What fraction of a family's total income goes towards savings if they spend one-fourth on the mortgage, one-eighth on car payments, one-eighth on groceries, and two-fifths on other expenses?

To determine what fraction of the family’s total income goes towards savings, we first need to calculate the total expenditures from the fractions given for various expenses.

The family spends:

• One-fourth on the mortgage, which can be represented as 1/4.

• One-eighth on car payments, represented as 1/8.

• One-eighth on groceries, also represented as 1/8.

• Two-fifths on other expenses, represented as 2/5.

To find the total fraction spent, we first need a common denominator for these fractions. The denominators are 4, 8, and 5. The least common multiple of these numbers is 40. We will convert each fraction to have a denominator of 40:

1. 1/4 becomes (1 * 10) / (4 * 10) = 10/40

2. 1/8 becomes (1 * 5) / (8 * 5) = 5/40

3. 1/8 becomes (1 * 5) / (8 * 5) = 5/40 (note this is repeated for groceries)

4. 2/5 becomes (2 * 8