To solve the problem of how much chalk the third teacher received, we need to break down the distribution of the chalk step by step. ### Step 1: Understand the Total Chalk Distribution Let’s assume the total amount of chalk is represented by 1 (or 100% of the chalk). ### Step 2: Calculate the Amount Received by the First Teacher The first teacher received \( \frac{2}{5} \) of the total chalk. To find out how much chalk is left after the first teacher took their share, we subtract the amount they received from the total: \[ \text{Chalk left} = 1 - \frac{2}{5} \] To perform this subtraction, we need a common denominator. The denominator of 5 can be converted to 1 by expressing 1 as \( \frac{5}{5} \): \[ \text{Chalk left} = \frac{5}{5} - \frac{2}{5} = \frac{3}{5} \] ### Step 3: Calculate the Amount Received by the Second Teacher The second teacher received \( \frac{2}{15} \) of the remainder. The remainder, as we calculated, is \( \frac{3}{5} \). To find out how much chalk the second teacher received, we multiply \( \frac{2}{15} \) by the amount of chalk left: \[ \text{Chalk received by the second teacher} = \frac{2}{15} \times \frac{3}{5} \] To multiply these fractions, we multiply the numerators and the denominators: \[ \text{Chalk received by the second teacher} = \frac{2 \times 3}{15 \times 5} = \frac{6}{75} \] Now, we can simplify \( \frac{6}{75} \): \[ \frac{6}{75} = \frac{2}{25} \quad (\text{dividing both numerator and denominator by 3}) \] ### Step 4: Calculate the Amount Received by the Third Teacher Now we need to find out how much chalk the third teacher received. We know the total chalk is 1, and we can find the amount received by the third teacher by subtracting the amounts received by the first and second teachers from the total: \[ \text{Chalk received by the third teacher} = 1 - \left(\frac{2}{5} + \frac{2}{25}\right) \] First, we need to add \( \frac{2}{5} \) and \( \frac{2}{25} \). To do this, we need a common denominator. The least common multiple of 5 and 25 is 25. We convert \( \frac{2}{5} \) to have a denominator of 25: \[ \frac{2}{5} = \frac{2 \times 5}{5 \times 5} = \frac{10}{25} \] Now we can add: \[ \frac{10}{25} + \frac{2}{25} = \frac{12}{25} \] Now we can find the amount of chalk the third teacher received: \[ \text{Chalk received by the third teacher} = 1 - \frac{12}{25} \] Again, we express 1 as \( \frac{25}{25} \): \[ \text{Chalk received by the third teacher} = \frac{25}{25} - \frac{12}{25} = \frac{13}{25} \] ### Conclusion The third teacher received \( \frac{13}{25} \) of the chalk. ### Answer The correct option is **D. 13/25**. ### Explanation of Other Options - **A. 8/15**: This option is incorrect because it does not account for the correct distribution of chalk after the first teacher's share. - **B. 11/25**: This option is incorrect as it miscalculates the total chalk remaining after both teachers have taken their shares. - **C. 12/25**: This option represents the total amount received by the first and second teachers combined, not the amount left for the third teacher. ### Revision Summary - The first teacher received \( \frac{2}{5} \) of the total chalk. - The second teacher received \( \frac{2}{15} \) of the remaining chalk, which simplifies to \( \frac{2}{25} \). - The third teacher's share is calculated by subtracting the total received by the first two teachers from the total chalk. - The final amount received by the third teacher is \( \frac{13}{25} \).