Calculate Remaining Fraction: From 2/7 Withdrawn to 1/2 Left

To solve this problem, we'll follow these steps:

• Step 1: Determine how much of the original amount remains after taking out $\frac{2}{7}$.
• Step 2: Calculate how much more needs to be removed so that only half of the original amount remains in the piggy bank.
• Step 3: Perform the necessary calculations to find the additional amount required to be taken out.

Now, let's work through each step:

Step 1: Initially, Marcos takes out $\frac{2}{7}$ of his money. Therefore, the remaining money is:

$1 - \frac{2}{7} = \frac{7}{7} - \frac{2}{7} = \frac{5}{7}$

Step 2: We want only half of the initial amount, or $\frac{1}{2}$, to remain. Let $x$ be the additional fraction of money taken out.

Equation: $\frac{5}{7} - x = \frac{1}{2}$

Step 3: Solve for $x$. First, get a common denominator for the fractions on the right.

$\frac{5}{7} - x = \frac{1}{2}$

Find a common denominator (here, 14 works):

$\frac{5 \times 2}{7 \times 2} - x = \frac{1 \times 7}{2 \times 7}$

$\frac{10}{14} - x = \frac{7}{14}$

Subtracting $\frac{7}{14}$ from both sides gives us:

$\frac{10}{14} - \frac{7}{14} = x$

Hence, $x = \frac{3}{14}$.

Therefore, the solution to the problem is that Marcos needs to take out an additional amount of $\frac{3}{14}$ of his money.