Prealgebra (7th Edition)

$2\frac{2}{3}$, $\frac{8}{3}$
When a fraction has an integer value followed by a fraction where the numerator of the fraction is less than the denominator of the fraction i.e. $x\frac{y}{z}$ where 1) $x, y$ and $z, \ne0$ 2) $y, z \gt0$ 3) $y\lt z$ It is called a mixed number. When a fraction has no integer value before it and the numerator is greater than or equal to the denominator i.e. $\frac{y}{z}$ where 1) $y$ and $z \ne0$ 2) $y\geq z$ It is called an improper fraction. We can convert a mixed number ($x\frac{y}{z}$) to an improper fraction \frac{y}{z} using the following formula: $x\frac{y}{z}=\frac{xz+y}{z}$ In this problem, we can express $2+\frac{2}{3}$ as a mixed number by "removing" the plus sign (any integer plus a fraction can be expressed as a mixed number by simply removing the addition sign): $2\frac{2}{3}$ We can convert this to an improper fraction using the formula: $2\frac{2}{3}=\frac{(2)(3)+2}{3}$ $=\frac{6+2}{3}$ $=\frac{8}{3}$