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Lesson Menu Five-Minute Check (over Lesson 6–3) Main Idea Example 1:Solve Using Equivalent Fractions Example 2:Solve Using Equivalent Fractions Example 3:Solve Using Equivalent Fractions Example 4:Make Predictions in Proportional Situations Example 5:Solve Using Unit Rates

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Main Idea/Vocabulary Solve proportions.

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Example 1 Solve Using Equivalent Fractions Find a value for x so the fractions are equivalent. Answer: Since 5 × 7 = 35, x = 35. Solve Since 4 × 7 = 28, multiply the numerator and the denominator by 7. ×7 x

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1.A 2.B 3.C 4.D Example 1 A.18 B.24 C.27 D.36 Solve

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Example 2 Solve Using Equivalent Fractions Answer: Since 4 × 4 = 16, b = 4. Since 5 × 4 = 20, multiply the numerator and the denominator by 4. Solve ×4 b

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1.A 2.B 3.C 4.D Example 2 A.1 B.2 C.3 D.5 Solve.

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Example 3 Solve Using Equivalent Fractions THINK What is 22 divided by 2? The answer is 11. Answer: So, n = 11. Since 38 ÷ 2 = 19, divide each denominator by 2. Solve. ÷2 n

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1.A 2.B 3.C 4.D Example 3 A.4 B.6 C.7 D.9 Solve.

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Example 4 SPORTS Out of the 40 students in a gym class, 12 rate soccer as their favorite sport. Based on this result, predict how many of the 4,200 students in the community would rate soccer as their favorite sport? Write and solve a proportion. Let s represent the number of students who can be expected to rate soccer as their favorite sport. Make Predictions in Proportional Situations Class soccer as favorite sport → total students → Community ← soccer as favorite sport ← total students

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Example 4 Since 40 × 105 = 4,200, multiply the numerator and denominator by 105. Answer: So, 1,260 of the students in the community can be expected to rate soccer as their favorite sport. Make Predictions in Proportional Situations ×105 s

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1.A 2.B 3.C 4.D Example 4 BUSINESS Out of 50 people in one department of a large corporation, 35 stated that they enjoy their job. Based on this result, how many of the 2,400 employees of this corporation can be expected to say that they enjoy their job? A.420 employees B.840 employees C.1,260 employees D.1,680 employees

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Example 5 WAGES Cedric earned $184 for 8 hours of work. At this rate, how much will he earn for 15 hours of work? Step 1Set up the proportion. Let d represent the dollar amount Cedric will earn for 15 hours of work. Solve Using Unit Rates Step 2Find the unit rate. ÷8÷8 ÷8÷8 Find an equivalent fraction with a denominator of 1.

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Example 5 Step 3Rewrite the proportion using the unit rate and solve using equivalent fractions. Answer: So, the value of d is $345. At the given rate, Cedric will earn $345 for 15 hours of work. Solve Using Unit Rates ×15 ÷8

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1.A 2.B 3.C 4.D Example 5 A.30 dogs B.36 dogs C.48 dogs D.56 dogs DOGS Marci walked 24 dogs in 6 days. At this rate, how many dogs will she walk in 14 days?

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End of the Lesson

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Resources Five-Minute Check (over Lesson 6–3) Image Bank Math Tools Ratios and Tangrams Ratios

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1.A 2.B Five Minute Check 1 Determine if the quantities in the following ratio are proportional. Explain your reasoning and express the proportional relationship as a proportion. $35 earned after 5 hours; $63 earned after 9 hours (over Lesson 6-3) A.Yes; The fractions are equivalent;. B.No; The fractions are not equivalent. h 5 h

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1.A 2.B Five Minute Check 2 Determine if the quantities in the following ratio are proportional. Explain your reasoning and express the proportional relationship as a proportion. 480 Calories burned in 60 minutes; 210 Calories burned in 30 minutes (over Lesson 6-3) A.Yes; The fractions are equivalent; B.No; The fractions are not equivalent.

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1.A 2.B Five Minute Check 3 Determine if the quantities in the following ratio are proportional. Explain your reasoning and express the proportional relationship as a proportion. $3 for 12 blank CDs; $5 for 25 blank CDs (over Lesson 6-3) A.Yes; The fractions are equivalent; B.No; The fractions are not equivalent.

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1.A 2.B Five Minute Check 4 Determine if the quantities in the following ratio are proportional. Explain your reasoning and express the proportional relationship as a proportion. 18 calculators for 36 students; 13 calculators for 26 students (over Lesson 6-3) A.Yes; The fractions are equivalent; B.No; The fractions are not equivalent.

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1.A 2.B 3.C 4.D Five Minute Check 5 A.30 boys, 45 girls B.36 boys, 60 girls C.32 boys, 44 girls D.27 boys, 35 girls The ratio of boys to girls in the school spirit club is 3 to 5. Which of these shows possible numbers of the boys and girls in the spirit club? (over Lesson 6-3)

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