Evaluate 1/16 - 5 x (1/4) + 5, giving the answer as a fraction in lowest terms.

Step-by-step solution

1. 1

   Do the multiplication first. The order of operations puts $\times$ ahead of $+$ and $-$, so evaluate $5\cdot\tfrac14$ before touching anything else:

   $5\cdot\frac14=\frac54.$

   The expression becomes

   $\frac{1}{16}-\frac54+5.$

   Working left to right instead — computing $\tfrac1{16}-5$ first — would give a completely different (and wrong) value.

2. 2

   Choose the common denominator. The denominators present are $16$, $4$ and $1$. Since $4$ and $1$ both divide $16$, the least common denominator is simply

   $\operatorname{lcm}(16,4,1)=16.$

   Using $16$ rather than, say, $64$ keeps the numerators small and the final reduction trivial.

3. 3

   Rewrite every term over 16. Multiply numerator and denominator by whatever makes the denominator $16$:

   $\frac54=\frac{5\times4}{4\times4}=\frac{20}{16},\qquad 5=\frac{5\times16}{16}=\frac{80}{16}.$

   The whole number $5$ is the term people forget to convert; leaving it as $5$ and adding it to a numerator would inflate the answer by a factor of $16$.

4. 4

   Combine the numerators. With a single denominator the arithmetic is one line:

   $\frac{1}{16}-\frac{20}{16}+\frac{80}{16}=\frac{1-20+80}{16}=\frac{61}{16}.$

   Since $61$ is prime and does not divide into $16$, the fraction is already in lowest terms; as a decimal it is $3.8125$, and as a mixed number $3\tfrac{13}{16}$.

5. 5

   Estimate to confirm. Roughly, $\tfrac1{16}\approx 0.06$, $\tfrac54=1.25$, so $0.06-1.25+5\approx 3.81$ — matching $\tfrac{61}{16}=3.8125$ ✓. A quick decimal estimate like this catches a mis-signed term instantly.