greg spends 1/5 of his take-home pay on his mortgage and property taxes, out of the remaining money he spends 1/4 on food and 3/8 on clothes, from the money left over after these expenses, he puts 1/6 into savings, what fractional part of his take-home pay does greg have left - solve with pie chart

We will use a pie chart to visualize and break down Greg's expenses as fractions of his total take-home pay. First, we summarize the information:

1. **Mortgage and Property Taxes**: Greg spends \( \frac{1}{5} \) of his take-home pay on mortgage and property taxes.
2. **Food**: From the remaining money after the mortgage, Greg spends \( \frac{1}{4} \) on food.
3. **Clothes**: From the remaining money after the mortgage, Greg spends \( \frac{3}{8} \) on clothes.
4. **Savings**: After all previous expenses, Greg puts \( \frac{1}{6} \) of the leftover money into savings.

### Step-by-Step Calculation

1. **Remaining after Mortgage**:
   Greg spends \( \frac{1}{5} \) of his income on the mortgage and property taxes. The remaining amount of his income is:
   \[
   1 - \frac{1}{5} = \frac{4}{5}
   \]

2. **Food and Clothes**:
   Now, Greg spends \( \frac{1}{4} \) on food and \( \frac{3}{8} \) on clothes from the remaining \( \frac{4}{5} \). So, we need to find how much of his take-home pay he spends on food and clothes combined.

   - **Food expense**: \( \frac{1}{4} \) of \( \frac{4}{5} \):
   \[
   \frac{1}{4} \times \frac{4}{5} = \frac{4}{20} = \frac{1}{5}
   \]
   
   - **Clothes expense**: \( \frac{3}{8} \) of \( \frac{4}{5} \):
   \[
   \frac{3}{8} \times \frac{4}{5} = \frac{12}{40} = \frac{3}{10}
   \]

   Total spent on food and clothes combined:
   \[
   \frac{1}{5} + \frac{3}{10} = \frac{2}{10} + \frac{3}{10} = \frac{5}{10} = \frac{1}{2}
   \]

3. **Remaining after Food and Clothes**:
   After spending on food and clothes, the remaining portion of Greg's take-home pay is:
   \[
   \frac{4}{5} - \frac{1}{2} = \frac{8}{10} - \frac{5}{10} = \frac{3}{10}
   \]

4. **Savings**:
   Greg puts \( \frac{1}{6} \) of the remaining \( \frac{3}{10} \) into savings:
   \[
   \frac{1}{6} \times \frac{3}{10} = \frac{3}{60} = \frac{1}{20}
   \]

5. **Final Amount Left**:
   After all the expenses and savings, the amount Greg has left is the remaining \( \frac{3}{10} \) minus his savings \( \frac{1}{20} \):
   \[
   \frac{3}{10} - \frac{1}{20} = \frac{6}{20} - \frac{1}{20} = \frac{5}{20} = \frac{1}{4}
   \]

### Conclusion
Greg has \( \frac{1}{4} \) of his take-home pay left after all expenses.

I can visualize this solution with a pie chart if you'd like! Let me know if you'd like more details or have any questions.

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Here are 5 relative questions for further exploration:
1. How would Greg's leftover change if he increased his savings to 1/5 of the remaining money?
2. What fraction of Greg's pay is spent on clothes alone?
3. If Greg's mortgage and taxes increased to 1/4 of his income, how much would he have left?
4. How much of his take-home pay does Greg spend on non-savings expenses?
5. What would happen if Greg reduced his clothing budget by half?

**Tip**: Visualizing your budget with a pie chart can help you easily track where your money is going!

Learn how to calculate the fractional part of Greg's take-home pay that he has left after spending on mortgage, property taxes, food, clothes, and savings. This step-by-step guide breaks down Greg's expenses with fractions and shows how to solve using a pie chart. Suitable for Grades 6-8.

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