Question

What is 8 − 7 1/4
? Express your answer as a fraction in simplified form.

Answer 1

To solve \( 8 - 7 \frac{1}{4} \), we first convert the whole number 8 into a fraction. We can express 8 as \( \frac{8}{1} \).

Next, we convert the mixed number \( 7 \frac{1}{4} \) into an improper fraction. To do this, we multiply the whole number 7 by the denominator 4 and then add the numerator 1:

\[
7 \times 4 + 1 = 28 + 1 = 29
\]
Thus, \( 7 \frac{1}{4} \) can be expressed as:

\[
\frac{29}{4}
\]

Now we rewrite the subtraction:

\[
8 - 7 \frac{1}{4} = \frac{8}{1} - \frac{29}{4}
\]

To perform this subtraction, we need a common denominator. The least common denominator for 1 and 4 is 4. We convert \( \frac{8}{1} \) into a fraction with a denominator of 4:

\[
\frac{8}{1} = \frac{8 \times 4}{1 \times 4} = \frac{32}{4}
\]

Now we perform the subtraction:

\[
\frac{32}{4} - \frac{29}{4} = \frac{32 - 29}{4} = \frac{3}{4}
\]

Thus, the final answer is:

\[
\boxed{\frac{3}{4}}
\]