QuestionInsert $<, >$ , or $=$ in the blank:
$\left|-\frac{2}{5}\right| \square \left|-\frac{5}{2}\right|$

Studdy Solution

STEP 1

Assumptions1. We are comparing the absolute values of two numbers. . The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

STEP 2

First, we need to calculate the absolute values of the two numbers.
The absolute value of a number is denoted as $|x|$ , and it is defined as $|x| =\begin{cases}x & \text{if } x \geq0 \\ -x & \text{if } x <0\end{cases}$

STEP 3

Calculate the absolute value of $-\frac{2}{5}$ .
Since $-\frac{2}{5}$ is less than0, we use the second case in the absolute value definition.
$\left|-\frac{2}{5}\right| = -\left(-\frac{2}{5}\right)$

STEP 4

implify the expression.
$\left|-\frac{2}{}\right| = \frac{2}{}$

STEP 5

Next, calculate the absolute value of $-\frac{5}{2}$ .
Since $-\frac{5}{2}$ is less than0, we use the second case in the absolute value definition.
$\left|-\frac{5}{2}\right| = -\left(-\frac{5}{2}\right)$

STEP 6

implify the expression.
$\left|-\frac{5}{2}\right| = \frac{5}{2}$

STEP 7

Now, we need to compare the two absolute values.We have $\frac{2}{5}$ and $\frac{5}{2}$ .

STEP 8

Since $\frac{2}{5} < \frac{5}{2}$ , we can insert $<$ in the blank to make a true statement.
$\left|-\frac{2}{5}\right| < \left|-\frac{5}{2}\right|$ So, the correct comparison operator to use is $<$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms