What Is 1/2 + 2/5?

Q: What is 1/2 + 2/5?

1/2 + 2/5 = 9/10 (0.9 as a decimal).

1/2 + 2/5 = 9/10, which is 0.9 as a decimal.

Result

Answer

\frac{1}{2} + \frac{2}{5} = \textcolor{#0b5c56}{\frac{9}{10}}

The sum is 9/10 in simplest form.

Decimal: \displaystyle 0.9
Percent: 90%

9 of 10 equal parts

Step-by-step solution

The problem

\frac{1}{2} + \frac{2}{5}

Write both fractions over 10. List multiples of each denominator until they meet:
Multiples of 2: 2, 4, 6, 8, 10
Multiples of 5: 5, 10
The least common denominator is 10. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.
\begin{aligned} \frac{1}{2} &= \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \\[10pt] \frac{2}{5} &= \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \end{aligned}
= \textcolor{#0b5c56}{\frac{5}{10}} + \textcolor{#0b5c56}{\frac{4}{10}}
Add the numerators. Keep the denominator 10.
= \frac{5 + 4}{10} = \textcolor{#0b5c56}{\frac{9}{10}}
Check that it can't be simplified. 9 and 10 have no common factor other than 1, so this is the simplest form.
\text{GCF}(9, 10) = 1

All the working together

\begin{aligned} &\frac{1}{2} + \frac{2}{5} \\[8pt]  &= \frac{1 \times 5}{2 \times 5} + \frac{2 \times 2}{5 \times 2} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt]  &= \frac{5}{10} + \frac{4}{10} \\[8pt]  &= \frac{5 + 4}{10} && \textcolor{#5b6660}{\textsf{add}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{9}{10}}\end{aligned}

The answer in other forms

Simplest form	9/10
Decimal	0.9
Percent	90%
Same fractions	1/2 − 2/5, 1/2 × 2/5, 1/2 ÷ 2/5

1/2 plus other fractions

Sum	Answer
1/2 + 1/2	1
1/2 + 1/3	5/6
1/2 + 2/3	7/6
1/2 + 1/4	3/4
1/2 + 3/4	5/4
1/2 + 1/5	7/10
1/2 + 2/5	9/10
1/2 + 3/5	11/10
1/2 + 4/5	13/10
1/2 + 1/6	2/3
1/2 + 5/6	4/3
1/2 + 1/8	5/8
1/2 + 3/8	7/8
1/2 + 5/8	9/8
1/2 + 7/8	11/8