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Understanding Proportions and Solving Problems with Cross Products

In this lesson, we explore the concept of proportions and how to effectively solve them. We’ll learn to find cross products to determine if two ratios form a proportion. Key examples will demonstrate how to solve various proportion problems using simple algebraic techniques. Students are encouraged to complete the assigned homework on page 300, exercises 2-40 (even), which reinforces this important concept. By the end of the lesson, learners will be equipped to recognize and apply proportions in real-world scenarios.

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Understanding Proportions and Solving Problems with Cross Products

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  1. Lesson 6-2 Proportions

  2. Obj: 1) To solve proportions2) To use proportions to solve problems • HWK: p 300 2-40 even • Vocab: 1) proportion • 2) cross products – products obtained after cross multiplying 2 ratios in a proportion

  3. Key Concepts: Cross Products • In a proportion, the cross products are equal • Arithmetic Algebra • 6 = 8a = c • 9 12 b d • 6 · 12 = 9 · 8 ad = bc where b≠0 and • d ≠0

  4. Tell whether the two ratios form a proportion. Explain • Ex 1) 3 , 21 Ex 2) 15 , 5 • 5 35 20 7

  5. Solve each proportion • Ex 3) 2 = y Ex 4) 22 = 6 • 7 14 d 21

  6. Ex 5) 7 = x • 12 30

  7. Ex 6) 100 rods is about 275 fathoms. About how many fathoms is 25 rods?

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