 59 Equivalent Fractions 2-9 and Mixed Numbers Learn to identify, write, and convert between equivalent fractions and mixed numbers. Equivalent Fractions 2-9 and Mixed Numbers Vocabulary equivalent fractions relatively prime Equivalent Fractions 2-9 and Mixed Numbers In some recipes the amounts of ingredients are given as fractions, and sometimes those fractions do not equal the fractions on a measuring cup. Knowing how fractions relate to each other can be very helpful. Different fractions can name the same number. 3 5 = 6 10 = 15 25 Equivalent Fractions 2-9 and Mixed Numbers In the diagram 3 = 6 = 15 . These are called 5 10 25 equivalent fractions because they are different expressions for the same nonzero number. To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same number. Equivalent Fractions 2-9 and Mixed Numbers Additional Example 1: Finding Equivalent Fractions Find two fractions equivalent to 5 7. 5 · 2 = 10 7·2 14 Multiply numerator and denominator by 2. 5·3 7·3 Multiply numerator and denominator by 3. = 15 21 Equivalent Fractions 2-9 and Mixed Numbers Check It Out: Example 1 Find two fractions equivalent to 6 . 12 6 · 2 = 12 12 · 2 24 Multiply numerator and denominator by 2. 6÷2 3 = 12 ÷ 2 6 Divide numerator and denominator by 2. Equivalent Fractions 2-9 and Mixed Numbers A fraction is in simplest form when the numerat or and denominator are relatively prime. Relatively prime numbers have no common factors other than 1. Equivalent Fractions 2-9 and Mixed Numbers Additional Example 2: Writing Fractions in Simplest Form 18 Write the fraction 24 in simplest form. Find the GCF of 18 and 24. 18 = 2 • 3 • 3 24 = 2 • 2 • 2 The GCF is 6 = 2 • • 3. 3 18 = 18 ÷ 6 = 3 24 24 ÷ 6 4 Divide the numerator and denominator by 6. Equivalent Fractions 2-9 and Mixed Numbers Check It Out: Example 2 15 Write the fraction 45 in simplest form. Find the GCF of 15 and 45. 15 = 3 • 5 45 = 3 • 3 The GCF is 15 = 3 • • 5. 5 15 = 15 ÷ 15 = 1 45 45 ÷ 15 3 Divide the numerator and denominator by 15. Equivalent Fractions 2-9 and Mixed Numbers Additional Example 3A: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent. 4 and 28 6 42 Both fractions can be written with a denominator of 3. 4 4÷2 2 = = 6 6÷2 3 28 = 28 ÷ 14 = 2 42 ÷ 14 3 42 The numerators are equal, so the fractions are equivalent. Equivalent Fractions 2-9 and Mixed Numbers Additional Example 3B: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent. 6 and 20 10 25 Both fractions can be written with a denominator of 50. 6 = 6 · 5 = 30 10 · 5 10 50 20 = 20 · 2 = 40 25 · 2 25 50 The numerators are not equal, so the fractions are not equivalent. Equivalent Fractions 2-9 and Mixed Numbers 8 is an improper 5 fraction. Its numerator is greater than its denominator. 8= 13 5 5 3 1 is a mixed 5 number. It contains both a whole number and a fraction. Remember! An improper fraction is a fraction where the numerator is than or equal to the denominator. Equivalent Fractions 2-9 and Mixed Numbers Additional Example 4: Converting Between Improper Fractions and Mixed Numbers A. Write 13 5 as a mixed number. First divide the numerator by the denominator. 13 = 2 3 5 5 Use the quotient and remainder to write a mixed number. B. Write 7 2 as an improper fraction. 3 First multiply the denominator and whole number, and then add the numerator. + Use the result to 2 = 3 · 7 + 2 = 23 write the improper 3 3 3 fraction. Equivalent Fractions 2-9 and Mixed Numbers Check It Out: Example 4 A. Write 15 6 as a mixed number. First divide the numerator by the denominator. 15 = 2 3 = 2 1 Use the quotient and remainder to 2 write a mixed number. 6 6 B. Write 8 1 as an improper fraction. 3 First multiply the denominator and whole number, and then add the numerator. + Use the result to 3 · 8 + 1 1 25 = 83 = write the improper 3 3 fraction. Equivalent Fractions 2-9 and Mixed Numbers Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems Equivalent Fractions 2-9 and Mixed Numbers Lesson Quiz 12 1. Write two fractions equivalent to 24 . 1 3 2, 6 2. Determine if 5 and 4 are equivalent. 12 10 16 3. Write the fraction 48 in simplest form. no 4. Write 17 as a mixed number. 8 21 8 5. Write 4 3 7 as an improper fraction. 31 7 1 3 Equivalent Fractions 2-9 and Mixed Numbers Lesson Quiz for Student Response Systems 1. Identify two fractions equivalent to 12 . 60 3 1 A. Possible answer: , 5 15 B. Possible answer: 1 , 3 5 5 C. Possible answer: 1 , 3 6 18 D. Possible answer: 1 , 3 10 30 Equivalent Fractions 2-9 and Mixed Numbers Lesson Quiz for Student Response Systems 2. Identify the fractions that are not equivalent. 7 , 14 10 20 A. 3 , 6 16 32 C. B. 3 , 7 16 10 D. 3 , 15 7 35 Equivalent Fractions 2-9 and Mixed Numbers Lesson Quiz for Student Response Systems 3. Which of the following represents the fraction 15 in simplest form? 30 1 A. C. 1 3 5 B. 1 4 D. 1 2 Equivalent Fractions 2-9 and Mixed Numbers Lesson Quiz for Student Response Systems 4. Which of the following represents 19 as a 6 mixed number? A. 5 1 C. 3 1 6 6 B. 4 1 6 D. 2 1 6 Equivalent Fractions 2-9 and Mixed Numbers Lesson Quiz for Student Response Systems 5. Which of the following represents the fraction 4 5 as an improper fraction? 6 A. 29 C. 27 6 6 B. 28 6 D. 25 6