frac

Find fractional part

Syntax

Y = frac(X)

Description

Y = frac(X) returns the fractional part of the specified symbolic number. If X contains a mixed number, frac(X) returns its proper fraction. If X contains an improper fraction, frac(X) divides the numerator of the fraction by its denominator and returns the remainder. This function is equivalent to X - fix(X).

Examples

Find Fractional Part of Symbolic Number

Find the fractional part of the improper fraction $\frac{8}{6}$. Define the improper fraction as a symbolic number. This improper fraction is equal to $1\frac{1}{3}$ in mixed number notation. The frac function returns $\frac{1}{3}$ as the fractional part.

X = sym(8)/6;
Y = frac(X)

Y = 
$$\frac{1}{3}$$

Find Fractional Part of Decimal Approximation of Irrational Number

Find the fractional part of $\pi$, approximated to 10 digits of precision. Set the number of significant digits to 10 when using vpa to approximate $\pi$.

digits(10)
X = vpa(sym(pi))

X = $$3.141592654$$

Use frac to find the fractional part of this approximated number.

Y = frac(X)

Y = $$0.1415926536$$

Restore the significant digits used by vpa to the default 32 digits.

digits(32)

Find Fractional Part of Symbolic Expression

Define a symbolic expression expr. Find the fractional part by using frac. Because the expression contains a symbolic variable n with an indeterminate value, frac returns a result that is equivalent to expr - fix(expr).

syms n
expr = 2*n - 2/3;
Y = frac(expr)

Y = 
$$2\hspace{0.17em}n-\mathrm{fix}\left(2\hspace{0.17em}n-\frac{2}{3}\right)-\frac{2}{3}$$

Input Arguments

X — Input array

symbolic number | symbolic variable | symbolic function | symbolic expression

Input array, specified as a symbolic number, variable, function, or expression.

Data Types: sym | symfun

Output Arguments

Y — Fractional part

symbolic number | symbolic variable | symbolic expression

Fractional part, returned as a symbolic number, variable, or expression.

Data Types: sym

Version History

Introduced in R2009b