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$Miss Shiva pours 2(3)/(5)ℓ of fruit punch equally into 4 glasses. (a) Find the amount of fruit punch in each glass. Give your answer as a fraction in its simplest form. (b) She buys another 2ℓ of fruit punch. How many more glasses containing the same amount of fruit punch as before can she fill at most?$

Miss Shiva pours $2 \frac{3}{5} \ell$ of fruit punch equally into $4$ glasses. $\newline$ (a) Find the amount of fruit punch in each glass. Give your answer as a fraction in its simplest form. $\newline$ (b) She buys another $2 \ell$ of fruit punch. How many more glasses containing the same amount of fruit punch as before can she fill at most?

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Math Problems

Grade 6

Convert between percents, fractions, and decimals: word problems

Full solution

Q. Miss Shiva pours

2 \frac{3}{5} \ell

of fruit punch equally into

4

glasses.

\newline

(a) Find the amount of fruit punch in each glass. Give your answer as a fraction in its simplest form.

\newline

(b) She buys another

2 \ell

of fruit punch. How many more glasses containing the same amount of fruit punch as before can she fill at most?

Convert to Improper Fraction: Convert the mixed number to an improper fraction to find the total amount of fruit punch. $\newline$ $2\left(\frac{3}{5}\right)\ell$ can be written as an improper fraction by multiplying the whole number by the denominator of the fraction, adding the numerator, and placing the result over the original denominator. $\newline$ $2\left(\frac{3}{5}\right)\ell = \left(2 \times 5 + 3\right)/5 = \left(10 + 3\right)/5 = \frac{13}{5}\ell$
Divide Total by Glasses: Divide the total amount of fruit punch by the number of glasses to find the amount in each glass. $\newline$ To find the amount in each glass, divide $\frac{13}{5}\ell$ by $4$ . $\newline$ $(\frac{13}{5})\ell \div 4 = (\frac{13}{5})\ell \times (\frac{1}{4}) = \frac{13}{20}\ell$
Simplify Fraction: Simplify the fraction, if necessary. $\newline$ The fraction $\frac{13}{20}$ is already in its simplest form, as $13$ and $20$ have no common factors other than $1$ .
Convert Additional to Fraction: Determine how many glasses can be filled with the additional $2\ell$ of fruit punch. $\newline$ First, convert $2\ell$ to a fraction with the same denominator as the amount per glass. $\newline$ $2\ell = (2 \times 20)/20 = 40/20$
Divide Additional by Each: Divide the additional amount of fruit punch by the amount in each glass to find the number of glasses that can be filled. $\newline$ $(40/20)\ell \div (13/20)\ell = 40/20 \times 20/13 = 40/13$
Determine Whole Number: Determine the whole number of glasses that can be filled. $\newline$ Since we can only fill whole glasses, we take the integer part of the division result. $\newline$ $40 \div 13 = 3$ with a remainder, so she can fill $3$ more glasses.