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Chapter 5: Problem 2

Find fraction notation for each ratio. You need not simplify. $$ 3 \text { to } 2 $$

Short Answer

Expert verified
\( \frac{3}{2} \)

Step by step solution

01

- Understand the Ratio

The given ratio is 3 to 2. Ratios compare two quantities to each other.
02

- Convert the Ratio to a Fraction

To express the ratio as a fraction, write the first number (the antecedent) as the numerator and the second number (the consequent) as the denominator. Thus, the ratio 3 to 2 can be written as \( \frac{3}{2} \).

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Key Concepts

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

ratio
A ratio compares two quantities to show the relative size of one quantity to the other. For example, when we write the ratio '3 to 2', we are comparing the number 3 with the number 2. This tells us that for every 3 of the first quantity, there are 2 of the second quantity.
Ratios can be written in different ways:
  • Using the word 'to': 3 to 2
  • Using a colon: 3:2
  • As a fraction: \( \frac{3}{2} \)
Each format tells us the same information. Understanding ratios is important in many areas such as cooking recipes, mixing chemicals, and comparing statistics.
fraction notation
Fraction notation is a way of representing a part of a whole or a division of quantities. When we convert a ratio into fraction notation, the first number (antecedent) becomes the numerator, and the second number (consequent) becomes the denominator.
Let's take the example of the ratio 3 to 2:
  • The first number, 3, is the numerator.
  • The second number, 2, is the denominator.
So, the ratio 3 to 2 is written in fraction notation as \( \frac{3}{2} \). This fraction represents 3 parts of a whole divided into 2 equal parts.
numerator
The numerator is the top part of a fraction. It tells us how many parts we are considering. For example, in the fraction \( \frac{3}{2} \), the numerator is 3.
Think of the numerator as the 'counting' number. It represents how many parts of the whole or how many items we are talking about.
In the context of ratios:
  • The numerator comes from the first number in the ratio.
  • It tells us how many times the first quantity is counted.
So in the ratio 3 to 2, when written as a fraction \( \frac{3}{2} \), the numerator 3 shows there are 3 parts of the first quantity.
denominator
The denominator is the bottom part of a fraction. It indicates how many equal parts the whole is divided into. In the fraction \( \frac{3}{2} \), the denominator is 2.
Think of the denominator as the 'dividing' number. It shows into how many equal parts the total quantity is split.
In the context of ratios:
  • The denominator comes from the second number in the ratio.
  • It tells us the total number of equal parts considered.
So in the ratio 3 to 2, when written as a fraction \( \frac{3}{2} \), the denominator 2 shows the division into 2 equal parts of the second quantity.

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