Question

Tina spent 2/5 of her salary at the supermarket 1/8 on bills and 1/4 on clothes. So what fraction of her money did she spend? And what fraction of her money remain? And what fraction is spent on supermarket and clothes?

Answer 1

Let's denote Tina's total salary as \( S \).

1. **Spendings**:
- At the supermarket: \( \frac{2}{5} S \)
- On bills: \( \frac{1}{8} S \)
- On clothes: \( \frac{1}{4} S \)

2. **Calculating Total Spendings**:
To find the total amount Tina spent, we need to sum these fractions. First, we need a common denominator:
- The denominators are 5, 8, and 4.
- The least common multiple of 5, 8, and 4 is 40.

Now, we convert each fraction to have a denominator of 40:
- \( \frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40} \)
- \( \frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40} \)
- \( \frac{1}{4} = \frac{1 \times 10}{4 \times 10} = \frac{10}{40} \)

Now we can add these fractions:
\[
\text{Total spent} = \frac{16}{40} + \frac{5}{40} + \frac{10}{40} = \frac{16 + 5 + 10}{40} = \frac{31}{40}
\]

So, **Tina spent \( \frac{31}{40} \) of her salary**.

3. **Fraction of Money Remaining**:
To find the fraction of her salary that remains, we subtract the fraction spent from the whole:
\[
\text{Remaining} = 1 - \frac{31}{40} = \frac{40}{40} - \frac{31}{40} = \frac{9}{40}
\]
So, **Tina has \( \frac{9}{40} \) of her salary remaining**.

4. **Fraction Spent on Supermarket and Clothes**:
To find the fraction spent on the supermarket and clothes, we sum the amounts spent on both:
\[
\text{Spent on supermarket and clothes} = \frac{2}{5} + \frac{1}{4}
\]
Using a common denominator (40):
\[
\text{Spent on supermarket} = \frac{16}{40} \quad \text{and} \quad \text{Spent on clothes} = \frac{10}{40}
\]

Now we sum them:
\[
\frac{16}{40} + \frac{10}{40} = \frac{26}{40}
\]
This can be simplified to:
\[
\frac{26}{40} = \frac{13}{20}
\]

Thus, **Tina spent \( \frac{13}{20} \) of her salary on the supermarket and clothes**.

### Summary:
- Total spent: \( \frac{31}{40} \)
- Remaining: \( \frac{9}{40} \)
- Spent on supermarket and clothes: \( \frac{13}{20} \)