PreAlgebra III Chapter 6-3: Multiplying Fractions

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PreAlgebra IIIChapter 6-3 Multiplying
Fractions

• Michelle A. OMalley
• League Academy of Communication Arts
• Greenville, South Carolina

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Standards

• 8-1.1 Generate and solve complex, abstract
  problems that involve modeling physical, social,
  or mathematical phenomena.
• 8-1.6 Use correct and clearly written/spoken
  words, variables, and notation to communicate
  about significant mathematical tasks.
• 8-2.2 Understand the effect of multiplying and
  dividing a rational number by another rational
  number.

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Essential Question

• Can you explain what compatible numbers are?
• How do you multiply and divide rational number
  problems involving fractions?

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Review Quiz

• Estimate the products or quotients
• 1. 27.2 x 8.1
• 2. 75.61 1.9
• 3. (1/9)(35)
• 4. 156 12 14/15
• 5. 68.04 0.96

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Multiplying Fractions

• When you multiply fractions you multiply the
  numerators and then multiply the denominators.
• For Example,
• For fractions a/b and c/d, where b ? 0, a/b x c/d
  ac/bd
• Such as, 5/12 x 2/9 (5x2)/(12x9) 10/108 or
  5/24

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Multiplying Fractions

• If the fractions have common factors in the
  numerators and denominators, you can simplify
  before you multiply.
• For example, 5 x 2
• 12 9
• The 2 and 12 have common factors
• Therefore, you can multiply smaller numbers
• 5 x 1 5 and 6 x 9 54
• For a final answer of 5/54

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Multiplying Fractions Area Model

• You can use grid paper to make an area model for
  multiplication of fractions. The diagram below
  models the product of 2/3 x 5/6. Notice that the
  rectangle has three rows to represent thirds and
  two rows are shaded yellow to represent 2/3. The
  rectangle has six columns to represent sixths.
  Five columns are shaded blue to represent 5/6.
  Notice that the overlapping area, 10/18 of the
  rectangle is shaded green. The product of 2/3
  and 5/6 is 10/18 or 5/9.

5/6
2/3
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Work Cited

• Alban, Yuria, et. al. Pre-Algebra An Integrated
  Transition to Algebra Geometry. New
  York Glencoe/McGraw-Hill, 2001.
• Greenville County Schools Math Curriculum Guide
• Van de Walle Teaching Student Centered
  Mathematics Grades 5-8. Pearson. New York. 2006
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