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aren had 1ℓ of juice. the drank (1)/(5)l and spilled (1)/(4)l low much juice did she have

aren had 1ℓ 1 \ell of juice.\newlinethe drank 15l \frac{1}{5} l and spilled 14l \frac{1}{4} l low much juice did she have

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Full solution

Q. aren had 1ℓ 1 \ell of juice.\newlinethe drank 15l \frac{1}{5} l and spilled 14l \frac{1}{4} l low much juice did she have
  1. Start with 11ℓ: Karen started with 1ℓ1\ell of juice. She drank 15ℓ\frac{1}{5}\ell, so let's subtract that from the total.\newline1−15=55−15=45ℓ1 - \frac{1}{5} = \frac{5}{5} - \frac{1}{5} = \frac{4}{5}\ell
  2. Subtract juice drank: Next, she spilled (1)/(4)(1)/(4)ℓ. We need to subtract this from what she had after drinking.(4)/(5)−(1)/(4)=(16)/(20)−(5)/(20)=(11)/(20)(4)/(5) - (1)/(4) = (16)/(20) - (5)/(20) = (11)/(20)ℓ
  3. Correct mistake in subtraction: But wait, I made a mistake in the previous step. I should have found a common denominator before subtracting. 45\frac{4}{5} - 14\frac{1}{4} = 1620\frac{16}{20} - 520\frac{5}{20} is not correct because I didn't convert 14\frac{1}{4} to twentieths correctly.

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