A soup kitchen had 6 1/2 gallons of soup at the start of the day. They had 2 1/10 gallons of soup left by the end of the day. How many gallons of soup did they use during the day?

Steps to Solve

1. Convert mixed numbers to improper fractions

Convert the mixed numbers for clarity.

• For $6 \frac{1}{2}$: $$ 6 \frac{1}{2} = \frac{12}{2} + \frac{1}{2} = \frac{13}{2} $$

• For $2 \frac{1}{10}$: $$ 2 \frac{1}{10} = \frac{20}{10} + \frac{1}{10} = \frac{21}{10} $$

2. Find the amount of soup used

Subtract the amount of soup left from the initial amount.

$$ \text{Amount used} = \frac{13}{2} - \frac{21}{10} $$

3. Find a common denominator

The least common multiple of 2 and 10 is 10. Convert the first fraction.

$$ \frac{13}{2} = \frac{13 \times 5}{2 \times 5} = \frac{65}{10} $$

4. Perform the subtraction

Now we can subtract the fractions.

$$ \frac{65}{10} - \frac{21}{10} = \frac{65 - 21}{10} = \frac{44}{10} $$

5. Simplify the fraction

Reduce the fraction to its simplest form.

$$ \frac{44}{10} = \frac{22}{5} $$

6. Convert back to a mixed number, if necessary

Convert $\frac{22}{5}$ back to a mixed number.

$$ \frac{22}{5} = 4 \frac{2}{5} $$