What Is 3/4 + 5/8?

Q: What is 3/4 + 5/8?

3/4 + 5/8 = 11/8 = 1 3/8 (1.375 as a decimal).

3/4 + 5/8 = 11/8, or 1 3/8 as a mixed number.

Result

Answer

\frac{3}{4} + \frac{5}{8} = \textcolor{#0b5c56}{\frac{11}{8} = 1\frac{3}{8}}

The sum is 11/8 in simplest form, or 1 3/8 as a mixed number.

Decimal: \displaystyle 1.375
Percent: 137.5%

1 whole + 3 of 8 equal parts

Step-by-step solution

The problem

\frac{3}{4} + \frac{5}{8}

Write both fractions over 8. 8 is a multiple of 4:
4 × 2 = 8
So 8 is the least common denominator. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
= \textcolor{#0b5c56}{\frac{6}{8}} + \frac{5}{8}
Add the numerators. Keep the denominator 8.
= \frac{6 + 5}{8} = \textcolor{#0b5c56}{\frac{11}{8}}
Check that it can't be simplified. 11 and 8 have no common factor other than 1, so this is the simplest form.
\text{GCF}(11, 8) = 1
Write it as a mixed number. Divide: 8 goes into 11 1 time with 3 left over. The whole number is 1, the remainder 3 becomes the numerator, and the denominator stays 8.
11 \div 8 = 1\ \text{R}\ 3
= \textcolor{#0b5c56}{1\frac{3}{8}}

All the working together

\begin{aligned} &\frac{3}{4} + \frac{5}{8} \\[8pt]  &= \frac{3 \times 2}{4 \times 2} + \frac{5}{8} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt]  &= \frac{6}{8} + \frac{5}{8} \\[8pt]  &= \frac{6 + 5}{8} && \textcolor{#5b6660}{\textsf{add}} \\[8pt]  &= \frac{11}{8} \\[8pt]  &= \textcolor{#0b5c56}{1\frac{3}{8}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}

The answer in other forms

Simplest form	11/8
Mixed number	1 3/8
Decimal	1.375
Percent	137.5%
Same fractions	3/4 − 5/8, 3/4 × 5/8, 3/4 ÷ 5/8

3/4 plus other fractions

Sum	Answer
3/4 + 1/2	5/4
3/4 + 1/3	13/12
3/4 + 2/3	17/12
3/4 + 1/4	1
3/4 + 3/4	3/2
3/4 + 1/5	19/20
3/4 + 2/5	23/20
3/4 + 3/5	27/20
3/4 + 4/5	31/20
3/4 + 1/6	11/12
3/4 + 5/6	19/12
3/4 + 1/8	7/8
3/4 + 3/8	9/8
3/4 + 5/8	11/8
3/4 + 7/8	13/8