What Is 1/2 ÷ 1/4?

1/2 ÷ 1/4 = 2, a whole number.

Result

Answer

\frac{1}{2} \div \frac{1}{4} = \textcolor{#0b5c56}{2}

The quotient is 2.

Decimal: \displaystyle 2
Percent: 200%

2 wholes

Step-by-step solution

The problem

\frac{1}{2} \div \frac{1}{4}

Flip \displaystyle \frac{1}{4} and multiply. Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{1}{4} \;\rightarrow\; \frac{4}{1}
= \textcolor{#0b5c56}{\frac{1}{2}} \times \textcolor{#0b5c56}{4}
Cancel common factors. Divide 4 and 2 by 2.
= \dfrac{1}{\cancel{2}_{\,\textcolor{#0b5c56}{1}}} \times \dfrac{\cancel{4}^{\,\textcolor{#0b5c56}{2}}}{1} = \textcolor{#0b5c56}{\frac{1}{1}} \times \textcolor{#0b5c56}{\frac{2}{1}}
Multiply. Top times top, bottom times bottom.
= \frac{1 \times 2}{1 \times 1} = \textcolor{#0b5c56}{2}

All the working together

\begin{aligned} &\frac{1}{2} \div \frac{1}{4} \\[8pt]  &= \frac{1}{2} \times 4 && \textcolor{#5b6660}{\textsf{flip}} \\[8pt]  &= \dfrac{1}{\cancel{2}_{\,1}} \times \dfrac{\cancel{4}^{\,2}}{1} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt]  &= \frac{1}{1} \times \frac{2}{1} \\[8pt]  &= \frac{1 \times 2}{1 \times 1} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt]  &= \textcolor{#0b5c56}{2}\end{aligned}

The answer in other forms

Simplest form	2
Decimal	2
Percent	200%
Same fractions	1/2 + 1/4, 1/2 − 1/4, 1/2 × 1/4

1/2 divided by other fractions

Sum	Answer
1/2 ÷ 1/3	3/2
1/2 ÷ 2/3	3/4
1/2 ÷ 1/4	2
1/2 ÷ 3/4	2/3
1/2 ÷ 1/5	5/2
1/2 ÷ 2/5	5/4
1/2 ÷ 3/5	5/6
1/2 ÷ 4/5	5/8
1/2 ÷ 1/6	3
1/2 ÷ 5/6	3/5
1/2 ÷ 1/8	4
1/2 ÷ 3/8	4/3
1/2 ÷ 5/8	4/5
1/2 ÷ 7/8	4/7