Question

example
what is the decimal form of $-\frac{11}{8}$?
you can use long division to express a fraction as a decimal. since $-\frac{11}{8}$ is the opposite of $\frac{11}{8}$, find the decimal form of $\frac{11}{8}$.
\\\

$$\begin{array}{r}1.375\\\\8\\overline{)11.000}\\\\ \\underline{-\\,8\\phantom{.000}}\\\\ 3\\,0\\phantom{.00}\\\\ \\underline{-\\,2\\,4\\phantom{.00}}\\\\ 60\\phantom{.0}\\\\ \\underline{-\\,56\\phantom{.0}}\\\\ 40\\\\ \\underline{-\\,40}\\\\ 0\\end{array}$$

\\
since $-\frac{11}{8}$ is the opposite of $\frac{11}{8}$, that means $-\frac{11}{8}$ is the opposite of $1.375$.
so, the decimal form of $-\frac{11}{8}$ is $-1.375$.
1 is $-\frac{11}{8}$ greater than or less than $-1.37$? show your work.

Explanation:

Step1: Convertir -11/8 a decimal

Primero, encontramos el decimal de 11/8 usando división larga (como en el ejemplo): 11 ÷ 8 = 1.375, así que -11/8 = -1.375.

Step2: Comparar -1.375 y -1.37

Recordar que para números negativos, el que está más cerca de cero es mayor. Convertimos -1.37 a fracción decimal extendida: -1.37 = -1.370. Ahora, comparamos -1.375 y -1.370. Como 1.375 > 1.370, entonces -1.375 < -1.370 (porque son negativos, el mayor valor absoluto da un número menor).

Answer:

\(-\frac{11}{8}\) es menor que \(-1.37\) (es decir, \(-\frac{11}{8} < -1.37\))