Find the quotient 31 ÷ 6.25.

Step-by-step solution

1. 1

   Deal with the decimal in the divisor first. Long division is awkward when the divisor has a decimal point. Two standard fixes exist: multiply both numbers by $100$, or convert the divisor to a fraction. The fraction route is faster here because $6.25$ is a familiar fraction.

2. 2

   Convert 6.25 to a fraction in lowest terms.

   $6.25=\frac{625}{100}=\frac{25}{4}$

   (Divide numerator and denominator by $25$.)

3. 3

   Turn division by a fraction into multiplication by its reciprocal.

   $31\div\frac{25}{4}=31\times\frac{4}{25}=\frac{124}{25}$

4. 4

   Convert back to a decimal. Since $\tfrac{1}{25}=0.04$,

   $\frac{124}{25}=124\times 0.04=4.96$

   $\boxed{4.96}$

5. 5

   Check with the other method and with multiplication. Scaling both numbers by $100$ gives $3100\div 625$, and $625\times 4=2500$ with $600$ left over, and $600/625=0.96$, so again $4.96$. Multiplying back: $6.25\times 4.96=31.00$. An estimate also fits — $31\div 6=5.17$, so an answer just under $5$ is right.