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Chapter 4: Problem 98

Simplify. $$\left|\frac{3}{20}\right|$$

Short Answer

Expert verified
\(\frac{3}{20}\)

Step by step solution

01

- Understand Absolute Value

Recall that the absolute value of a number is its distance from 0 on the number line, regardless of direction. Thus, for any number \(x\), \(|x|\) is always non-negative.
02

- Evaluate the Absolute Value

Here, we need to find the absolute value of \(\frac{3}{20}\). Since \(\frac{3}{20}\) is already a positive fraction, its absolute value is the fraction itself.
03

- Simplified Form

Since the absolute value of \(\frac{3}{20}\) is \(\frac{3}{20}\) itself, the simplified form remains \(\frac{3}{20}\).

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Key Concepts

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

Simplification
Simplification is the process of reducing a mathematical expression to its simplest form. Simplifying makes problems easier to understand and solve.
For example, let's take the fraction \( \frac{3}{20} \). Here, we can see that the numerator (3) and the denominator (20) do not have any common factors other than 1. This means the fraction is already in its simplest form.
In addition, when dealing with absolute values, the simplification process can sometimes become even more straightforward, especially when the number or fraction is already positive.
Fractions
Fractions represent a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number).
For instance, in the fraction \( \frac{3}{20} \), 3 is the numerator and 20 is the denominator. This fraction means that 3 parts out of 20 equal parts make up this amount.
Understanding fractions is crucial in many areas of math. They can describe everything from portions of a pizza to parts of an equation.
  • Proper Fractions: where the numerator is less than the denominator (like \( \frac{3}{20} \)).
  • Improper Fractions: where the numerator is greater than or equal to the denominator (like \( \frac{22}{7} \)).
  • Mixed Numbers: which consist of a whole number and a fraction (like 1 \( \frac{1}{2} \)).
Number Line
A number line is a visual representation of numbers placed at equal intervals along a straight line. It helps in understanding the position and value of numbers, including fractions and their absolute values.
In the context of absolute value, the number line is particularly helpful. The absolute value of a number is its distance from 0 on the number line, without considering direction.
For example, \( \frac{3}{20} \) on the number line is a small positive fraction to the right of zero. Its absolute value, \( \frac{3}{20} \), is simply its distance from zero, which is \( \frac{3}{20} \). This distance is always non-negative and thus the same as the fraction itself in this case.

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Most popular questions from this chapter

Divide. Write the quotient as a mixed number. $$4257 \div 23$$

For Exercises 85鈥�94, plot the fraction on the number line. $$\frac{3}{4}$$

Divide. Write the quotient as a mixed number. $$187 \div 15$$

For Exercises 95鈥�102, simplify. $$\left|-\frac{3}{4}\right|$$

Label the fraction as proper or improper. $$\frac{10}{10}$$
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