What Is 1/4 + 1/5?

Q: What is 1/4 + 1/5?

1/4 + 1/5 = 9/20 (0.45 as a decimal).

1/4 + 1/5 = 9/20, which is 0.45 as a decimal.

Result

Answer

\frac{1}{4} + \frac{1}{5} = \textcolor{#0b5c56}{\frac{9}{20}}

The sum is 9/20 in simplest form.

Decimal: \displaystyle 0.45
Percent: 45%

9 of 20 equal parts

Step-by-step solution

The problem

\frac{1}{4} + \frac{1}{5}

Write both fractions over 20. List multiples of each denominator until they meet:
Multiples of 4: 4, 8, 12, 16, 20
Multiples of 5: 5, 10, 15, 20
The least common denominator is 20. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.
\begin{aligned} \frac{1}{4} &= \frac{1 \times 5}{4 \times 5} = \frac{5}{20} \\[10pt] \frac{1}{5} &= \frac{1 \times 4}{5 \times 4} = \frac{4}{20} \end{aligned}
= \textcolor{#0b5c56}{\frac{5}{20}} + \textcolor{#0b5c56}{\frac{4}{20}}
Add the numerators. Keep the denominator 20.
= \frac{5 + 4}{20} = \textcolor{#0b5c56}{\frac{9}{20}}
Check that it can't be simplified. 9 and 20 have no common factor other than 1, so this is the simplest form.
\text{GCF}(9, 20) = 1

All the working together

\begin{aligned} &\frac{1}{4} + \frac{1}{5} \\[8pt]  &= \frac{1 \times 5}{4 \times 5} + \frac{1 \times 4}{5 \times 4} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt]  &= \frac{5}{20} + \frac{4}{20} \\[8pt]  &= \frac{5 + 4}{20} && \textcolor{#5b6660}{\textsf{add}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{9}{20}}\end{aligned}

The answer in other forms

Simplest form	9/20
Decimal	0.45
Percent	45%
Same fractions	1/4 − 1/5, 1/4 × 1/5, 1/4 ÷ 1/5

1/4 plus other fractions

Sum	Answer
1/4 + 1/2	3/4
1/4 + 1/3	7/12
1/4 + 2/3	11/12
1/4 + 1/4	1/2
1/4 + 3/4	1
1/4 + 1/5	9/20
1/4 + 2/5	13/20
1/4 + 3/5	17/20
1/4 + 4/5	21/20
1/4 + 1/6	5/12
1/4 + 5/6	13/12
1/4 + 1/8	3/8
1/4 + 3/8	5/8
1/4 + 5/8	7/8
1/4 + 7/8	9/8