MODULE 5

• DISCIPLINE • GOOD TASTE • EXCELLENCE
• Writer: Daren V. Perez
• Cover Illustrator: Joel J. Estudillo
• Department of Education National Capital Region SCHOOLS DIVISION OFFICE MARIKINA CITY
• MATHEMATICS Quarter 3: Module 5 Illustrating Proportions and Problems Solving Involving Proportions
• Proportion


  A statement that two ratios are equal
• Proportion


  • Can be written as two equal fractions or using a colon
• Determining if two ratios are in proportion

  1. Check if cross-product is equal

  2. Check if simplified ratios are equal

  3. Check if product of means and extremes is equal
• Cross-Product Property


  If a/b = c/d, then ad = bc; where b ≠ 0 and d ≠ 0
• Reciprocal Property


  If a/b = c/d, then b/a = d/c; where a ≠ 0 and c ≠ 0
• Alternation Property


  If a/b = c/d, then a/c = b/d; where c ≠ 0 and d ≠ 0
• Addition Property


  If a/b = c/d, then (a+b)/b = (c+d)/d; where b ≠ 0 and d ≠ 0
• Subtraction Property


  If a/b = c/d, then (a-b)/b = (c-d)/d; where b ≠ 0 and d ≠ 0
• Sum Property


  If a/b = c/d, then a/b = c/d = (a+c)/(b+d) = k; where b ≠ 0, d ≠ 0, and k is the constant of proportionality
• Proportion 1


  • 4/6 = 8/12
• Proportion 2


  • 2x/3 = 6x/9
• Properties of Proportion

  • Reciprocal Property
  • Alternation Property
  • Addition Property
  • Subtraction Property
  • Sum Property
• Reciprocal Property


  If x/w = y/z, then w/x = z/y; where w ≠ 0 and z ≠ 0
• Alternation Property


  If x/w = y/z, then x/y = w/z; where w ≠ 0 and z ≠ 0
• Addition Property


  If x/w = y/z, then (x+w)/w = (y+z)/z; where w ≠ 0 and z ≠ 0
• Subtraction Property


  If x/w = y/z, then (x-w)/w = (y-z)/z; where w ≠ 0 and z ≠ 0
• Sum Property

  If x/w = y/z, then x/w = y/z = k; where x/w, y/z and k are all equal
• The Cross-Product Property is applied to the statement: If u/5 = v/7, then 5v = 7u
• The Subtraction Property is applied to the statement: If 9/7 = r/s, then (r-s)/s = 2/7
• The Sum Property is applied to the statement: If 4/6 = 6/9, then 4/6 = 6/9 = 10/15
• The expression 24/15 = 16/10 is a proportion
• The expression 2x/3y = 6x/9y is a proportion
• The expression 18/30 = 10/20 is not a proportion
• The expression 7/9 = 13/15 is not a proportion
• The expression 20/30 = 20/30 is a proportion
• Ms. Magalong's garden


  Rectangular<|>Area of 300 square meters<|>Perimeter of 80 meters
• Scoring Rubrics

  • Understands the Problem
  • Uses Representations
  • Answers the Problem
• Understands the Problem


  • Demonstrates a clear understanding of the problem
  • Accurately identifies key elements of the problem and the relationship of these elements to each other
• Uses Representations


  • Uses a representation that is unusual in its mathematical precision
  • Uses a representation that clearly depicts the problem
  • Uses a representation that gives some important information about the problem
  • Uses a representation that gives little or no significant information about the problem
• Answers the Problem


  • The answer is correct with complete solution and explanation
  • The answer is correct with complete solution but no explanation
  • The answer is correct but the solution is incomplete
  • The answer is incorrect or no answer
• A rectangular field has an area of 1000 m2 and the ratio of the width to the length is 2:5
• Equations

  • 5𝑥 + 2𝑥 = 1000
  • (2𝑥)(5𝑥) = 1000
  • 5𝑥 − 2𝑥 = 1000
  • 
    

  2𝑥

  5𝑥 = 100
• Dimensions


  • 10 m and 100 m
  • 20 m and 50 m
  • 20 m and 80 m
  • 30 m and 40 m
• There are 4800 students in Parang High School. The ratio of boys to girls in the school is 3:5
• Equations

  • 3𝑥 + 5𝑥 = 4800
  • 3𝑥 − 5𝑥 = 4800
  • 5𝑥 − 3𝑥 = 4800
  • 
    

  5𝑥

  3𝑥 = 4800