Lesson 1: Estimating Sums and Differences

1
Chapter 5
2
Lesson 1 Estimating Sums and Differences

• You know how to estimate when adding and
  subtracting decimals. Now you will learn how to
  estimate when adding and subtracting mixed
  numbers.

3
Examples

• 2 2/3 3/4
• 314
• 1 7/8 2 1/4
• 224
• 4 1/10 - 2 11/12
• 4-31
• 3 9/10 - 1 1/3
• 4-13

• 17 1/2 total
• 2 1/4 3 1/2 Saturday
• 246
• 18-612 rest of the time

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Lesson 2 Adding and Subtracting with Like
Denominators

• You know how to estimate sums and differences of
  fractions and mixed numbers. Now you will learn
  how to find the exact sum or difference of these
  numbers.

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Examples

• 3/8 1/84/81/2
• 9 3/8 7 7/8
• 9716
• 3/87/810/8
• 1 2/81617 2/817 1/4
• 7/10- 3/104/102/5

• 4 1/4 - 2 3/4
• 17/4-11/46/4 1 2/41 1/2
• 3 5/4- 2 3/4 1 2/4 1 1/2
• 3 3/8 6 5/8
• 3/85/88/81
• 369110

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Lesson 5-3 Multistep Problems

• Information
• Question

• 3 day trip
• 1 adult-5 students
• 120 per student
• 0 for adults
• Students paid for adult expenses
• Student expensesadult expenses
• How much did each student contribute?
• What are the steps to solve this problem?

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Lesson 5-3 Multistep Problems

• Procedures (Steps)
• 80 students
• 5 students
• 80/516 adults
• 80 16 96 total
• 120x809,600 collected
• 9,600/96100
• 120-10020
• Each student contributed 20

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Lesson 5-3 Multistep Problems

• GP 1-Information
• 800 departure
• 7 1/2 hrs. total driving time
• Add the total driving time to departure time
• Add 5/6 1 1/3 5/6 7 1/2
• 5/6 1 2/6 5/6 7 3/6
• 8 15/6 82 3/610 3/610 1/2
• 800 after 10 1/2630

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Lesson 5-3 Multistep Problems

• Information
• 21 5/8 lbs backpacks by adults
• 8 1/2 lbs. lighter by students
• 1 1/4 lbs. Canteen

• Solve
• 21 5/8 - 8 1/2
• 21 - 813
• 5/8 - 1/2
• 5/8 - 4/81/8
• 13 1/8-student backpack
• 13 1/8 1 1/4
• 13114
• 1/8 1/4
• 1/82/83/8
• 14 3/8

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Lesson 5-4 Adding and Subtracting with Unlike
Denominators

• You can use what you know about finding the least
  common multiple (LCM) to add and subtract
  fractions with unlike (different) denominators.
• Before you can add or subtract fractions with
  different denominators, you have to write
  equivalent fractions with like denominators. The
  least common denominator (LCD)is the least common
  multiple of the denominators of two or more
  fractions.

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Examples

• 3/4 - 1/3
• 9/12-4/125/12
• 5/12 2/15
• 25/60 8/60 33/6011/20
• 8 2/3 10 3/4
• 8 8/12 10 9/12 18 17/1219 5/12

• 8/9 4/15
• 40/45 12/45
• 52/451 7/45
• 1/9 1/6 1/30
• 10/90 15/90 3/90 28/90 14/45
• 1/2 - 1/10
• 5/10 - 1/104/10 2/5

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Examples

• 9 1/4 2 1/3
• 6 13/15 4 2/33
• 12 3/8 - 3 7/10
• 6 1/7 - 4 2/3

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Lesson 5-5 Solving Addition and Subtraction
Equations

• You know how to solve equations with whole
  numbers and decimals. Now you will solve
  equations with fractions

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Examples

• n 3/51
• n3/5-3/51-3/5
• n1-3/5
• n5/5-3/52/5
• 2 1/3x2 1/18
• 2 1/3-2 1/18x
• 2 6/18 - 2 1/185/18

• a-5/6 1/16
• a1/16 5/6
• a4/48 40/48
• a44/4811/12
• y 2 1/18 3 1/4
• y3 1/4- 2 1/18
• y3 9/36 -2 2/36
• y1 7/36
• 12 7/12 - 7 3/8
• 12 14/24 - 7 9/24
• 5 5/24

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Lesson 5-6 Estimating Products

• You know how to estimate when multiplying
  decimals. Now you will learn how to estimate
  when multiplying fractions and mixed numbers.

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Examples

• 4 7/8 x 18 1/4
• 5x1890
• 1/6 x 539
• 1/6 x 549
• 12 7/8 x 4 2/7
• 13x452

• 1/4 x 122
• 1/4x12030
• 1/6 x 177
• 1/6x18030
• 49 3/4 x 1 5/6
• 50x2100

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Estimating Whole with Fraction

• 185 x 7/91. Round the whole number to a
  compatible number of the denominator.
• 185 - 180 (9-denominator)
• 2. Whole denominator x numerator
• 180 9 x 7140

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Lesson 5-7 Multiplying Fractions and Mixed
Numbers

• You know how to multiply whole numbers and
  decimals. Now you will learn how to multiply
  fractions and mixed numbers.

