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Chapter 1: Problem 28

Write each division using a fraction bar. $$ h \div 15 $$

Short Answer

Expert verified
The division \( h \div 15 \) is written as \( \frac{h}{15} \).

Step by step solution

01

Understand the Division

The expression \( h \div 15 \) represents the division of \( h \) by 15. Our goal is to express this division as a fraction.
02

Use Fraction Bar to Express Division

To express the division using a fraction, write \( h \) as the numerator and 15 as the denominator. This makes the fraction \( \frac{h}{15} \).

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Key Concepts

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

Understanding Fractions
A fraction is a way to express a part of a whole or a division between two numbers.
It consists of two main components: the numerator and the denominator.
  • The numerator is the top part of the fraction, representing the number of parts we have or are considering.
  • The denominator is the bottom part, showing the total number of equal parts into which the whole is divided.
When you see a fraction, like \( \frac{h}{15} \), it tells us that \( h \) is divided by 15 parts.
So, fractions are a convenient way to represent division, providing insight into how many parts of a whole you have or need to consider.
The Concept of Division
Division is a fundamental arithmetic operation used to determine how many times one number is contained within another.
It is essentially the process of distributing a number into equal parts.
When you perform a division, like \( h \div 15 \), you are figuring out how much each part would be if \( h \) is split into 15 equal portions.

Division can be thought of in two ways:
  • Partitive or sharing division, where you know the number of parts and find out how many are in each part.
  • Quotitive or measurement division, where you know how many objects are in each group and find out how many groups there are.
These interpretations show why division and fractions go hand-in-hand, as a fraction is simply another way to express this division.
Numerators in Fractions
In fractions, the numerator plays a critical role. It tells us about the number of parts we are interested in.
For instance, in the fraction \( \frac{h}{15} \), \( h \) is the numerator. This means you are looking at \( h \) parts out of 15.

Here are a few important points about numerators:
  • The numerator determines the fraction's size relative to its denominator.
    If \( h \) is large, \( \frac{h}{15} \) will represent more parts out of the whole.
  • If the numerator is zero, the value of the fraction is zero, regardless of the denominator.
  • When comparing fractions with the same denominator, a larger numerator indicates a larger fraction.
Understanding how the numerator interacts with the denominator can help you better interpret and manipulate fractions.

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