What Is 2/3 + 3/5?

2/3 + 3/5 = 19/15, or 1 4/15 as a mixed number.

Result

Answer

\frac{2}{3} + \frac{3}{5} = \textcolor{#0b5c56}{\frac{19}{15} = 1\frac{4}{15}}

The sum is 19/15 in simplest form, or 1 4/15 as a mixed number.

  • Decimal: \displaystyle 1.2\overline{6} (the 6 repeats forever, about 1.2667)
  • Percent: 126.67%

1 whole + 4 of 15 equal parts

Step-by-step solution

The problem

\frac{2}{3} + \frac{3}{5}

  1. Write both fractions over 15. List multiples of each denominator until they meet:
    Multiples of 3: 3, 6, 9, 12, 15
    Multiples of 5: 5, 10, 15
    The least common denominator is 15. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.

    \begin{aligned} \frac{2}{3} &= \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \\[10pt] \frac{3}{5} &= \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \end{aligned}
    = \textcolor{#0b5c56}{\frac{10}{15}} + \textcolor{#0b5c56}{\frac{9}{15}}

  2. Add the numerators. Keep the denominator 15.

    = \frac{10 + 9}{15} = \textcolor{#0b5c56}{\frac{19}{15}}

  3. Check that it can't be simplified. 19 and 15 have no common factor other than 1, so this is the simplest form.

    \text{GCF}(19, 15) = 1

  4. Write it as a mixed number. Divide: 15 goes into 19 1 time with 4 left over. The whole number is 1, the remainder 4 becomes the numerator, and the denominator stays 15.

    19 \div 15 = 1\ \text{R}\ 4
    = \textcolor{#0b5c56}{1\frac{4}{15}}

All the working together

\begin{aligned} &\frac{2}{3} + \frac{3}{5} \\[8pt] &= \frac{2 \times 5}{3 \times 5} + \frac{3 \times 3}{5 \times 3} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt] &= \frac{10}{15} + \frac{9}{15} \\[8pt] &= \frac{10 + 9}{15} && \textcolor{#5b6660}{\textsf{add}} \\[8pt] &= \frac{19}{15} \\[8pt] &= \textcolor{#0b5c56}{1\frac{4}{15}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}

The answer in other forms

Simplest form19/15
Mixed number1 4/15
Decimal1.2666… (the 6 repeats forever)
Percent≈ 126.67%
Same fractions2/3 − 3/5, 2/3 × 3/5, 2/3 ÷ 3/5

2/3 plus other fractions

SumAnswer
2/3 + 1/27/6
2/3 + 1/31
2/3 + 2/34/3
2/3 + 1/411/12
2/3 + 3/417/12
2/3 + 1/513/15
2/3 + 2/516/15
2/3 + 3/519/15
2/3 + 4/522/15
2/3 + 1/65/6
2/3 + 5/63/2
2/3 + 1/819/24
2/3 + 3/825/24
2/3 + 5/831/24
2/3 + 7/837/24

Frequently asked questions

What is 2/3 + 3/5?

2/3 + 3/5 = 19/15 = 1 4/15 (1.2667 as a decimal).

How do you add 2/3 and 3/5?

Write both over a common denominator, add the numerators and simplify. The working above shows each step.

Other fractions, mixed numbers or up to five terms: use the Fraction Calculator.