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Chapter 1: Problem 99

Simplify. \(\frac{5 a p}{2 c m}\)

Short Answer

Expert verified
The simplified form is \(\frac{5ap}{2cm}\).

Step by step solution

01

Identify the Numerator and Denominator

The given expression is \(\frac{5ap}{2cm}\). Here, 5ap is the numerator and 2cm is the denominator.
02

Look for Common Factors

Next, check if there are any common factors in the numerator and denominator. In this case, there are no common factors among 5, 'a', 'p', 2, 'c', and 'm'.
03

Simplify the Fraction

Since there are no common factors, the fraction is already in its simplest form. Therefore, the simplified form is \(\frac{5ap}{2cm}\).

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Key Concepts

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

Numerator
The numerator is the top part of a fraction. It tells us how many parts we are focusing on out of the whole.

In the fraction \(\frac{5ap}{2cm}\), the numerator is 5ap.

When working with fractions, it's important to clearly identify the numerator, as it helps to understand what is being divided.

If the numerator has common factors with the denominator, we may use them to simplify the fraction.
Denominator
The denominator is the bottom part of a fraction. It indicates the total number of equal parts into which the whole is divided.

For the fraction \(\frac{5ap}{2cm}\), the denominator is 2cm.

Knowing the denominator helps us understand the size of each part. Like with the numerator, identifying common factors between the numerator and denominator can help to simplify the fraction.
Common Factors
Common factors are numbers or variables that both the numerator and denominator share.

If a numerator and denominator have common factors, we can divide them by these factors to simplify the fraction.

For example, in \(\frac{6x^2}{3x}\), both 6 and 3 (as well as \(x^2\) and \(x\)) share a factor of 3 and x.

So, we can simplify to \(\frac{2x}{1} = 2x\).

In the given expression \(\frac{5ap}{2cm}\), there are no common factors, so we can't simplify further.
Simplest Form
The simplest form of a fraction is when the numerator and the denominator have no common factors other than 1.

This means that the fraction cannot be reduced further.

To check if a fraction is in its simplest form:
  • Identify the numerator and denominator.
  • Look for any common factors between them.
  • If there are no common factors, then the fraction is in its simplest form.
In our example, \(\frac{5ap}{2cm}\), there are no common factors between the numerator 5ap and the denominator 2cm, so it is already in its simplest form.

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