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Chapter 10: Problem 52

Find the absolute value. $$ \left|-\frac{10}{7}\right| $$

Short Answer

Expert verified
The absolute value is \(\frac{10}{7}\).

Step by step solution

01

- Understand the absolute value concept

The absolute value of a number is its distance from 0 on the number line, regardless of direction. So, it is always a non-negative number.
02

- Apply the absolute value

To find the absolute value of \(\frac{-10}{7}\), remove the negative sign to make the number non-negative.
03

- Write the result

Removing the negative sign from \(\frac{-10}{7}\), we get \(\frac{10}{7}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distance from zero
The absolute value of a number is all about how far the number is from zero on the number line. Imagine you are standing at zero and you want to measure the distance to your number. It doesn't matter if you go left to a negative number or right to a positive number, the distance will always be positive.

Consider \(-\frac{10}{7}\). Even though it is negative, its distance from zero is the same as what it would be if it was positive. This distance is \(\frac{10}{7}\) units away from zero.

Also, remember:
  • Absolute value ignores the direction, it only looks at distance.
  • It is always a non-negative result.
Number line
The number line is a helpful tool for understanding the absolute value. Picture a straight line with zero in the middle. Positive numbers are on the right and negative numbers are on the left.

For instance, \(-10\) is to the left of zero and it's 10 units away from zero. When we talk about absolute value, we're talking about this distance but without considering the direction.

So for \(-\frac{10}{7}\), we move \(-\frac{10}{7}\) units to the left of zero on the number line. But when we calculate its absolute value, we only consider the distance, which is \(\frac{10}{7}\) units.

Visualize the number line:
  • Mark the positions of positive and negative numbers.
  • Notice the equal distances from zero.
  • Use it to see that absolute value changes direction to distance.
Non-negative number
A non-negative number is either positive or zero. When we talk about absolute value, it translates any number into its non-negative form.

For example, if you take a negative number like \(-\frac{10}{7}\), its absolute value becomes positive \(\frac{10}{7}\). This is because absolute value measures distance and distance cannot be negative.

Key points to understand:
  • Absolute value always results in a non-negative number.
  • If the number is already positive or zero, it stays the same.
  • If the number is negative, it becomes positive.


With this in mind, you can see that the absolute value simplifies everything to a non-negative form, making math problems easier to handle.

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Most popular questions from this chapter

Divide. $$ -\frac{5}{8} \div\left(-\frac{6}{5}\right) $$

Simplify. $$ 9 \div(-3)+16 \div 8 $$

Multiply. \(-8 \cdot(-1.3) \cdot(-5)\)

Divide. $$ \frac{3}{4} \div\left(-\frac{2}{3}\right) $$

Simplify. $$ 8-(2 \cdot 3-9) $$
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