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9 15 9 3 15 3 = What are we going to do? CFU Students, you already know how to generate equivalent fractions. Now, we will use that skill to add fractions with unlike denominators. Make Connection We will add fractions with unlike denominators. Learning Objective Introduction 2 3 numerator denominator Fraction Which fraction is equivalent to ? Equivalent fractions are fractions that have the same value. 2525 Which fraction is equivalent to ? 1212 = 3535 4 10 = 4 2 10 2 = 2525 5 10 = 5 5 10 5 = 1212 2828 = 22822282 = 1414 Common Core Standards 7.NS.1 – 7.NS.3 Prerequisite Skills Apply and extend previous understandings of addition, subtraction, multiplication, and division of integers (AND other rational numbers); Students will reinforce skills learned in 6 th grade.

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6 15 What are we going to do? CFU Students, you already know how to generate equivalent fractions. Now, we will use that skill to subtract fractions with unlike denominators. Make Connection We will subtract fractions with unlike denominators. Learning Objective Introduction 2 3 numerator denominator Fraction 12 20 12 4 20 4 = Which fraction is equivalent to ? Equivalent fractions are fractions that have the same value. 3535 Which fraction is equivalent to ? 1212 = 3535 = 6 3 15 3 = 2525 6 18 = 6 6 18 6 = 1313 2424 = 22422242 = 1212 Common Core Standards 7.NS.1 – 7.NS.3 Prerequisite Skills Apply and extend previous understandings of addition, subtraction, multiplication, and division of integers (AND other rational numbers); Students will reinforce skills learned in 6 th grade.

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What are we going to do? CFU Students, you already know how to find the least common denominator of fractions. Now, we will use that skill to add fractions with unlike denominators. Make Connection We will add fractions with unlike denominators. Learning Objective Activate Prior Knowledge The least common denominator (LCD) is the lowest multiple shared by a set of denominators. Find the least common denominator of the fractions below. 1. 2. 5: 5, 10, 15, 20 2: 2, 4, 6, 8, 10 The LCD of and is 10. 2 3 numerator denominator Fraction 2: 2, 4, 6, 8 3: 3, 6, 9, 12 The LCD of and is 6. Common Core Standards 7.NS.1 – 7.NS.3 Prerequisite Skills Apply and extend previous understandings of addition, subtraction, multiplication, and division of integers (AND other rational numbers); Students will reinforce skills learned in 6 th grade.

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What are we going to do? CFU Students, you already know how to find the least common denominator of fractions. Now, we will use that skill to subtract fractions with unlike denominators. Make Connection The least common denominator (LCD) is the lowest multiple shared by a set of denominators. We will subtract fractions with unlike denominators. Learning Objective Activate Prior Knowledge 2: 2, 4, 6, 8 3: 3, 6, 9, 12 Find the least common denominator of the fractions below. 1. 2. 5: 5, 10, 15, 20 2: 2, 4, 6, 8, 10 The LCD of and is 6. The LCD of and is 10. 2 3 numerator denominator Fraction Common Core Standards 7.NS.1 – 7.NS.3 Prerequisite Skills Apply and extend previous understandings of addition, subtraction, multiplication, and division of integers (AND other rational numbers); Students will reinforce skills learned in 6 th grade.

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Concept Development 2 3 numerator denominator Fraction Fractions with unlike denominators have a different number of equal parts. Fractions with like denominators have the same number of equal parts. To add fractions, both fractions must have like denominators. To add fractions with unlike denominators use the least common denominator (LCD) to create equivalent 1 fractions with like denominators. Which pair of fractions is ready to be added? How do you know? A B In your own words, how do you add fractions with unlike denominators? “To add fractions with unlike denominators ________.” CFU 4 10 5 9 2 5 The LCD of and 1 2 is 10. Adding Fractions with Unlike Denominators 2 5 1 2 Equivalent Fractions 2 2 2 5 4 10 = 5 5 1 2 5 = 1 equal value Vocabulary

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Which pair of fractions is ready to be subtracted? How do you know? A B In your own words, how do you subtract fractions with unlike denominators? “To subtract fractions with unlike denominators ________.” CFU Concept Development 2 3 numerator denominator Fraction Subtracting Fractions with Unlike Denominators 6 10 5 1 3 5 1 2 3 5 The LCD of and 1 2 is 10. Equivalent Fractions 2 2 3 5 × 6 10 = 5 5 1 2 × 5 = Fractions with unlike denominators have a different number of equal parts. Fractions with like denominators have the same number of equal parts. To subtract fractions, both fractions must have like denominators. To subtract fractions with unlike denominators use the least common denominator (LCD) to create equivalent fractions with like denominators. 2323 2525 2323 1313