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Examples

• 1.Numerator x numerator
• 2. Denominator x denominator
• 3. Simplify
• 1/6 x 4/5
• 4/302/15
• 1. Convert mixed fractions to improper fractions
• 5 1/2 x 1 1/3
• 11/2 x 4/3
• 44/67 2/67 1/3

• 11/12 x 48/55
• 528/660
• 1/1 x 4/54/5
• 1. If possible, reduce the first numerator with
  the second denominator
• 2. Reduce the first denominator with the second
  numerator.
• 5 5/6 x 2 4/7
• 35/6 x 18/7
• 5/1 x 3/115/115

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Lesson 5-8 Dividing Fractions and Mixed Numbers

• You know how to multiply fractions and mixed
  numbers. Now you will use the same skills to
  divide fractions and mixed numbers.
• To divide fractions, multiply the dividend by the
  reciprocal of the divisor. Two numbers are
  reciprocals if their product is 1.
• Example
• 3 3/43x4/312/34
• 3/1 x 4/34/14

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Examples

• Use (x) reciprocal for the second fraction
• 6 3/4 1 1/8
• 27/4 9/8
• 27/4 x 8/9
• 3/1 x 2/16/1 6
• 2/3 16
• 2/3 16/1
• 2/3 x 1/16
• 1/3 x 1/81/24

• 3 3/8 2 1/4
• 27/8 9/4
• 27/8 x 4/9
• 3/2 x 1/13/2
• 1 1/2
• 7 1/4 3
• 29/4 3/1
• 29/4 x 1/3
• 29/122 5/12

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Lesson 5-9 Solve a Simpler Problem

• Information
• 1/2 grass, 1/2 flowers, 1/4 of the flowers area
  is roses, 4,000 ft.2 is the area of the roses
• Question
• What is the area of the park?
• Solve
• 4 x 416
• 16 x 2 32

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Examples

• 1. Lot A 28,000 x 1/47,000
• Lot B 32,000 x 1/48,000
• Lot C 36,000 x 1/4 9,000
• 7,0008,0009,00024,000 square feet

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Examples

• 2. Information 480 sq. ft. of material, 1/8 was
  for Mr. J, 1/4 for Mrs. K, 5/8 for school.
• Question How many more on Mrs. K than Mr. J.
• Solve
• Mr. J480 x 1/860
• Mrs. K 480 x 1/4120
• 120-6060 sq. ft.

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Examples

• 3. Information24,000 sq. ft. land, 3 lots, lot 1
  2/3, lot 2lot 3
• Question what is the area of each lot?
• Solve
• Lot 124,000 x 2/316,000
• 24,000-16,0008,000
• Lot 2 and 3 8,000/24,000/each

Lot 1
Lot 2
Lot 3
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Examples

• 4. R148
• R224
• R312
• Pattern is divide by 2
• R412/26
• R56/23
• R63/21.51 1/2

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Examples

• 5. Information 1/2 of books -birds, 1/4 about
  wild flowers, 2 about wildlife
• Questions How many books total?
• Solve
• 1/21/4 x1 x1/4
• 1/2 1/4 2
• 1/2 22
• 4228

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Lesson 5-10 Solving Equations Using Fractions

• You know how to solve equations using
  multiplication and division of whole numbers.
  Now you will learn how to solve equations by
  using multiplication and division of fractions.

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Examples

• 3/4 n 22 1/2
• n22 1/2 3/4
• n45/2 x 4/3
• n15/1 x 2/130
• 1 2/7 n 1 17/28
• 1. Convert to improper fractions
• 9/7n56/28
• 2. Use opposite operation to make the letter be
  by itself
• n56/28 9/7

• 3. Write it as a multiplication and use the
  reciprocal of the second number
• n56/28 x 7/9
• 4. Simplify
• n56/4 x 1/956/36
• n1 20/361 5/9
• 2/5x4/15
• x4/15 2/5
• x4/15 x 5/2
• x2/3 x 1/12/3

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Examples

• 6/7a16
• a16 6/7
• a16/1 x 7/6
• a8/1 x 7/3
• a56/318 2/3
• 3/25c2 3/10
• 3/25c23/10
• c23/10 3/25
• c23/10 x 25/3
• c23/2 x 5/3
• c115/619 1/6

• 1 1/4x10

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Lesson 5-11 Using Fractions and Mixed Numbers

• 20-1/419 3/4
• 247 buy 26 shares
• 9 1/2 is price for BR
• 247 9 1/2
• 247 19/2
• 247/1 x 2/19
• 13/1 x 2/126

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• GSO43 1/2144 1/2