What Is 1/3 + 3/4?

1/3 + 3/4 = 13/12, or 1 1/12 as a mixed number.

Result

Answer

\frac{1}{3} + \frac{3}{4} = \textcolor{#0b5c56}{\frac{13}{12} = 1\frac{1}{12}}

The sum is 13/12 in simplest form, or 1 1/12 as a mixed number.

  • Decimal: \displaystyle 1.08\overline{3} (the 3 repeats forever, about 1.0833)
  • Percent: 108.33%

1 whole + 1 of 12 equal parts

Step-by-step solution

The problem

\frac{1}{3} + \frac{3}{4}

  1. Write both fractions over 12. List multiples of each denominator until they meet:
    Multiples of 3: 3, 6, 9, 12
    Multiples of 4: 4, 8, 12
    The least common denominator is 12. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.

    \begin{aligned} \frac{1}{3} &= \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \\[10pt] \frac{3}{4} &= \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \end{aligned}
    = \textcolor{#0b5c56}{\frac{4}{12}} + \textcolor{#0b5c56}{\frac{9}{12}}

  2. Add the numerators. Keep the denominator 12.

    = \frac{4 + 9}{12} = \textcolor{#0b5c56}{\frac{13}{12}}

  3. Check that it can't be simplified. 13 and 12 have no common factor other than 1, so this is the simplest form.

    \text{GCF}(13, 12) = 1

  4. Write it as a mixed number. Divide: 12 goes into 13 1 time with 1 left over. The whole number is 1, the remainder 1 becomes the numerator, and the denominator stays 12.

    13 \div 12 = 1\ \text{R}\ 1
    = \textcolor{#0b5c56}{1\frac{1}{12}}

All the working together

\begin{aligned} &\frac{1}{3} + \frac{3}{4} \\[8pt] &= \frac{1 \times 4}{3 \times 4} + \frac{3 \times 3}{4 \times 3} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt] &= \frac{4}{12} + \frac{9}{12} \\[8pt] &= \frac{4 + 9}{12} && \textcolor{#5b6660}{\textsf{add}} \\[8pt] &= \frac{13}{12} \\[8pt] &= \textcolor{#0b5c56}{1\frac{1}{12}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}

The answer in other forms

Simplest form13/12
Mixed number1 1/12
Decimal1.08333… (the 3 repeats forever)
Percent≈ 108.33%
Same fractions3/4 − 1/3, 1/3 × 3/4, 1/3 ÷ 3/4

1/3 plus other fractions

SumAnswer
1/3 + 1/25/6
1/3 + 1/32/3
1/3 + 2/31
1/3 + 1/47/12
1/3 + 3/413/12
1/3 + 1/58/15
1/3 + 2/511/15
1/3 + 3/514/15
1/3 + 4/517/15
1/3 + 1/61/2
1/3 + 5/67/6
1/3 + 1/811/24
1/3 + 3/817/24
1/3 + 5/823/24
1/3 + 7/829/24

Frequently asked questions

What is 1/3 + 3/4?

1/3 + 3/4 = 13/12 = 1 1/12 (1.0833 as a decimal).

How do you add 1/3 and 3/4?

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.