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Skill Development/Guided Practice 1 explain 2 answer to an addition problem Vocabulary Find a like denominator by multiplying both denominators. Create equivalent fractions with like denominators. Add fractions. Hint: Add the numerators, keep the denominator the same. Interpret 1 the sum 2. “____ plus ____ equals _____.” Add fractions with unlike denominators. 1 2 3 4 To add fractions, both fractions must have like denominators. How did I/you find a like denominator? How did I/you create equivalent fractions? How did I/you add fractions? CFU 1 2 3 2×32×3 1. 1212 + 1313 = 1×32×31×32×3 + 1×23×21×23×2 = 3636 + 2626 = 5656 2×52×5 2. 1212 + 2525 = 1×52×51×52×5 + 2×25×22×25×2 = 5 10 + 4 10 = 9 10 6×46×4 3. 1616 + 3434 = 1×46×41×46×4 + 3×64×63×64×6 = 4 24 + 18 24 = 22 24 10 × 3 4. 3 10 + 1313 = 3 × 3 10 × 3 + 1 × 10 3 × 10 = 9 30 + 10 30 = 19 30

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Skill Development/Guided Practice To subtract fractions, both fractions must have like denominators. 1 explain 2 answer to a subtraction problem Vocabulary Find a like denominator by multiplying both denominators. Create equivalent fractions with like denominators. Subtract fractions. Hint: subtract the numerators, keep the denominator the same. Interpret 1 the difference 2. “____ minus ____ equals _____.” Subtract fractions with unlike denominators. 1 2 3 4 How did I/you find a like denominator? How did I/you create equivalent fractions? How did I/you subtract fractions? CFU 1 2 3 2×32×3 1. 1212 – 1313 = 1×32×31×32×3 – 1×23×21×23×2 = 3636 – 2626 = 1616 2×52×5 2. 1212 – 2525 = 1×52×51×52×5 – 2×25×22×25×2 = 5 10 – 4 10 = 1 10 6×46×4 3. 3434 – 1616 = 3×64×63×64×6 – 1×46×41×46×4 = 18 24 – 4 24 = 14 24 3 × 10 4. 1313 – 3 10 = 1 × 10 3 × 10 – 3 × 3 10 × 3 = 10 30 – 9 30 = 1 30

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5. Sierra had of a pint of water left in her water bottle. She poured another of a pint more water into her bottle. How much water does Sierra have? __________________________________________________________________ Skill Development/Guided Practice (continued) 4: 4, 8, 12, 16 2: 2, 4, 6, 8 6. Theodore bought of a pound of apples and of a pound of oranges. How much fruit did he buy? __________________________________________________________________ 3: 3, 6, 9, 12, 15 5: 5, 10, 15, 20 Sierra has of a pint of water. Theodore bought of a pound of fruit Adding Fractions How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 2 1 3 4 5 Find the least common denominator. Hint: Find the lowest shared multiple. Create equivalent fractions with like denominators. Hint: Use the least common denominator. Add fractions. Hint: Add the numerators, keep the denominators the same. Reduce the sum, if possible. Interpret the sum. “____ plus ____ equals _____.” Add fractions with unlike denominators. 1 2 3 4 a

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Skill Development/Guided Practice (continued) 5. Sherry bought of a pound of milk chocolate and of a pound of white chocolate. How much more milk chocolate than white chocolate does Sherry have? 4: 4, 8, 12, 16 2: 2, 4, 6, 8 6. Tom bought of a pound of cauliflower and of a pound of celery. How much more cauliflower than celery did he buy? ×× 3: 3, 6, 9, 12, 15 5: 5, 10, 15, 20 ×× Sherry bought ____ of a pound more ______________ than _______________. milk chocolate white chocolate Tom bought ____ of a pound more __________ than ___________. cauliflower celery How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 2 1 3 4 5 required = needed relevant = has to do with problem reasonableness = possible

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1 2 Relevance To add fractions, both fractions must have like denominators. Adding fractions will help solve real-life problems. There is of a pie left. of one pie was left over after the party. There was of another pie left over. How much pie is there? += += There is of the pie left. of the pie was left over after the party. Erick just ate of the pie. How much pie is left? += = – = Subtracting fractions will help solve real-life problems.

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2. Carmen bought of a pound of grapes and of a pound of nectarines. How many pounds of fruit did Carmen buy? __________________________________________________________ Find the least common denominator. Hint: Find the lowest shared multiple. Create equivalent fractions with like denominators. Hint: Use the least common denominator. Add fractions. Hint: Add the numerators, keep the denominators the same. Reduce the sum, if possible. Interpret the sum. “____ plus ____ equals _____.” Add fractions with unlike denominators. 1 2 3 4 a What did you learn today about adding fractions with unlike denominators? (Pair-Share) Use words from the word bank. Skill Closure Access Common Core Summary Closure To add fractions, both fractions must have like denominators. Which pair of fractions is ready to be added? Explain your answer. A B 1. 4: 4, 8, 12, 16 8: 8, 16, 24, 32 4: 4, 8, 12, 16 8: 8, 16, 32, 40 Carmen bought pound of fruit Word Bank fractions like/unlike denominator least common denominator equivalent

