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?

1 answer

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.

  1. 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.

  2. 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: \( \frac{13}{20} \)