6 3 Solving Proportions Using Cross Products Skill

6. 3 Solving Proportions Using Cross Products Every pair of ratios has two cross

6. 3 Solving Proportions Using Cross Products EXAMPLE 1 Determining if Ratios Form a

6. 3 Solving Proportions Using Cross Products You can use the multiplication property of

6. 3 Solving Proportions Using Cross Products Property Words The cross products of a

6. 3 Solving Proportions Using Cross Products EXAMPLE 2 Writing and Solving a Proportion

6. 3 Solving Proportions Using Cross Products Methods for Solving a Proportion SUMMARY To

6. 3 Solving Proportions Using Cross Products Lesson Quiz Tell whether the ratios form

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6. 3 Solving Proportions Using Cross Products Skill Check Lesson Presentation Lesson Quiz

6. 3 Solving Proportions Using Cross Products Skill Check 1. 36 • 7 = ? 252 2. 61 • 4 = ? 244 3. 83 • 5 = ? 415 4. 47 • 6 = ? 282

6. 3 Solving Proportions Using Cross Products Every pair of ratios has two cross products. A cross product of two ratios is the product of the numerator of one ratio and the denominator of the other ratio. 3 6 , 5 10 Ratios: Cross products: 3 • 10 3 2 6 , 3 11 5 • 6 2 • 11 3 • 6 6 Notice that for the ratios 5 and 10 , the ratios are equal and their cross products 2 6 are also equal. For the ratios and , the ratios are not equal, and neither are 3 11 their cross products. You can use cross products to tell whether two ratios form a proportion. If the cross products are equal, then the ratios form a proportion.

6. 3 Solving Proportions Using Cross Products EXAMPLE 1 Determining if Ratios Form a Proportion Tell whether the ratios form a proportion. Write proportion. Form cross products. 306 = 306 ANSWER Multiply. The ratios form a proportion.

6. 3 Solving Proportions Using Cross Products EXAMPLE 1 Determining if Ratios Form a Proportion Tell whether the ratios form a proportion. ANSWER The ratios form a proportion. 12 32 , 20 50 12 ? 32 = 20 50 Write proportion. 12 • 50 =? 20 • 32 600 = 640 ANSWER Form cross products. Multiply. The ratios do not form a proportion.

6. 3 Solving Proportions Using Cross Products You can use the multiplication property of equality to demonstrate an important property about the cross products of a proportion. a = c b d 1 1 Given. 1 a bd c bd • = • b 1 d 1 1 ad = cb Multiply each side by bd. Divide out common factors. Simplify. This result proves the cross products property.

6. 3 Solving Proportions Using Cross Products Property Words The cross products of a proportion are equal. 2 6 Numbers Given that 5 = 15 , you know that 2 • 15 = 5 • 6. Algebra If a c = , where b = 0 and d = 0, then ad = bc. b d You can use the cross products property to solve proportions.

6. 3 Solving Proportions Using Cross Products EXAMPLE 2 Writing and Solving a Proportion Hair Growth Human hair grows about 0. 7 centimeter in 2 weeks. How long does hair take to grow 14 centimeters? SOLUTION 0. 7 14 = x 2 0. 7 • x = 2 • 14 Length of hair grown Number of weeks Cross products property 0. 7 x = 28 Multiply. 0. 7 x = 28 = 0. 7 Divide each side by 0. 7. x = 40 ANSWER Simplify. Hair takes about 40 weeks to grow 14 centimeters.

6. 3 Solving Proportions Using Cross Products Methods for Solving a Proportion SUMMARY To solve the proportion 5 x = , use one of the following: 12 36 Equivalent ratios 5 x 12 3 36 5 3 15 12 36 Algebra 5 x 36 • 12 = 36 • 36 15 = x Multiply each side by 36. Simplify. Cross products 5 • 36 = 12 x 15 = x Cross products property Divide each side by 12.

6. 3 Solving Proportions Using Cross Products Lesson Quiz Tell whether the ratios form a proportion. 1. yes 3. no Solve the proportion. 3. b=5 4. f = 18 5. Challenge For what whole number values of a less than 25 will the value of x in the proportion integer? a = 2, 8, 18 be an