Question

Fawn plants 2/3 of the garden with vegetables. Her son plants the remainder of the garden. He decides to use 1/2 of his plant flowers, and in the rest, he plants herbs. What fraction of the entire garden is planted in flowers?

Answer 1

Given that Fawn plants vegetables into garden = $\frac{2}{3}$

Exact amount of garden is not given so we can assume that amount of garden is 1.

Then remaining amount of garden $=1-\frac{2}{3}=\frac{3}{3}-\frac{2}{3}=\frac{3-2}{3}=\frac{1}{3}$

Now half of the remaining part of garden that is half of $\frac{1}{3}$ rd part of garden is planted with flowers

so that will be $\frac{1}{2}*\frac{1}{3}=\frac{1}{6}$

Hence required fraction for the answer will be 1/6.

Answer 2

¹/₆

Further explanation

Given:

• Fawn plants $\frac{2}{3}$ of the garden with vegetables.
• Her son plants the remainder of the garden.
• He decides to use $\frac{1}{2}$ of his plant flowers, and in the rest, he plants herbs.

Question:

What fraction of the entire garden is planted in flowers?

The Process:

Pay attention to the first step we have to do with $\frac{2}{3}$.

$\boxed{ \ \frac{2}{3} \times \frac{2}{2} = \frac{4}{6} \ }$

Let us draw a diagram of 6 units representing the entire garden.

$\boxed{\circ} \ \boxed{\circ} \ \boxed{\circ} \ \boxed{\circ} \ \boxed{\circ} \ \boxed{\circ}$

• Fawn plants $\frac{4}{6}$ of the garden with vegetables, or 4 of 6 units.
• $Vegetables: \boxed{\circ} \ \boxed{\circ} \ \boxed{\circ} \ \boxed{\circ}$

The rest is 6 - 4 = 2 units.

$The \ rest: \boxed{\circ} \ \boxed{\circ}$

• Her son decides to plant $\frac{1}{2}$ of the remainder of the garden with flowers or 1 of 2 units of the rest.
• $Flowers: \boxed{\circ}$

Look at the diagram of 1 unit from the flowers above, representing 1 of 6 units of the entire garden.

Thus, $\frac{1}{6}$ of the entire garden planted in flowers.

- - - - - - - - - -

Quick Steps

$\boxed{ \ \frac{1}{2} \times \bigg( 1 - \frac{2}{3} \bigg) = \ ? \ }$

$\boxed{ \ = \frac{1}{2} \times \bigg( \frac{3}{3} - \frac{1}{3} \bigg) \ }$

$\boxed{ \ = \frac{1}{4} \times \frac{2}{3} \ }$

We crossed out 4 and 2.

$\boxed{ \ = \frac{1}{2} \times \frac{1}{3} \ }$

$\boxed{\boxed{ \ \frac{1}{6} \ }}$

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