Respuesta :
Answer:
leftover cards:
[tex]2\dfrac{1}{2}, 3\dfrac{1}{4}[/tex]
Step-by-step explanation:
- There are total 6 cards
- the numbers on the cards follow a pattern
- 4 cards were taken out, and they are:
[tex]\dfrac{1}{2}, 6\dfrac{1}{2}, 1\dfrac{1}{4}, \dfrac{1}{4}[/tex]
we can covert these directly into decimal forms (remember [tex]\frac{1}{4}[/tex] = 0.25 and [tex]\frac{1}{2}[/tex] = 0.5)
[tex]0.5, 6.5, 1.25, 0.25[/tex]
we can now easily arrange them from least to greatest
[tex]0.25, 0.5, 1.25, 6.5[/tex]
a pattern is still not coming out, but we needed to arrange them in order to understand the pattern
we can convert these into just fractions
[tex]\dfrac{1}{4}, \dfrac{1}{2}, \dfrac{5}{4}, \dfrac{13}{2}[/tex]
And a pattern is indeed emerging here:
the denominators change alternatively between 2 and 4, and the numerator stays the same during this change. (see the first two fractions in the series)
originally all the six cards when aligned in ascending order should look like
[tex]\dfrac{1}{4}, \dfrac{1}{2}, \dfrac{5}{4}, \dfrac{5}{2}, \dfrac{13}{4}, \dfrac{13}{2}[/tex]
Now you clearly see which ones are the missing ones: 5/2 and 13/4
we rewrite them as mixed fractions (as they originally printed on the cards)
[tex]\dfrac{5}{2} = 2\dfrac{1}{2}[/tex]
[tex]\dfrac{13}{4} = 3\dfrac{1}{4}[/tex]
These were the leftover cards from the bag!
