To determine which statements are true or false, we must analyze the fractions given for each type of bird in relation to a common denominator. The given fractions are:
- Blue jay: \( \frac{1}{8} \)
- Finch: \( \frac{6}{7} \)
- Blackbird: \( \frac{1}{3} \)
- Owl: \( \frac{11}{24} \)
To compare these fractions, it's helpful to convert them to have a common denominator. The least common multiple (LCM) of the denominators \( 8, 7, 3, \) and \( 24 \) is \( 168 \).
Now we convert each fraction:
- Blue Jay: \[ \frac{1}{8} = \frac{21}{168} \]
- Finch: \[ \frac{6}{7} = \frac{144}{168} \]
- Blackbird: \[ \frac{1}{3} = \frac{56}{168} \]
- Owl: \[ \frac{11}{24} = \frac{77}{168} \]
Now, we compare the converted fractions:
- Blue Jay: \( 21/168 \)
- Finch: \( 144/168 \)
- Blackbird: \( 56/168 \)
- Owl: \( 77/168 \)
Now let's analyze each statement:
-
Over half the students found a finch:
- True, since \( \frac{144}{168} \) is greater than \( \frac{84}{168} \) (which is half).
-
More students found a blackbird than a finch:
- False, since \( 56/168 < 144/168 \).
-
More students found a blue jay than an owl:
- False, since \( 21/168 < 77/168 \).
-
More students found a finch than a blackbird:
- True, since \( 144/168 > 56/168 \).
-
More students found a blackbird than an owl:
- False, since \( 56/168 < 77/168 \).
Final Assessment:
- Over half the students found a finch - True
- More students found a blackbird than a finch - False
- More students found a blue jay than an owl - False
- More students found a finch than a blackbird - True
- More students found a blackbird than an owl - False