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Comparing and Ordering Fractions

Comparing and Ordering Fractions. Section 4.5. Kayaking Julie and Seth are kayaking down a river. Julie kayaks a distance of mile and Seth kayaks mile. Who kayaked the greater distance?. 7. 3. —. —. 10. 4. In the Real World. Comparing and Ordering Fractions.

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Comparing and Ordering Fractions

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  1. Comparing and Ordering Fractions Section 4.5

  2. Kayaking Julie and Seth are kayaking down a river. Julie kayaks a distance of mile and Seth kayaks mile. Who kayaked the greater distance? 7 3 — — 10 4 In the Real World Comparing and Ordering Fractions

  3. Kayaking Julie and Seth are kayaking down a river. Julie kayaks a distance of mile and Seth kayaks mile. Who kayaked the greater distance? 7 3 — — 10 4 In the Real World Comparing and Ordering Fractions You can compare fractions by using the least common denominator. The least common denominator (LCD) of two or more fractions is the least common multiple of the denominators.

  4. BOOK NOTE Comparing and Ordering Fractions Comparing Two or More Fractions Find the LCD of the fractions. Use the LCD to write equivalent fractions. Compare the numerators.

  5. Comparing and Ordering Fractions To find who kayaked a greater distance, as described above, you need to compare and . 1 EXAMPLE 1 3 2 7 7 7 3 — — — — 10 10 10 4 15 14 15 14 × 2 ×2 × 5 ×5 = = 3 3 20 20 20 20 — — Julie: Seth: = = 4 4 7 3 < , so < . 10 4 Comparing Fractions Using the LCD Find the LCD of the fractions. Because the LCM of 10 and 4 is 20, the LCD is 20. Use the LCD, 20, to write equivalent fractions. Compare the numerators: ANSWER Seth kayaked the greater distance.

  6. Comparing and Ordering Fractions so < < < . 2 EXAMPLE Order the fractions , , , and from least to greatest. 3 2 — — 1 3 8 — — 3 6 4 3 2 1 2 3 1 2 3 3 1 3 — — — — — — — — 4 8 4 6 6 3 3 8 × 3 ×3 × 6 ×6 × 8 ×8 × 4 ×4 16 18 16 18 2 3 9 4 4 1 9 3 — — — — — — — — — — — — = = = = = = = = 24 24 24 24 24 24 24 24 3 6 8 4 Compare the numerators: < < < , 1 3 2 3 — — — — From least to greatest, the fractions are , , , . 6 8 3 4 Ordering Fractions Using the LCD Find the LCD of the fractions. Because the LCM of 3, 8, 6 and 4 is 24, the LCD is 24. Use the LCD to write equivalent fractions. ANSWER

  7. Comparing and Ordering Fractions Use approximation to tell which fraction is greater, or . Notice that and are both approximately equal to because the numerator of each fraction is about half the denominator. Because = , you know that > . Because = , 17 13 15 13 15 12 13 15 13 15 1 1 1 1 1 — — — — — — — — — — — — — — — 24 34 24 34 34 24 24 24 34 34 2 2 2 2 2 So, > . 3 EXAMPLE you know that < . Comparing Fractions Using Approximation ANSWER

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