Problem 337
Question
In the following exercises, simplify. $$ \frac{0}{u-4.99}, \text { where } u \neq 4.99 $$
Step-by-Step Solution
Verified Answer
0
1Step 1: Identify the Expression
The given expression is \( \frac{0}{u-4.99} \).
2Step 2: Consider the Numerator
The numerator of the fraction is 0.
3Step 3: Apply the Zero Property of Division
Any time 0 is divided by any non-zero number, the result is always 0.
4Step 4: Check the Denominator
Ensure that the denominator \(u - 4.99 \) is not zero. Given that \( u eq 4.99 \), the expression in the denominator is not zero.
5Step 5: Simplify the Expression
Thus, \( \frac{0}{u-4.99} = 0 \).
Key Concepts
Zero Property of DivisionNumeratorDenominator
Zero Property of Division
The zero property of division is a simple, yet fundamental rule in arithmetic. It states that any number divided by zero is undefined. Conversely, when zero is the numerator, and it is divided by any non-zero number, the result is always zero.
For example, in the fraction \(\frac{0}{u - 4.99}\), the numerator is zero. Regardless of what value the denominator takes (as long as it’s not zero), the fraction simplifies to zero. This is because zero divided by anything still gives zero.
For example, in the fraction \(\frac{0}{u - 4.99}\), the numerator is zero. Regardless of what value the denominator takes (as long as it’s not zero), the fraction simplifies to zero. This is because zero divided by anything still gives zero.
Numerator
The numerator is the number above the line in a fraction. It represents the number of parts we have. In the fraction \(\frac{0}{u - 4.99}\), the numerator is 0.
Understanding the numerator helps simplify and solve fractions effectively. When the numerator is zero, as it is here, it doesn't matter what the denominator is (as long as it’s not zero), the whole fraction will always be zero.
Why? Because zero parts of any whole is still zero.
Understanding the numerator helps simplify and solve fractions effectively. When the numerator is zero, as it is here, it doesn't matter what the denominator is (as long as it’s not zero), the whole fraction will always be zero.
Why? Because zero parts of any whole is still zero.
Denominator
The denominator is the number below the line in a fraction. It tells us into how many parts the whole is divided. In \(\frac{0}{u - 4.99}\), the denominator is \( u - 4.99 \).
In our given fraction, it's specified that \( u eq 4.99 \), which means the denominator is not zero. This is crucial because division by zero is undefined.
With a non-zero denominator and a zero numerator, the fraction simplifies effortlessly to zero, confirming our solution is valid. This underscores both the importance and simplicity of the denominator in determining the value of a fraction.
In our given fraction, it's specified that \( u eq 4.99 \), which means the denominator is not zero. This is crucial because division by zero is undefined.
With a non-zero denominator and a zero numerator, the fraction simplifies effortlessly to zero, confirming our solution is valid. This underscores both the importance and simplicity of the denominator in determining the value of a fraction.
Other exercises in this chapter
Problem 335
In the following exercises, simplify. $$ \frac{3}{20} \cdot \frac{49}{11} \cdot \frac{20}{3} $$
View solution Problem 336
In the following exercises, simplify. $$ \frac{13}{18} \cdot \frac{25}{7} \cdot \frac{18}{13} $$
View solution Problem 338
In the following exercises, simplify. $$ 0 \div\left(y-\frac{1}{6}\right), \text { where } x \neq \frac{1}{6} $$
View solution Problem 342
In the following exercises, simplify. $$ \left(\frac{5}{16} n-\frac{3}{7}\right) \div 0, \text { where } \frac{5}{16} n-\frac{3}{7} \neq 0 $$
View solution