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Francine uses
(2)/(3) cup of pineapple juice for every
(1)/(3) cup of orange juice to make a smoothie.
Enter the number of cups of pineapple juice Francine uses for 1 cup of orange juice.
cups of pineapple juice

Francine uses $\frac{2}{3}$ cup of pineapple juice for every $\frac{1}{3}$ cup of orange juice to make a smoothie. $\newline$ Enter the number of cups of pineapple juice Francine uses for $1$ cup of orange juice. $\newline$ $\square$ cups of pineapple juice

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GCF and LCM: word problems

Full solution

Q. Francine uses

\frac{2}{3}

cup of pineapple juice for every

\frac{1}{3}

cup of orange juice to make a smoothie.

\newline

Enter the number of cups of pineapple juice Francine uses for

1

cup of orange juice.

\newline

\square

cups of pineapple juice

Set up ratio: To find out how many cups of pineapple juice Francine uses for $1$ cup of orange juice, we need to set up a ratio based on the given information. We know that Francine uses $\frac{2}{3}$ cup of pineapple juice for every $\frac{1}{3}$ cup of orange juice.
Set up proportion: To find the equivalent amount of pineapple juice for $1$ cup of orange juice, we can set up a proportion. If $(\frac{2}{3})$ cup of pineapple juice corresponds to $(\frac{1}{3})$ cup of orange juice, then we want to find the amount of pineapple juice that corresponds to $1$ cup of orange juice. We can write this as: $\newline$ $\frac{\frac{2}{3} \text{ cup pineapple juice}} {\frac{1}{3} \text{ cup orange juice}} = \frac{x \text{ cup pineapple juice}}{1 \text{ cup orange juice}}$
Cross-multiply and divide: To solve for $x$ , we can cross-multiply and divide. This gives us: $\newline$ $x = \frac{2}{3} \times \frac{1 \text{ cup orange juice}}{\frac{1}{3}}$
Simplify equation: Simplifying the right side of the equation, we multiply $(\frac{2}{3})$ by $1$ and divide by $(\frac{1}{3})$ . Dividing by a fraction is the same as multiplying by its reciprocal, so we get: $\newline$ $x = (\frac{2}{3}) \times (\frac{3}{1})$
Final calculation: Multiplying $(\frac{2}{3})$ by $(\frac{3}{1})$ gives us: $\newline$ $x = \frac{2 \times 3}{3}$ $\newline$ Simplifying the multiplication and division, we get: $\newline$ $x = 2 \times (\frac{3}{3})$ $\newline$ $x = 2 \times 1$ $\newline$ $x = 2$ $\newline$ Therefore, Francine uses $2$ cups of pineapple juice for $1$ cup of orange juice.

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