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Name ——————————————————————— SECTION 3 Date ———————————— Ratio, Proportion, and Percent Lesson 3: Writing Proportions a b c d It is written as a fraction equal to a fraction, } 5 }. Two fractions are equal if, when written in simplest form, they have the same numerator and denominator. A proportion is an equation stating that two ratios are equal. EXAMPLE 1 1 Write two different proportions using the ratio }2 . Write equivalent fractions: Write proportions: }5}5} 1 2 132 232 2 4 }5} 1 2 133 233 3 6 }5} }5}5} EXAMPLE 2 1 2 2 4 1 2 3 6 HINT Multiplying or dividing the numerator and denominator by the same number creates an equal fraction. Can you write a proportion using the ratios 6 8 2 3 } and }? Copyright © by McDougal Littell, a division of Houghton Mifflin Company. 6 332 3 2 5} 5 }4 and }3 8 432 2 3 No; }4 Þ }3, so you cannot write a proportion. } Practice: First Try Write two different proportions using the given ratio. 1 1. } 3 2 2. } 5 3 3. } 4 4 4. } 7 1 5. } 12 5 6. } 8 3 7. } 3 5 8. } 2 3. RATIO, PROPORTION 3. Writing Proportions Write fractions in simplest form, then compare: Tell whether you can write a proportion using the two ratios. 8 3 9 3 1 2 8 4 } 9. }, } 10. }, } 11. }, } 12. } 9 , 27 5 10 12 2 15 5 1 } 4 13. } 3 , 12 9 16 14. }, } 8 18 8 } 2 15. } 4, 1 10 } 3 16. } 15 , 4 McDougal Littell Middle School Math Remediation Book Lesson 3.3 69 Name ——————————————————————— Date ———————————— Practice: Second Try 1 1. } 4 2. } 5 3 2 3. } 3 4. } 4 5. } 10 6. } 5 6 9 7. } 4 8. } 3 9. } 1 10. } 7 7 5 11. } 8 12. } 3 13. } 4 14. } 4 3 1 15. } 5 16. } 20. }, } 1 6 4 5 7 6 Tell whether you can write a 1 3 17. }, } 18. 3 9 proportion using the two ratios. 6 2 4 16 }, } 19. }, } 10 5 1 4 12 4 21. }, } 9 3 22. }, } 6 4 6 4 1 5 23. }, } 2 10 24. }, } 3 6 25. }, } 8 24 26. }, } 5 10 1 1 3 15 27. }, } 4 20 28. }, } 5, 8 29. } } 5 8 30. }, } 10 90 11 99 9 1 31. }, } 3 3 32. }, } Extend Your Skills 33. A seventh grade math class has 8 boys and 12 girls. An eighth grade math class has 10 boys and 15 girls. For each class, write the ratio of boys to girls. Can you write a proportion using these two ratios? Explain what this means for the classes. Puzzle Shade each box in the first grid that contains a fraction which forms a 4 proportion with }5. Shade each box in the second grid that contains a fraction which forms a proportion 2 with }3 . When done correctly, you will form the two-digit number of bathrooms in the White House. } 32 40 } 28 35 } } 12 16 } 50 40 } } 15 20 } 36 45 } } 8 12 } 28 30 } 40 50 } 16 20 } } 70 8 9 McDougal Littell Middle School Math Remediation Book Lesson 3.3 20 25 12 15 24 30 8 10 48 60 24 36 10 } 15 16 } 24 6 } 12 12 } 18 } 6 9 12 } 21 20 } 30 25 } 30 8 } 12 } 18 27 15 } 12 4 } 6 30 } 45 14 } 21 } 1 5 5 10 12 4 20 5 4 16 3 12 32 8 16 4 Copyright © by McDougal Littell, a division of Houghton Mifflin Company. 3. RATIO, PROPORTION 3. Writing Proportions Write two different proportions using the given ratio. !NSWER+EY -iVÌÊÎÊ,>Ì]Ê*À«ÀÌ]Ê>`Ê*iÀViÌ iÃÃÊÎÊ««°ÊÈÇä® *À>VÌVi\Ê ÀÃÌÊ/ÀÞÊÊÊ £°n°3AMPLEANSWERSAREGIVENÊÊÊ £°] z] z] z] zÊÓ°] z] z] z] zÊΰ] z] z] z] zÊ{°] z] z] z] zÊx°] z] z] z] zÊ È°] z] z] z] zÊÇ°] z] z] z]zÊÊn°] z] z] z] zÊ °YESÊÊ£ä°NOÊÊÊ££°YESÊÊ£Ó°NOÊÊʣΰYESÊÊ£{°NOÊÊÊ£x°YESÊʣȰNO -iV`Ê/ÀÞÊÊ £°£È°3AMPLEANSWERSAREGIVENÊÊÊ £°] z] z] z] zÊÊÓ°]z]z]z]zÊΰ]z]z]z]zÊ{°]z]z]z]zÊx°Ê]z]z]z]zÊ È°]z] z]z]zÊÇ°]z]z]z]zÊn°]z]z]z]zÊ°]z]z]z]zÊ£ä°]z]z]z]zÊ ££°]z] z]z]z£Ó°]z]z]z]zʣΰ]z]z]z]z£{°]z]z]z]zÊÊ £x°]z] z]z]zʣȰ]z]z]z]z £Ç°YESÊÊ£n°NOÊÊÊ£°YESÊÊÓä°NOÊÊÊÓ£°YESÊÊÊÓÓ°YESÊÊÊ ÓΰYESÊÊÓ{°NOÊÊÊÓx°NOÊÊÊÓÈ°NOÊÊÊÓÇ°YESÊÊÊ Ón°YESÊÊÓ°YESÊÊÊÎä°YESÊÊΣ°NOÊÊÊÎÓ°YESÊÊÊ Îΰ] zOR]z]zOR]z YES4HECLASSESHAVETHESAMERATIOOFBOYSTOGIRLS *Õââi