Question

Perform the indicated operation. \(12 \frac{1}{4}-5\)

Short answer

Answer: The result is 7 1/4.

Step-by-step solution

Convert mixed number to improper fraction

To subtract a whole number from a mixed number, first, we need to convert the mixed number into an improper fraction. A mixed number is in the form of \(a \frac{b}{c}\), where the whole number is \(a\) and the fraction is \(\frac{b}{c}\). To convert it to an improper fraction, use the formula: \({a * c + b}{\div}c\). In our case, the mixed number is \(12 \frac{1}{4}\). So, \(a = 12, b = 1, c = 4\). Using the formula, we get the improper fraction: \(12 * 4 + 1 \div 4 = 49{\div}4.\) Thus, our mixed number, \(12 \frac{1}{4}\), equals the improper fraction \(\frac{49}{4}\).

Rewrite the problem as subtraction

Now that we have the improper fraction, rewrite the problem as subtraction of two fractions: \(\frac{49}{4} - \frac{20}{4}\). Notice that, in order to rewrite the whole number (\(5\)) as a fraction, we multiplied it by \(\frac{4}{4}\) to make it compatible with the mixed number (having the same denominator): \(5 * \frac{4}{4} = \frac{20}{4}.\)

Perform the subtraction

Now we can perform subtraction since both fractions have the same denominator: \(\frac{49}{4} - \frac{20}{4} = \frac{49-20}{4}=\frac{29}{4}.\)

Convert the improper fraction back to a mixed number

The result is currently an improper fraction, so let's convert it back to a mixed number. To do this, we need to divide the numerator by the denominator: \(29 \div 4 = 7\text{ with a remainder of }1\). This means our mixed number is \(7\text{ and } \frac{1}{4}\) (7 as the whole number and \(\frac{1}{4}\) as the fraction). In conclusion, the result of the subtraction is \(12 \frac{1}{4}-5=7 \frac{1}{4}\).