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2. Carmen bought of a pound of grapes and of a pound of nectarines. How many more pounds of nectarines than grapes did Carmen buy? What did you learn today about subtracting fractions with unlike denominators? (Pair-Share) Use words from the word bank. Access Common Core Summary Closure Read the problem and identify fractions, if necessary. (circle) Find the least common denominator. Hint: Find the lowest shared multiple. Create equivalent fractions with like denominators. Hint: Use the least common denominator. Subtract fractions. Hint: Subtract the numerators, keep the denominators the same. Reduce the difference, if possible. Interpret the difference. “___ minus ____ equals ____.” Subtract fractions with unlike denominators. 1 2 3 4 5 a To subtract fractions, both fractions must have like denominators. Skill Closure Which pair of fractions is ready to be subtracted? Explain your answer. A B 1. 4: 4, 8, 12, 16 8: 8, 16, 24, 32 ×× 4: 4, 8, 12, 16 2: 2, 4, 6, 8 × × Carmen bought ____ of a pound more __________ than ___________. grapes nectarines Word Bank fractions like/unlike denominator least common denominator equivalent

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Independent Practice To add fractions, both fractions must have like denominators. 6: 6, 12, 18, 24 1. 3: 3, 6, 9, 12 2. 3. The Smith family bought some pizzas. One pizza had left over. The other had left. How much pizza is there left over? __________________________________________________________________ 8: 8, 16, 24, 32 12: 12, 24, 36, 48 7: 7, 14, 21, 28, 35 4: 4, 8, 12, 16, 20, 24, 28 There is of the pizza left over. Find the least common denominator. Hint: Find the lowest shared multiple. Create equivalent fractions with like denominators. Hint: Use the least common denominator. Add fractions. Hint: Add the numerators, keep the denominators the same. Reduce the sum, if possible. Interpret the sum. “____ plus ____ equals _____.” Add fractions with unlike denominators. 1 2 3 4 a

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Independent Practice To subtract fractions, both fractions must have like denominators. 6: 6, 12, 18, 24 1. 3: 3, 6, 9, 12 2. 3. The Smith family bought a pizza. Jason ate of the pizza and Jamie ate of the pizza. How much more pizza did Jason eat than Jamie? × × 8: 8, 16, 24, 32 12: 12, 24, 36, 48 × × 7: 7, 14, 21, 28, 35 4: 4, 8, 12, 16, 20, 24, 28 ×× _________ ate ____ of a pizza more than _________. Jamie Jason Read the problem and identify fractions, if necessary. (circle) Find the least common denominator. Hint: Find the lowest shared multiple. Create equivalent fractions with like denominators. Hint: Use the least common denominator. Subtract fractions. Hint: Subtract the numerators, keep the denominators the same. Reduce the difference, if possible. Interpret the difference. “___ minus ____ equals ____.” Subtract fractions with unlike denominators. 1 2 3 4 5 a

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Periodic Review 1 Access Common Core 1. 2. 3. Geoff has of a pound of cashews and buys of a pound of pecans. How many pounds of nuts does he have? __________________________________________________________ Anita added the fractions below. Her teacher, Mrs. Caudill, says that her answer is incorrect. Explain the mistake that Anita made. 12: 12, 24, 36 4: 4, 8, 12, 16 6: 6, 12, 18, 24, 32 12: 12, 24, 36, 48 4: 4, 8, 12, 16 6: 6, 12, 18 Geoff has of a pound of nuts Anita did not make sure that the fractions had like denominators before adding. Instead, she just added both the numerators and denominators.

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Periodic Review 1 Access Common Core 12: 12, 24, 36 1. 4: 4, 8, 12, 16 × × 2. 6: 6, 12, 18, 24, 32 12: 12, 24, 36, 48 × × 3. Geoff has of a pound of cashews and buys of a pound of pecans. How many more pounds of cashews does he have than pecans? Geoff has ____ of a pound more ___________ than __________. 4: 4, 8, 12, 16 6: 6, 12, 18 ×× Abdul subtracted the fractions below. His teacher, Mrs. Treadwell, says that his answer is incorrect. Explain the mistake that Abdul made. pecans cashews ¼ was not converted to a common denominator first. Also, denominators are incorrectly subtracted.

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Periodic Review 2 Access Common Core 1. 2. 10: 10, 20, 30, 40 4: 4, 8, 12, 16, 20 For each addition problem, place a check mark in the box to classify the sum as less than ½ or greater than ½. 6: 6, 12, 18, 24 8: 8, 16, 24 less than ½greater than ½.

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Periodic Review 2 Access Common Core 6: 6, 12, 18, 24 1. 8: 8, 16, 24 2. × × 10: 10, 20, 30, 40 4: 4, 8, 12, 16, 20 × × Horatio added the fractions below. Some of his answers are incorrect. Circle all the incorrect answers and write the correct solutions.

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Periodic Review 3 Access Common Core 1. 2. 12: 12, 24, 36 4: 4, 8, 12, 16 5: 5, 10, 15, 20 10: 10, 20, 30 Choose Yes or No to show whether each choice represents the sum of. YesNo

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Periodic Review 3 (THIS PAGE IS HOMEWORK) Access Common Core 12: 12, 24, 36 1. 4: 4, 8, 12, 16 2. × × 5: 5, 10, 15, 20 10: 10, 20, 30 × × Choose Yes or No to show whether each choice is equal to the difference of. YesNo

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