At the museum, Emek and Luna were helping finish a dinosaur exhibit. Two models showed the same-sized dinosaur tail. One model had 2/3 of its tail completed, and the other had 3/4 completed. The pieces were divided differently, so Emek and Luna looked carefully at how much of each whole tail was present. They noticed that 3/4 was more than 2/3. They chose the 3/4 model for the nearly finished display and added the missing section.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
The tails are the same size, but they are divided into different numbers of equal parts.
Luna says 2/3 must be greater than 3/4 because thirds are bigger pieces than fourths. What did she forget to consider?
Only the number of pieces in a whole matters.She must compare how much of each same-sized whole tail is completed.A fraction with 3 on the bottom is always greater.The two fractions must be equal because both are parts of tails.Correct! The amount of each whole tail that is completed must be compared.
Try again. Think about the completed amount of each same-sized whole tail, not just the size of one part.
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Hint
The whole tail has 4 sections, and 3 are already completed.
The model Emek and Luna chose has 3/4 of its tail completed. If the whole tail is divided into 4 equal sections, how many sections are still missing?
Correct! One section of the tail is still missing.
Try again. Count how many more sections are needed to go from 3 completed sections to all 4.
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Hint
Think of each third as 4 twelfths and each fourth as 3 twelfths.
Emek wants to check that 3/4 is greater than 2/3. He divides each same-sized tail into 12 equal parts. Which comparison correctly checks the fractions?
2/3 is 6/12 and 3/4 is 9/122/3 is 8/12 and 3/4 is 6/122/3 is 8/12 and 3/4 is 9/122/3 is 9/12 and 3/4 is 8/12Correct! 2/3 is 8/12 and 3/4 is 9/12, so 3/4 is greater.
Try again. Rewrite both fractions as twelfths and compare the number of equal parts.
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