At the fossil lab, Emek and Luna found four labeled sections of a dinosaur tail mixed up on a table. The labels showed 3/8, 5/8, 5/6, and 5/9 of equal-sized reference sections. They needed to arrange them from smaller to larger portions. Emek first compared 3/8 and 5/8, using their matching denominators. Luna then compared the three fractions with numerator 5, knowing that a larger denominator means smaller equal parts. Together they determined the order: 3/8, 5/9, 5/8, and 5/6. They placed each section correctly, and the reconstructed tail display was ready for the museum.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Imagine dividing equal-sized sections into 6 equal parts and 9 equal parts. Which parts would be larger?
Emek says 5/9 is greater than 5/6 because 9 is greater than 6. Which statement correctly checks his reasoning?
Emek is correct because a larger denominator always makes a fraction larger.Emek is correct because both fractions have numerator 5.Emek is incorrect because with the same numerator, the larger denominator makes the fraction smaller.Emek is incorrect because 5/9 and 5/6 are equal.Correct! With the same numerator, a larger denominator means smaller equal parts and therefore a smaller fraction.
Try again. When numerators are equal, think about how the size of each equal part changes as the denominator increases.
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Hint
Since both fractions are measured in eighths, compare their numerators.
The 3/8 and 5/8 tail sections have the same denominator. How many eighths larger is the 5/8 section than the 3/8 section?
Correct! The 5/8 section is 2 eighths larger than the 3/8 section.
Try again. Find the difference between 5 eighths and 3 eighths.
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Hint
All four fractions have numerator 5. For equal numerators, compare the denominators in reverse order.
Luna finds another tail section labeled 5/7. Where should it be placed among the three sections with numerator 5 when they are ordered from smaller to larger?
Before 5/9Between 5/9 and 5/8Between 5/8 and 5/6After 5/6Correct! The order is 5/9, 5/8, 5/7, 5/6.
Try again. With the same numerator, a larger denominator gives a smaller fraction.
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