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Some friends are planning to make a neighborhood garden. The total area available for the garden is 210 square meters, and they want this to be
1(1)/(3) times the area of the plant beds in the garden.
What should the area of the plant beds be?
square meters

Some friends are planning to make a neighborhood garden. The total area available for the garden is $\mathbf{2 1 0}$ square meters, and they want this to be $1 \frac{1}{3}$ times the area of the plant beds in the garden. $\newline$ What should the area of the plant beds be? $\newline$ square meters

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GCF and LCM: word problems

Full solution

Q. Some friends are planning to make a neighborhood garden. The total area available for the garden is

\mathbf{2 1 0}

square meters, and they want this to be

1 \frac{1}{3}

times the area of the plant beds in the garden.

\newline

What should the area of the plant beds be?

\newline

square meters

Calculate Division by Fraction: To find the area of the plant beds, we need to divide the total area by the factor $1 \frac{1}{3}$ which is the same as $\frac{4}{3}$ . $\newline$ Calculation: $210 \div \left(\frac{4}{3}\right)$
Multiply by Reciprocal: To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{4}{3}$ is $\frac{3}{4}$ . $\newline$ Calculation: $210 \times \left(\frac{3}{4}\right)$
Perform Multiplication: Now we perform the multiplication to find the area of the plant beds. $\newline$ Calculation: $210 \times \left(\frac{3}{4}\right) = \frac{630}{4}$
Final Division: Finally, we divide $630$ by $4$ to get the area of the plant beds. $\newline$ Calculation: $\frac{630}{4} = 157.5$

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