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$Miss Shiva pours ?_(5)^(3)f of fruit punch equally inte 4 glasses. (a) Find the amount of fruit punch in sach glass. Glve your answer as a fraction in its simplest form. (b) She buys another 2 of frult punch. How many more glasses containing the same amount of fruit punch as belore can she fill at most?$

Miss Shiva pours $?_{5}^{3} f$ of fruit punch equally inte $4$ glasses. $\newline$ (a) Find the amount of fruit punch in sach glass. Glve your answer as a fraction in its simplest form. $\newline$ (b) She buys another $2$ of frult punch. How many more glasses containing the same amount of fruit punch as belore can she fill at most?

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Math Problems

Grade 6

Convert between percents, fractions, and decimals: word problems

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Q. Miss Shiva pours

?_{5}^{3} f

of fruit punch equally inte

4

glasses.

\newline

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

\newline

(b) She buys another

2

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

Divide Total Amount: Divide the total amount of fruit punch by the number of glasses to find the amount in each glass. $\newline$ Miss Shiva has $\frac{3}{5}$ of fruit punch, and she wants to pour it equally into $4$ glasses. To find the amount in each glass, we divide $\frac{3}{5}$ by $4$ . $\newline$ Calculation: $\left(\frac{3}{5}\right) / 4 = \left(\frac{3}{5}\right) \cdot \left(\frac{1}{4}\right) = \frac{3}{20}$
Simplify Fraction: Simplify the fraction, if necessary, to find the simplest form. $\newline$ The fraction $\frac{3}{20}$ is already in its simplest form, as $3$ and $20$ have no common factors other than $1$ .
Determine Glasses Filled: Determine how many glasses can be filled with the additional $\frac{2}{5}$ of fruit punch. $\newline$ Miss Shiva buys another $\frac{2}{5}$ of fruit punch. To find out how many more glasses she can fill, we need to divide $\frac{2}{5}$ by the amount that goes into one glass, which is $\frac{3}{20}$ . $\newline$ Calculation: $\frac{2}{5} / \frac{3}{20} = \frac{2}{5} \cdot \frac{20}{3} = \frac{2\cdot20}{5\cdot3} = \frac{40}{15}$
Simplify Fraction: Simplify the fraction obtained in Step $3$ to find the number of whole glasses that can be filled. $\newline$ Calculation: $\frac{40}{15}$ can be simplified by dividing both numerator and denominator by their greatest common divisor, which is $5$ . $\newline$ $\frac{40}{15} = \frac{(40/5)}{(15/5)} = \frac{8}{3}$ $\newline$ Since we can only fill whole glasses, Miss Shiva can fill $2$ whole glasses with a remainder.
Determine Glasses Filled: Determine the number of additional whole glasses that can be filled. $\newline$ Since $\frac{8}{3}$ is equal to $2$ whole glasses with some fruit punch left over, Miss Shiva can fill $2$ more glasses.